MAT560

1st Course in Operator Theory

4.00

Undergraduate

Overview: Hermitian, Unitary and Normal operators are used widely. To understand the
questions (and the answers) asked about these operators, it is essential to understand the
situation in finite dimensional linear spaces. This course aims to do just that. The spectral
theorems for Self-adjoint and Normal operators will be proved. If time permits, we shall look at
either tensor products or quadratic forms.
.
Detailed Syllabus
1. Review: Vector spaces, subspaces, linear span, linear independence, quotient spaces,
basis, dimension, linear transformations, linear functionals, dual spaces, annihilators,
transpose, matrix of a linear transformation, determinants, characteristic polynomial,
Cayley-Hamilton theorem, minimal polynomial, characteristic roots, eigenvalues,
eigenvectors.
2. Linear Transformations: Range, null space, rank, nullity, row rank, column rank,
projections.
3. Inner Product Spaces: Inner products, Cauchy-Schwarz Inequality, Gramian, orthogonal
and orthonormal sets, Gram-Schmidt orthogonalisation, complete orthonormal sets, orthogonal complements, perpendicular projections, Complexification.
4. Adjoints: Adjoint of a linear transformation, existence in finite dimensional inner
product spaces, inner products on dual space, orthogonal projections.
5. Spectral Theorem: Self-adjoint operators, matrix of self-adjoint operators, Hermitian,
Unitary and Normal operators, Positive operators, Spectral theorems for self-adjoint and
Normal operators, orthogonal linear transformations, polar decomposition, other
consequences of the spectral theorem.
6. If time permits – Tensor Products or Quadratic Forms

PHY207

Abridge course for Minor students

4.00

Undergraduate

PHY207 is a bridge course specially designed for students who have already taken PHY101 and PHY102 instead of PHY103 and PHY104. The course supplements and develops their understanding of Newtonian physics and classical electromagnetism.
The content is as follows:
Review of Newtonian mechanics
Solving planetary motion using a personal computer
A brief introduction to Lagrangian formulation of mechanics
Review of simple harmonic motion
Introduction to coupled oscillators and normal modes
Introduction to special theory of relativity, space-time diagrams and four vectors
Review of electrostatics and magnetostatics
Review of Maxwell’s equation
Wave equation from Maxwell’s equation, plane wave solution, polarization
Light as an electromagnetic wave

BIO701

Adv. Molecular & Cell Biology

4.00

Graduate

Advanced Molecular and Cell Biology

PHY548

Adv. topics in non-linear dyn

3.00

Graduate

Advanced topics in non-linear dynamics

MAT641

Advanced Algebra

4.00

Graduate

Advanced Algebra

CHY352

Advanced Biochemistry

3.00

Undergraduate

General Introduction: Biomolecules: Carbohydrates, Proteins, Nucleic Acids, Lipids, Enzymes and Vitamins Carbohydrates: Structure and Functions Carbohydrates metabolism, Kreb’s Cycle and Glycolysis. Proteins: Properties, Structure and Functions Protein Sequencing Edman degradation Sanger’s reagent and Dansyl chloride Sequence by Mass Spectrometry (MALDI, ESI-MS, Tandem MS). Nucleic Acids: Introduction of Nucleic acids Gene expression, Genetic Code DNA Sequencing Sanger dideoxy method Maxam Gilbert Bisulfite Functions of nucleic acids DNA replication Repair and recombination DNA chemistry DNA damage Methylation and demethylation Oxidative DNA damage DNA-DNA crosslinks DNA-Protein crosslinks Mutagenesis Diseases and carcinogenesis
4.9. Gene Sequence,
4.10. PCR, RT-PCR techniques,
4.11. DNA Finger printing (Agarose gel electrophoresis)
4.11.1. Forensics,
4.11.2. Relationships,
4.11.3. Medical Diagnostics Lipids: Fats: Properties and functions Fatty Acids, Classes of Lipids Nomenclature of fatty acids Examples of diff. Lipids Phospholipids, Steroids Beta Oxidation mechanism Enzymes: Co-factors, Co-enzymes, Apo-enzyme, Halo enzymes Factors effecting Enzymes (Con., pH, T) Nomenclature, Mechanism of Enzymes Biosynthesis of cofactors NAD+-NADPH Biosynthesis of Niacin (Vitamin B3) FAD-FADH-FADH2 Thiamine pyrophosphate TPP Enzyme assay in Diagnostic Medicine
Hormones and Vitamins Classifications of Hormones, Examples and Function of Hormones Classifications of Vitamins Examples and Function of Vitamins

BIO601

Advanced Biostatistics

2.00

Graduate

Advanced Biostatistics

MAT425

Advanced Complex Analysis

4.00

Undergraduate

Course description not available.

PHY408

Advanced Condensed Matter Physics

3.00

Undergraduate

This is an advanced course in condensed matter emphasizing the special properties of solids: magnetism, super fluidity and superconductivity, dielectrics and ferroelectrics.

PHY308

Advanced Experimental Physics - II

3.00

Undergraduate

PHY 308 is a lab course offering an opportunity for hands-on learning through physics experiments based on various physics concepts covering Condensed matter physics and interaction of matter and energy.

PHY208

Advanced Experimental Physics I

3.00

Undergraduate

PHY 208 is an advanced lab course which aims to offer an experiential learning through a wide range of experiments and projects based on Thermodynamics, Optics and Modern Physics.

CHY343

Advanced Inorganic Chemistry

3.00

Undergraduate

Advanced Inorganic Chemistry
PART A: COURSE IDENTIFIERS
School SNS Department Chemistry Course Code CHY343 Course Title Advanced Inorganic Chemistry Credits (L:T:P) 2:1:0 Contact Hours (L:T:P) 2:1:0 Prerequisites CHY111/CHY112 Course Type Major Elective for B.Sc. (R) Chemistry Instructor’s Name Dr. Gouriprasanna Roy (R block, Room # 118) Visiting Time Monday and Friday (4 pm – 5 pm)
Curriculum Content Ionic equilibrium
A. General principle of equilibrium, equilibrium in solutions of acids and bases – strong acids and strong bases – weak acids and weak bases – polyprotic acids and bases, the equilibrium constant - Strength of acids and bases in aqueous solution in terms of Ka, Kb; OH the pH scale, pKw, pKa, pKb, etc., numerical problems, aqueous solutions of salts – hydrolysis salts – equilibrium in hydrolysis of salts – salts derives from weak acids and strong bases - salts derives from strong acids and weak bases - salts derives from weak acids and weak bases, numerical problems on hydrolysis of salts, buffer solutions – pH of a buffer solution – Henderson equations – Numerical problems, acid-base titrations – choice of indicator – neutralization of a strong acid by a strong base - neutralization of a weak acid with a strong base - neutralization of a weak base with a strong acid - neutralization of a weak acid by a weak base - neutralization of a weak acid with a strong base - neutralization of a weak base with a strong acid - neutralization of polyprotic acids with strong base.
B. Solid – solution equilibrium, the solubility and solubility product (Ksp), common ion effect, effect of H/OH– and complexing agents. Application of the concept in qualitative analysis; calculation on pH condition and precipitation. Acid-Base
i) Theories of acids – bases : Bronsted – Lowry theory, conjugate acid – base pairs, solvent system definition, periodic trends in aqua acid strength, oxoacids, anhydrous oxides, amphoterism, Lux concept, factors affecting strength of acids and bases, proton affinities, Lewis theory of acids – bases, examples of Lewis acids and bases – group characteristics of Lewis acids – reactions and properties of Lewis acids and bases – the fundamental types of reaction,complex formation as acid – base reaction; levelling effect;general strength of acid and base; the concept of Hard and Soft Acids and Bases (HSAB).
Chemistry in nonaqueous solvents/Molecular structure and bonding/The s–block and p–block elements.
Teaching and Learning Strategy Teaching and Learning Strategy Description of Work Class Hours Out-of-Class Hours Teaching Problem solving, Quizzes, presentations 40 hours Learning 8 hours 8 hours
PART C: ASSSESSMENT.
Assessment Strategy
Formative Assessment: Assignments/Quizzes/presentation (seminars)
Summary Assessment Final Exam
Mapping of Learning Outcomes to Assessment Strategy
Assessment Scheme Type of Assessment Percentage Continuous assessment from assignments/quizzes/performance on presentation 60 Final Examination 40 Total 100%
Bibliography Shriver and Atkin’s INORGANIC CHEMISTRY. Inorganic Chemistry: Principles of Structure and Reactivity by James E. Huheey,
Ellen A. Keiter and Richard L. Keiter. Inorganic Chemistry: Catherine Housecroft, Alan G. Sharpe. Atkins' Physical Chemistry, Peter W. Atkins, Julio de Paula. Advanced Inorganic Chemistry by F. A. Cotton and G. Wilkinson Inorganic Chemistry, A. G. Sharpe Concise Inorganic Chemistry, J. D. Lee Douglas, B.; McDaniel, D.H.; Alexander, J.J. Concepts and Models of Inorganic Chemistry General Inorganic Chemistry by R Sarkar. General Chemistry – Principles and modern application by Ralph H. Petrucci, F. Geoferey Herring, J D Madura, Carey Bissonnette. Greenwood, Norman, and A. Earnshaw. Chemistry of Elements.
Other reading materials will be assigned as and when required.

BIO705

Advanced Instrumentation

3.00

Graduate

Advanced Instrumentation

MAT661

Advanced Linear Algebra

4.00

Graduate

Advanced Linear Algebra

PHY547

Advanced mathematical Methods

3.00

Graduate

Advanced mathematical Methods in Physics

CHY512

Advanced Molecular Spectroscopy

4.00

Graduate

Group theory: Theorems of linear algebra Time-independent and time-dependent perturbation theory Discrete and Continuous Groups, Group multiplication tables, Generators Symmetry Elements, Symmetry Operations and Point Groups Reducible and Irreducible Representations, the Great Orthogonality Theorem and Character Tables Projection Operators and symmetry-adapted linear combinations Selection Rules for Molecular Spectroscopy Electron Density, Structure Factor, Density Matrix, Density Operator and Bloch equations
Molecular Spectroscopy: Microwave spectroscopy IR spectroscopy of organic molecules Raman Spectroscopy Atomic and molecular spectroscopy UV-Vis spectroscopy of organic molecules Detection of functional groups of organic molecules by IR spectroscopy (labs) UV-Vis Spectroscopy of various Organic Molecules (labs). NMR spectroscopy Mass spectrometry Moessbauer spectroscopy
Textbooks: F. A. Cotton, Chemical Applications of Group Theory (Wiley Eastern, New Delhi, 1976) B. S. Garg, Chemical Applications of Molecular Symmetry and Group Theory (MacMillan India, 2012) E. B. Wilson, J. C. Decius and P. C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, New York, 1955) J. I. Steinfeld, Molecules and Radiation: An Introduction to Modern Molecular Spectroscopy (MIT Press, Cambridge, MA, 1979) H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950) C. N. Banwell, Fundamentals of Molecular Spectroscopy (Tata McGraw-Hill, New Delhi, 1987) N. Sukumar, ed. A Matter of Density: Exploring the Electron Density Concept in the Chemical, Biological, and Materials Sciences (John Wiley, Hoboken, NJ, 2013) S.K. Dewan, Organic Spectroscopy (CBS Publishers).

PHY406

Advanced Quantum Mechanics

3.00

Undergraduate

This course introduces a student to relativistic quantum mechanics. It includes The Dirac equation and an introduction to quantum electrodynamics.

PHY564

Advanced Simulation Techniques

3.00

Graduate

This course gives an introduction to various simulation techniques such as Monte Carlo, Classical Molecular Dynamics, Quantum Simulations: time-independent Schrödinger equation in one dimension (radial or linear equations); scattering from a spherical potential, Born approximation, bound state solutions; single particle time-dependent Schrödinger equations; Hartree-Fock theory: restricted and unrestricted theory applied to atoms; Schrödinger equation in a basis: matrix operations, variational principle, density functional theory, quantum molecular dynamics.

PHY554

Advanced Statistical Physics

3.00

Graduate

This course covers the critical phenomena, Landau-Ginzburg theory of phase transition, renormalisation group, time-dependent phenomena in condensed matter, Correlation and response, Langevin theory, Fokker Plank and Smoluchowski equations, broken symmetry, hydrodynamics of simple fluids, stochastic models and dynamical critical phenomena, nucleation and spinodal decomposition, and topological defects.

MAT484

Advanced Statistics

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 184 Probability
Overview: Regression, the most widely used statistical technique, estimates relationships between independent (explanatory) variables and a dependent (outcome) variable. In this course you will learn different ways of estimating the parameter of the statistical models, criteria for these estimations, and then use them for deriving the coefficients of the regression models, use software (R) to implement them, learn what assumptions underlie the models, learn how to test whether your data meet those assumptions and what can be done when those assumptions are not met, and develop strategies for building and understanding useful models.
Detailed Syllabus: Review: Introduction, Descriptive Statistics; Sampling Distributions. Graphical representation of data, Basic distributions, properties, fitting, and their uses; Estimation: Point and interval estimation, Histogram and Kernel density estimation, Sufficiency, Exponential family, Bayesian methods, Moment methods, Least squares, Maximum likelihood estimation; Criteria for estimation: UMVUE, Large sample theory Consistency; asymptotic normality, Confidence intervals, Elements of hypothesis testing; Neyman-Pearson Theory, UMP tests, Likelihood ratio and related tests, Large sample tests; Linear Models: Simple and Multiple linear regression, Analysis and Inference.
References: Mathematical Statistics: Basic Ideas and Selected Topics by Peter J. Bickel and Kjell A. Doksum Testing Statistical Hypotheses by Erich L. Lehmann Statistical Decision Theory: Foundations, Concepts and Methods by James O. Berger
Past Instructors: Charu Sharma

MAT240

Algebra I

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics or MAT100 (Foundations)
Overview: Algebraic structures like groups, rings, integral domains, fields, modules and vector spaces are present in almost all mathematical applications as well as in development of more complicated structures in mathematics. The basic building block of these structures is the group. This, a first course in Abstract Algebra, concentrates mainly on groups and their basic properties. If there is time, we shall also take a brief look at Rings.
It is desirable that the student already has a basic understanding of sets, relations, functions, binary operations, equivalence relations, and sets of numbers.
Detailed Syllabus: Groups: Definition, Examples and Elementary Properties. Subgroups: Subgroup Tests, Subgroups Generated by Sets, Cyclic Groups, Classification of Subgroups of Cyclic Groups, Cosets and Lagrange's Theorem. Normal Subgroups and Quotient Groups, Homomorphisms, Isomorphisms and Automorphisms of a Group. Conjugates, centre, centralizer, normalizer. Cayley’s Theorem. Direct Products, Finite Abelian Groups. Permutation Groups: Definition, Examples and Properties, Symmetric Group of n Letters (Sn), Alternating Group on n Letters (An). (If time permits) Rings, Homomorphisms, Ideals and Quotient Rings, Integral Domains.
References: Contemporary Abstract Algebra by Joseph A. Gallian, 4th edition. Narosa, 1999. Algebra by Michael Artin, 2nd Edition. Prentice Hall India, 2011. Topics in Algebra by I.N. Herstein, 2nd Edition. Wiley India, 2006. A First Course in Abstract Algebra by John B. Fraleigh, 7th Edition. Pearson, 2003. Undergraduate Algebra by Serge Lang, 2nd Edition. Springer India, 2009. Abstract Algebra by David S. Dummit and Richard M. Foote, 3rd Edition. John Wiley and Sons, 2011.
Past Instructors: Neha Gupta, Sanjeev Agrawal

MAT241

Algebra II

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Algebra I (MAT 240)
Overview: The course continues the work done in MAT 240 on the one hand by extending the study of groups to include group actions and applications, and on the other by studying the algebraic structures of rings and fields.
Detailed Syllabus: Groups – Definition, subgroups, cyclic groups, homomorphisms, normal subgroups, semi-direct products, group actions, Sylow theorems. Rings – Definition and examples of rings, ideals, quotient rings, maximal ideals, prime ideals, ring homomorphisms, integral domains, Euclidean domains, PID, UFD. Polynomial Rings and Fields – Polynomial rings, irreducible polynomials, definition and examples of fields, characteristic, field extensions, finite fields.
References: I. N. Herstein, Topics in Algebra, 2/e, Wiley Eastern, 1994. Bhattacharya, Jain and Nagpaul, Basic Abstract Algebra, 2nd edition, CUP, 1995. Joseph A. Gallian, Contemporary Abstract Algebra, 4th edition, Narosa, 1999. M. Artin, Algebra, 2nd edition. Prentice Hall India, 2011. Dummit and Foote, Abstract Algebra, 3rd edition, Wiley. Serge Lang, Undergraduate Algebra, 2nd edition. Springer India, 2009. Thomas W. Hungerford, Algebra, GTM 73, Springer India, 2004.

MAT340

Algebra II

4.00

Undergraduate

Overview: The course continues the work done in MAT 240 and MAT 260 by studying the algebraic structures of rings and fields on the one hand and abstract linear algebra and module theory on the other. After laying the groundwork in these topics, diverse applications - such as finite fields, the structure of abelian groups and the Jordan canonical form of a matrix - are studied.
Detailed Syllabus:
1. Review - definition and examples of rings, ideals, quotient rings, maximal ideals, prime ideals, ring homomorphisms
2. Types of rings - integral domains, Euclidean domains, PIDs, UFDs, polynomial rings, factorization of polynomials, irreducibility criteria
3. Vector spaces - abstract vector spaces, examples, dimension, subspaces, linear transformations, matrix representations, change of basis, rank of linear transformations
4. Modules - definition and examples of modules, submodules, finitely generated modules, free modules, quotient modules and module homomorphisms
5. Fields – definition and examples of fields, characteristic, field extensions, finite extensions, zeroes of an irreducible polynomial, algebraic extensions, splitting fields, algebraic closures, finite fields - Definition, constructions and properties
6. Modules over PID - rank of matrices over PID, Smith normal form of a matrix, structure theorem for modules over PID, application to finitely generated abelian groups, applications to linear algebra - rational, Jordan canonical forms of a matrix

MAT643

Algebraic Graph Theory

4.00

Graduate

Algebraic Graph Theory

MAT807

Algebraic Graph Theory

4.00

Graduate

Algebraic Graph Theory

MAT808

Algebraic Number Theory

4.00

Graduate

Algebraic Number Theory

MAT550

Algebraic Topology

4.00

Undergraduate

Course description not available.

MAT722

Algebraic Topology

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 640, MAT 622. Undergraduates can substitute MAT 640 with MAT 240.
Overview: Algebraic topology is a tool which captures key information about geometrical properties of a topological space. We shall focus on two basic algebraic invariants of topological spaces: the fundamental group and the simplicial homology groups. If time permits, we shall also get a glimpse of singular homology.
Detailed Syllabus: The Fundamental Group Homotopy, Fundamental Group, Introduction to Covering Spaces, The Fundamental Group of the circle S 1 , Retractions and fixed points, Application to the Fundamental Theorem of Algebra, The Borsuk-Ulam Theorem, Homotopy Equivalence and Deformation Retractions, Fundamental group of a product of spaces, torus, n-sphere, and the real projective n-space. van Kampen’s Theorem: Free Products of Groups, The van Kampen Theorem, Fundamental Group of a Wedge of Circles, Definition and construction of Cell Complexes, Application of Van Kampen Theorem to Cell Complexes, Statement of the Classification Theorem for Surfaces. Covering Spaces: Universal Cover and its existence, Unique Lifting Property, Homomorphisms and automorphisms of Covering Spaces, Action of the fundamental group on the fibers, Deck Transformations, Group Actions, Covering Space Actions, Normal or Regular Covering Spaces. Simplicial Homology (If time permits): Finite Simplicial complexes, Polyhedra and Triangulations, Simplicial approximation, Barycentric subdivision. Orientation of simplicial complexes, Simplical chain complex and homology. Invariance of homology groups. Computations and applications.
References: A.Hatcher, Algebraic Topology, Cambridge Univ. Press, Cambridge, 2002. S. Deo, Algebraic Topology, Hindustan Book Agency, 2006. W. Massey, A Basic Course in Algebraic Topology, Springer-Verlag, Berlin, 1991. W. Fulton, Algebraic topology: A First Course, Springer-Verlag, 1995. J.R. Munkres, Elements of Algebraic Topology, Addison Wesley, 1984. J.J. Rotman, An Introduction to Algebraic Topology, Springer (India), 2004. J.W. Vick, Homology Theory, Springer-Verlag, 1994. E. H. Spanier, Algebraic Topology, Springer, 1994.

MAT723

Algebras of Operators

4.00

Graduate

Algebras of Operators

MAT832

Analysis and Geometry

4.00

Graduate

Analysis and Geometry

MAT621

Analysis I

4.00

Graduate

Core course for M.Sc. Mathematics
Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 231/320 Real Analysis II (for undergraduates)
Overview: The aim of this course is to build a rigorous base for advanced topics such as Complex Analysis, Measure & Integration, Numerical Analysis, Functional Analysis, and Differential Equations. The course design also attempts to take into account the diverse backgrounds of our students.
Detailed Syllabus:
Topics under each section are divided in two parts. Part (a) contains topics that will be covered only briefly whereas topics in part (b) will be done in detail. Real number system Archimedean property, density of rationals, extended real numbers, countable sets, uncountable sets. Cauchy completeness of reals, Axiom of Choice, Zorn’s Lemma, equivalence of AC & ZL. Metric spaces Definitions and examples, open sets, closed sets, limit points, closure,equivalent metrics, relative metric, product metric, convergence, continuity, connectedness, compactness. Uniform continuity, completion of a metric space, Cantor’s intersection property, finite intersection property, totally bounded spaces, characterization of compact metric spaces. Sequences and Series of Functions Pointwise and uniform convergence, uniform convergence and continuity, uniform convergence and integration, differentiation, Weierstrass M-test. Power series, exponential and logarithmic functions, Fourier series, equicontinuous family of functions, Stone-Weierstrass approximation theorem, Arzela-Ascoli theorem.
References: Principles of Mathematical Analysis by Walter Rudin, Tata McGraw-Hill Mathematical Analysis by Tom M. Apostol, Narosa Topology of Metric Spaces by S. Kumaresan, Narosa Introduction to Topology & Modern Analysis by G. F. Simmons, Tata McGraw-Hill Real Analysis by N. L. Carothers, Cambridge University Press

MAT623

Analysis II

4.00

Graduate

Core course for M.Sc. Mathematics
Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 621 (Analysis I)
Overview: This course puts the concept of integration of a real function in its most appropriate setting. It is also a prerequisite for the study of general measures, which is the foundation for a large part of pure and applied mathematics – such as spectral theory, probability, stochastic differential equations, harmonic analysis, and partial differential equations.
Detailed Syllabus: Lebesgue Measure: Outer measure, measurable sets, Lebesgue measure, measurable functions, pointwise convergence, almost everywhere convergence. The Lebesgue Integral: Riemann integral, Lebesgue integral of a bounded measurable function over a set of finite measure, Lebesgue integral of a non-negative and a general measurable function. Differentiation and Integration: Differentiation of monotone functions, functions of bounded variation, differentiation of an integral, absolute continuity. The Classical Banach spaces: Lp spaces, Minkowski and Hölder inequalities, completeness of Lp spaces, bounded linear functions on Lp spaces. Introduction to General Topology: Open and closed sets, bases, separation properties, countability and separation, continuous maps, compactness, connectedness.
References: Real Analysis by H. L. Royden and P. Fitzpatrick. 4th edition, Prentice-Hall India, 2010. Measure Theory and Integration by G. de Barra, New Age International, reprint 2006. Real Analysis by N. L. Carothers, Cambridge University Press.

MAT741

Analytic Number Theory

4.00

Graduate

Analytic Number Theory

BIO702

Analytical Methodology

3.00

Graduate

Analytical Methodology

BIO301

Animal Biotechnology

3.00

Undergraduate

Basic techniques of cell, tissue and organ culture. Primary culture and subculture of cells. kinetics of cell growth. Properties of normal and transformed cells. Role of carbondioxide, serum and other supplements in cell culture. Different types of culture media- natural media, BSS, MEM, serum free media. Different methods for the estimation of cell viability and cytotoxicity. Applications of cell culture. Stem cells – Embryonic and adult stem cells. Isolation and culture of stem cells. Induced pluripotency of stem cells. Stem cell markers. Stem cell plasticity and differentiation. Application of stem cells in medicine. Apoptosis- mechanism and significance with reference to degenerative diseases – Parkinson’s disease, stroke and diabetes.
Organ culture and tissue engineering: Organ cultures, histolytic cultures, three dimensional cultures, organotypic cultures. Production of bio-artificial skin, liver and pancreas. Tissue engineering- cell source and culture, culture of cells, design engineering of tissues, tissue modeling. Embryonic stem cell engineering.
Production of monoclonal antibodies, Production of Transgenic Animals -Mouse, sheep, cattle and fish by microinjection, retroviral vector method and embryonic stem cell method. Animal cloning-Somatic cell nuclear transfer and embryonic stem cell nuclear transfer methods. Bio pharming and gene knockout.
Recommended books: Culture of Animal cells; A manual of Basic techniques (6th ed.), Freshney, R. I., Pub: Wiley-Blackwell. Molecular Biotechnology: Principles and Applications of Recombinant DNA, Glick, B. R., Pasternak, J. J., Pub: ASM Press. Elements of Biotechnology, Gupta, P. K., Pub: Rastogi & Co. Concepts of Biotechnology, Balasubrahmanian, et al., Pub: University press.

BIO106

Animal Sciences 2

3.00

Undergraduate

Chordate classification up to phyla, with special reference to pisces, amphibians, reptiles, birds and mammals. Comparative development of heart and respiratory organs in chordates. Composition of blood, coagulation of blood and fibrinolysis. Physiology of heart and neurohumoral regulation of cardiovascular function. Gastrointestinal system –digestion and absorption of foods in GIT. Physiology of kidney and its role in the regulation of electrolyte, water and acid base balance in the body. Structure and organization of muscle cells. Biochemical changes associated with muscle contraction and relaxation. Structure of nerve cell, origin of membrane potential, mechanism of propagation of nerve impulse in unmyelinated and myelinated nerve fibres. Neurotransmitters. Reproductive physiology-male and female reproductive systems and sex hormones. Spermotogenesis, oogenesis, menstrul cycle. Placenta and its functions. Pregnancy and lactation.
Animal development: Introduction, history and concepts of developmental biology; the current understanding on the mechanisms of development of organisms using vertebrate (mouse, chick, frog, fish) and invertebrate (fly, worm) models; how does a complex, multicellular organism arise from a single cell; the beginning of a new organism (fertilization), the creation of multicellularity (cellularization, cleavage), reorganization into germ layers (gastrulation), cell type determination; creation of specific organs (organogenesis); molecular mechanisms underlying morphogenesis and differentiation during development; stem cells and regeneration; evolution of developmental mechanisms. Drosophila Development, Development of Other Invertebrates, Plant Development, Model Organisms and the Human Connection, Signal Transduction, Germ Cells and Sex, Regeneration and Growth, Post-Embryonic Development, Evolution and Development.
Recommended books: Text book of Medical Physiology (11th ed.), Ed: Guyton, A.G., Harcourt, J. E., Pub: Elsevier Saunders. Essentials of Medical Physiology, Shambulingam, K., Shambulingam, P., Pub: Jaypee Brothers, Medical Publishers. Harper’s Biochemistry, Murray, R. K., Harper, H. A., Pub: Appleton and Lange.

BIO103

Animal Sciences I

3.00

Undergraduate

Introduction to Vertebrates and Invertebrates: General characters, classification of up to different phyla from protozoa to echinoderms with special reference to protozoa and arthropod. Type study of human pathogens: Plasmodium vivax, Trypanosoma gambiense, Entamoeba histolytica, Faciola hepatica, Tenia solium and Ascaris lumbricoides. Introduction to model systems: C.elegans, Drosophila and zebra fish.
Recommended Books: Modern Text book of Zoology: Invertebrates, Kotpal, R.L., Pub: Rastogi. Invertebrate Zoology, Anderson, D. T., Pub: Oxford University Press.

MAT805

Application of complex network

4.00

Graduate

Application of Complex Networks to Landscape Ecology

CHY504

Applications of Analytical Techniques

3.00

Graduate

Course Summary
Various applications of Vibrational, UV-Visible, Mass and NMR spectroscopy methods to characterize organic compounds will be discussed in this course. A detailed tutorial will be provided to students so that they will be able to identify molecular and electronic structure and properties from molecular spectra.
Course Aims
The main aim of this course is to expose the students towards various analytical techniques and their application in structure elucidation of organic molecules and determination of properties. Our goal is to give a hands on experience on interpretation of these spectroscopic data.
Learning Outcomes
On successful completion of this course, students will be able to
(i) characterize new organic molecules utilizing these spectroscopic techniques .
(ii) apply these spectroscopic tools to study organic reaction mechanisms.
(iii) analyse the NMR, IR and UV-visible spectra and predict molecular properties from molecular spectra.
Curriculum Content
Lecture contents: Introduction to Spectroscopy Origin of Spectra and factors affecting the spectral line and intensity Rotational Spectroscopy Overview of IR Spectroscopy IR Spectroscopy IR Spectroscopy Overview of UV Spectroscopy UV Spectroscopy Overview of mass spectroscopy Overview of 1H NMR spectroscopy 1H NMR spectroscopy Overview 13C NMR Spectroscopy Solvent, concentration and temperature effects in NMR Overview of multi-dimensional NMR Coupling and deuterium exchange in NMR
Tutorials: Basics of Spectroscopy. Origin of Spectra and factors affecting the spectral line and intensity. Rotational Spectroscopy. IR Spectroscopy tutorial (characteristic absorption of common classes of organic compounds) IR Spectroscopy tutorial (application of IR spectroscopy to isomerism, identification of functional groups) IR Spectroscopy tutorial (effects of water and hydrogen bonding) UV Spectroscopy tutorial (calculation of for conjugated organic compounds) UV Spectroscopy tutorial ( for α, β unsaturated organic compounds and solvent effects) Role of fragmentation and rearrangement reaction during mass spectroscopic analysis. Application of shielding and deshielding effects. Chemical shift and coupling constants of alkane. Chemical shift and coupling constants of alkenes and alkynes. Assignment of 1H and 13C NMR signals of aromatic compounds. How to determine enantiomeric excess by NMR spectroscopy. Interpretation of 2D NMR and it’s application for the characterization of organic molecules.

CHY411

Applications of Group Theory

3.00

Undergraduate

Advanced Chemical Applications of Group Theory Topics Learning Objectives Introduction Importance of Group Theory in Chemistry Symmetry elements And symmetry operations Use molecular models to identify symmetry elements of different molecules. Understanding of the interrelation of different symmetry elements present in a molecule, product of symmetry operations Point Group Concepts and properties of a group, group multiplication Tables, Similarity transformation, Class, Determination of symmetry point group of molecules, Matrix representations and Character Table Matrix representation of groups, reducible and irreducible representations, Great orthogonality theorem, character tables SALC, direct product, Molecular vibration Direct Product and Spectroscopic selection rule, Molecular Vibrations, Normal coordinates, Symmetry of normal mode vibrations, Symmetry Adapted Linear Combination, Infrared and Raman active vibrations, Molecular orbital Theory, Hybrid orbital Molecular orbitals, LCAO MO approach, HMO method, Hybrid orbitals, Terms and states, Transition metal chemistry Free ion configuration, terms and states, splitting of levels and terms in a chemical environment, correlation diagrams, spectral and magnetic properties of the transition metal complexes.

CHY101

Applied Chemistry

5.00

Undergraduate

Applied Chemistry
COURSE DESCRIPTION:
1: Atomic structure, Periodic table, Quantum Chemistry, Spectroscopy
2: Thermodynamics, Energy, Chemical Kinetics, Photosystems
3: Nano materials, Organic Chemistry, Polymers
4: Water Corrosion and Biochemistry"
ASSESSMENT SCHEME :
Grading in the lecture will be based on a mid-term and a final examination with 10% of the lecture grade based on class participation. The student needs to achieve 40% in both the theory and lab separately to pass the course. To pass the course you will have to pass the lab and lecture portion separately and achieve 40% independently in each part. These parts will be weighted as 40% for lab and 60% for lecture.

MAT161

Applied Linear Algebra

4.00

Undergraduate

Course description not available.

MAT712

Automata Theory

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites:
Overview:
Detailed Syllabus: Formal Logic: Statements and notation, Connectives, Normal Forms, Predicate Logic and Inference Theory, Propositional Logic, Proof in Propositional Logic Syntax of First-Order Logic: First-Order Languages, Formulas of a Language, First-Order Theories Semantics of First-Order Languages: Structures of First-Order Languages, Truth in a Structure, Model of a Theory, Embeddings and Isomorphisms Regular Languages and Regular Grammars: Regular Expressions, Regular Languages, Properties of Regular Languages, Regular Grammars Finite Automata: Finite State machines, Finite Automata, Deterministic Finite Automata, Nondeterministic Finite Automata Context-Free Grammars and Languages: Context-Free Grammars, Parsing, Ambiguity in Grammars and Languages, Pushdown Automata, Chomsky Normal Forms Computability: Turing Machines, Decidable Languages, the Halting Problem, Undecidability, Reducibility Time Complexity: Measuring Complexity, the Complexity Class P, the Complexity Class NP, NP-Completeness
References: S.M. Srivastava A Course on Mathematical Logic, Springer. J. E. Hopcroft, R. Motwani, J. D. Ullman Introduction to Automata Theory, Languages and Computations, Pearson. J. P. Tremblay, R. Manohar Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw-Hill.

MAT444

Basic Category Theory

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 160 Linear Algebra I and MAT 240 Algebra I
Overview: Category theory is a branch of mathematics which studies and isolates the fundamental structures, underlying constructions and techniques appearing across different areas of mathematics, physics and computer science. The goal of this course is to exhibit the power of category theory as a language for understanding and formalizing common concepts occurring in various branches of mathematics and computers.
Detailed Syllabus:
Unit 1: The category of sets
Sets and functions, Commutative diagrams, Products and coproducts, Finite limits in Set, Finite colimits in Set, other notions in Set.
Unit 2: Categories and functors, without admitting it
Monoids, Groups, Graphs, Orders, Databases: schemas and instances.
Unit 3: Basic Category theory
Categories and functors, natural transformations, Categories and schemas are equivalent (Cat ~ Sch), Yoneda's lemma, Limits and colimits.
Unit 4: Categories at work
Adjoint functors, Categories of functors, Monads.
References: Steven Awodey, Category Theory. Oxford University Press, 2006. Lawvere & Schanuel, Conceptual Mathematics: A First Introduction to Categories. Cambridge University Press. Michael Barr and Charles Wells, Category Theory for Computing Science, Centre de Recherches Mathématiques, 1999. Benjamin Pierce, Basic Category Theory for Computer Scientists. MIT Press Cambridge Saunders Mac Lane, Categories for the Working Mathematician. (the standard reference) David I Spivak, Category Theory for Scientists. MIT Press; 1st edition
Past Instructors: Neha Gupta

CHY122

Basic Organic Chemistry I

4.00

Undergraduate

Intermolecular forces of attraction: van der Waals forces, ion-dipole, dipole-dipole and hydrogen bonding Homolytic and heterolytic bond fission. Hybridization- Bonding Electron displacements: Inductive, electromeric, resonance, hyperconjugation effect Reaction intermediate- their shape and stability a. carbocations, b. carbanions, c. free radicals, d. carbenes, e. benzynes Acidity and basicity of organic molecules: Alkanes/Alkenes, Alcohols/Phenols/Carboxylic acids, Amines pKa, pKb. Electrophiles and nucleophiles. Nucleophilicity and Basicity Aromaticity and Tautomerism Molecular chirality and Isomerism a. Cycloalkanes (C3 to C8): Relative stability, Baeyer strain theory and Sachse Mohr theory. b. Conformations and Conformational analysis: Ethane, n-butane, ethane derivatives, cyclohexane, monosubstituted and disubstituted cyclohexanes and their relative stabilities. Stereochemistry (Structural- and Stereo-isomerism) Molecular representations: Newman, Sawhorse, Wedge & Dash, Fischer projections and their inter conversions. Geometrical isomerism in unsaturated and cyclic systems: cis–trans and, syn-anti isomerism, E/Z notations. Geometrical isomerism in dienes- Isolated and conjugated systems, determination of configurations. Chirality and optical isomerism: Configurational isomers. Molecules with one or two chiral centres- constitutionally symmetrical and unsymmetrical molecules; Enantiomers and diastereomers. Optical activity, disymmetry, meso compounds, racemic modifications and methods of their resolution; stereochemical nomenclature: erythro/threo, D/L and R/S nomenclature in acyclic systems. Measurement of optical activity: specific rotation.
Books: Morrison, Robert Thornton & Boyd, Robert Neilson Organic Chemistry, Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Seventh Edition, 2005. Finar, I. L. Organic Chemistry (Volume 1), Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Sixth Edition, 2003. Finar, I. L. Organic Chemistry (Volume 2: Stereochemistry and the Chemistry of Natural Products), Dorling Kindersley (India) Pvt. Ltd. (Pearson Education). Fifth Edition, 1975. Graham Solomons, T.W., Craig B. Fryhle Organic Chemistry, Ninth edition Eliel, E. L. & Wilen, S. H. Stereochemistry of Organic Compounds; First Edition, Wiley: London, 1994. Clayden, Greeves Warren and Wothers, Organic Chemistry, Oxford University Press. Oxford Chemistry Primers, Introduction to Organic Chemistry, Oxford University Press.
Prerequisite: Chemical Principles (CHY111).

CHY221

Basic Organic Chemistry II

4.00

Undergraduate

Organic reactions; nucleophilic substitution, elimination, addition and electrophilic aromatic substitution reactions with examples will be studied.
COURSE CONTENT:
A. Substitution reactions:
Free radical halogenation, relative reactivity and selectivity, allylic and benzylic bromination
Nucleophilic Subsititution (SN1, SN2, SN1′, SN2′,SNi)
Electrophilic Substitution (SNAr, Addition Elimination vs. Elimination addition)
Electrophilic aromatic substitution will be studied in detail
B. Elimination reactions:
Formation of alkenes and alkynes by elimination reactions, Mechanism of E1, E2, E1cB reactions.
Saytzeff and Hofmann eliminations.
C. Addition reactions:
a. Alkanes sigma bonds
Chemistry of alkanes: Formation of alkanes, Organometallic reagents, Wurtz reaction, Wurtz-Fittig reactions.
b. Alkenes and alkynes pi bonds
Electrophilic additions their mechanisms (Markownikoff/ Anti-Markownikoff addition), mechanism of oxymercuration-demercuration, hydroboration oxidation, ozonolysis, reduction (catalytic and chemical), syn and anti-hydroxylation(oxidation). 1,2-and 1,4-addition reactions in conjugated dienes and Diels-Alder reaction; electrophilic and nucleophilic additions. Hydration to form carbonyl compounds, alkylation of terminal alkynes.
RECOMMENDED BOOK(S): Morrison, Robert Thornton & Boyd, Robert Neilson Organic Chemistry, Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Seventh Edition, 2005. Finar, I. L. Organic Chemistry (Volume 1), Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Sixth Edition, 2003. Clayden, Greeves, Warren and Wothers, Organic Chemistry, Oxford University Press (2001). Peter Sykes, Mechanism in Organic Chemistry, (Pearson Education), Sixth Edition. Paula Yurkains Bruice Organic Chemistry, Prentice Hall; 7th edition (2013)
Prerequisites: Chemical Principles (CHY111), Basic Organic Chemistry-I (CHY122).

MAT084

Basic Probability and Statistics

4.00

Undergraduate

Core course for B.Sc. (Research) Biotechnology. Only available as UWE with prior permission of Department of Mathematics. Does not count towards Minor in Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures +1 tutorial weekly)
Prerequisites: Class XII Mathematics or MAT 020 (Elementary Calculus) or MAT 101 (Calculus I)
Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course provides an introduction to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course will act as an introduction to probability and statistics for students from natural sciences, social sciences and humanities.
Detailed Syllabus: Describing data: scales of measurement, frequency tables and graphs, grouped data, stem and leaf plots, histograms, frequency polygons and ogives, percentiles and box plots, graphs for two characteristics Summarizing data: Measures of the middle: mean, median, mode; Measures of spread: variance, standard deviation, coefficient of variation, percentiles, interquartile range; Chebyshev’s inequality, normal data sets, Measures for relationship between two characteristics; Relative risk and Odds ratio Elements of Probability: Sample space and events, basic definitions and rules of probability, conditional probability, Bayes’ theorem, independent events Sampling: Population and samples, reasons for sampling, methods of sampling, standard error, Population parameter and sample statistic Special random variables and their distributions: Bernoulli, Binomial, Poisson, Uniform, Normal, Exponential, Gamma, distributions arising from the Normal: Chi-‐square, t, F Distributions of Sampling statistics: Sampling distribution of the mean, The central limit theorem, Determination of sample size, standard deviation versus standard error, the sample variance, sampling distributions from a normal population, sampling from a finite population Estimation: Maximum likelihood estimator; Interval estimates; Estimating the confidence interval for population mean, variance and proportions; Confidence intervals for the difference between independent means Hypothesis testing: Null and alternate hypothesis; Significance levels; Type I and Type II errors; Tests based on Normal, t, F and Chi-‐Square distributions for testing of mean, variance and proportions, Tests for independence of attributes, Goodness of fit; Non-‐parametric tests: the sign test, the Signed Rank test, Wilcoxon Rank-‐Sum Test. Analysis of variance: Comparing three or more means: One-‐way analysis of variance, Two-‐factor analysis of variance, Two-‐way analysis of variance with interaction Correlation and Regression: Correlation, calculating correlation coefficient, coefficient of determination, Spearman’s rank correlation; Linear regression, Least square estimation of regression parameters, distribution of the estimators, assumptions and inferences in regression; analysis of residuals: assessing the model; transforming to linearity; weighted least squares; polynomial regression
Main References: Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross, 2nd edition, Harcourt Academic Press.
Other References: Basic and Clinical Biostatistics by Beth Dawson-‐Saunders and Robert G. Trapp, 2nd edition, Appleton and Lange. John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011.
Past Instructors: Sneh Lata, Suma Ghosh

MAT600

Basic Tools in Mathematics

4.00

Graduate

Basic Tools in Mathematics

BIO527

Bio-Ethics, Bio-Reg & IPR

3.00

Graduate

Bio-Ethics, Bio-Regulatory Affairs and IPR

CHY346

Bio-inorganic chemistry

3.00

Undergraduate

General discussion about bioinorganic chemistry Biological important elements, Biological ligands Alkali and alkaline earth metal in biology: Role of Na, K (Na-K pump, chelate chemistry, SHAB theory); Mg (ATP hydrolysis and chlorophyll) and Ca Importance of Oxygen, Great oxygenation event Iron based chemistry in nature; Iron metabolism: Iron transport, Iron storage; Iron cycle. Oxygen utilization: (i) Oxygen transport and storage (ii) Oxidases enzyme: Cytochrome c oxidase, Electron transport chain, Cytochrome c oxidase vs. Cytochrome in respiratory cycle; electron transfer reaction in biology Oxygenase: Cyt P450: Reaction mechanism (iv) Peroxidase: HRP. Fe-S protein, Hydrogenase enzyme. Toxicity: Superoxide dismutase and Catalase Mo- containing enzyme: Nitrogenase, nitrogen cycle. Co, V containing enzymes. Zn containing enzymes. Photosynthesis: O-H bond activation, role of Mn in OEC f-orbitals and oxidation states; atoms and ion sizes (lanthanoid contractions); coordination no. Spectroscopic and magnetic properties of lanthanoids and actinoids. Lanthanoids metals: Complexes of Ln(III), Organometallic complexes. Actinoids metals: Inorganic and Organometallic complexes of Th and U. Nuclear Property: Mass defect and binding energy; Nuclear emissions (alpha and beta particles, gamma radiations); Nuclear transformations, the kinetics of radioactivity decay, units of radioactivity, Nuclear fission vs. fusion. Applications of isotopes: Kinetic isotope effects, Radiocarbon dating.
Books: Inorganic Chemistry; Principles of Structures and Reactivity: James E. Huheey; Allen A. Keiter;Richard L. Keiter, Pearson Edition. Principles of Bioinorganic Chemistry: Stephen J. Lippard, Jeremy M. Berg, University Science Books, 1994. Physical Methods in Bioinorganic Chemistry: Spectroscopy and Magnetism: Lawrence Que, University Science Books, 1999.
Reference Materials: Other reading materials will be assigned as and when required.

BIO205

Bioanalytical Techniques

3.00

Undergraduate

Instruments, basic principles and usage pH meter, absorption and emission spectroscopy, Principle and law of absorption, fluorimetry, colorimetry, spectrophotometry (visible, UV, infra-red), polarography, centrifugation, atomic absorption, NMR, X-ray crystallography. Chromatography techniques: Paper chromatography, thin layer chromatography, column chromatography, HPLC, gas chromatography, gel filtration and ion exchange chromatography, affinity chromatography, NMR, CD, MS MS, ES MS, LC MS, AFM, Confocal Microscopy, Fluorescent microscopy, FACS analysis, Electrophoresis Agarose gel electrophoresis, SDS polyacrylamide gel electrophoresis, immune electrophoresis, Isoelectric focusing., Radioisotope tracer techniques and autoradiography.
Recommended Books:
Principles and Techniques of Biochemistry and Molecular Biology Ed. Wilson KM, Valker, JM Pub: Cambridge University Press. Advanced Instrumentation, Data Interpretation, and Control of Biotechnological Processes, Impe., J. F. V., Vanrolleghem, P. A., Iserentant, D. M., Pub: Kluwer Academic. Crystal Structure Analysis A primer, Glusker, J. P., Trueblood, K. N., Pub: Oxford University Press. Modern Spectroscopy, Hollas, J. M., Pub: John Wiley and Son Ltd. NMR Spectroscopy: Basic Principles, Concepts and Applications in Chemistry, Gunther, H., Pub: John Wiley and Sons Ltd. Principles of Physical Biochemistry, Holde, K. E. V., Johnson, W. C., Ho, P. S., Pub: Prentice Hall. Microscopic Techniques in Biotechnology, Hoppert M., Pub: Wiley VCH. Principles of Fermentation Technology, Stanbury P. F., Whitaker. A., Hall, S. J., Pub: Butterworth-Heinemann Ltd.

CHY354

Biochemical Toxicology

3.00

Undergraduate

COURSE CONTENT:
1. General Principals of toxicology
2. Classes of toxicants 3. Metabolism
4. P450 and P450 catalyzed reactions
5. Other phase 1 reactions
6. Phase II/Conjugation reactions
7. Bioactivation and Reactive intermediates 8. Reaction of Chemicals with DNA
9. DNA adducts and its consequences (Mutagenesis, DNA repair and Translesion DNA synthesis)
10. Protein adducts 11. Genetic toxicology (polymorphism)
12. Molecular basis of toxicology
13. Biomarkers
14. Natural Products
15. Cellular Oncogenesis
16. Metals
17. Drug induced liver damage
18. Mass spectrometry and other analytical methods

BIO204

Biochemistry

3.00

Undergraduate

Properties and importance of water, intra and intermolecular forces, non-covalent
interactions- electrostatic, hydrogen bonding, Vander Waals interactions, hydrophobic and hydrophilic interactions. Disulphide bridges. pH, pK, acid base reactions and buffers.
Carbohydrates: Different carbohydrates and with examples of glucose, galactose, sucrose, starch and glycogen. Carbohydrates metabolism: Glycolysis, Kreb’s Cycle and oxidative phosphorylation. Gluconeogenesis, Pentose phosphate pathway, Glyoxylate cycle.
Proteins: Classification and properties of amino acids, Classification based on structure and functions, structural organization of proteins (primary, secondary, tertiary and quaternary structures), biosynthesis of protein. Enzymes and enzyme kinetics. Michaelis-Menten equation, significance of Km , Vmax and Kcat. Lineweaver – Burk plot. Biosynthesis and degradation of aromatic and branched chain amino acids.
Nucleic acids: Structure and properties of nucleic acids. Different forms of DNA-A, B, Z. Circular DNA and DNA supercoiling. Different types of RNA- mRNA, and non coding RNA – tRNA, rRNA, snRNA, miRNA and siRNA. Synthesis and regulation of purine nucleotides by de novo pathway. Salvage of purine nucleotides. Synthesis and regulation of pyramidine nucleotides. Formation of deoxyribonucleotides and their regulation. Degradation of purines and pyrimidine nucleotides, disorders of nucleotide metabolism
Lipids: Classification, structure, properties and functions of fatty acids, triglycerides, phospholipids, sphingolipids, cholesterol and eicosanoids- prostaglandlins. Saturated and unsaturated fatty acids - synthesis, β-oxidation and regulation. Ketone bodies. Synthesis of triacylglycerides, phospholipids, and cholesterol.
Vitamins: Source, structure, biological role and deficiency disorders of vitamins .
Recommended Books: Lehninger Principles of Biochemistry (5th ed.), Nelson, D., Cox, D., Pub: Macmillan Pub. Biochemistry (6th ed.), Stryer, L., Pub: Freeman-Tappan. Text Book of Biochemistry by West, E. S., Todd, W. R., Bruggen, J. T V., Pub: Mac Milan. Principles of Biochemistry by White, A., Handler, P., Smith, E. L., Pub: McGraw Hill. Harper's Biochemistry, Murray, R. K., et al., 27 ed., Pub: Langeman Biochemistry (3rd ed.), Voet, D., Voet, J. G., Pub: John Wiley. Biochemistry, Mathews, et. al., Pub: Pearson

BIO208

Bioinformatics

3.00

Undergraduate

Introduction to Bioinformatics, Review on Biological Databases concept: Primary, secondary and composite databases, Nucleotide Sequence databases (EMBL, GenBank, DDBJ) Protein Databases –(UNIPROT, PIR, TREMBL), Protein family/domain databases (PROSITE, PRINTS, Pfam,), Metabolic & Pathway databases (KEGG), Structural databases (PDB).
Structural Bioinformatics: Classification of protein structures, Primary, Secondary and Tertiary structures, Quaternary structure, Protein folding concept, Potential energy map and Ramachandran plot. Secondary structure prediction methods, Classification of Three Dimensional Structures of Proteins, Motifs, Folds and Domains, Classification of Three Dimensional Structures in PDB (HSSP, SCOP, FSSP, CATH). Structural Alignment Methods, Homology Modeling, fold recognition and ab initio methods. Computer aided drug design (CADD), Molecular Docking.
Genomics: The Human Genome, Comparative Genomics (Comparative genomics of Model organisms), gene identification methods, primary gene expression analysis. Primary Sequence Analysis: Sequence alignment, Homology concept, pairwise sequence alignment, multiple sequence alignment, Phylogenetic Analysis, concept of SNP and snip analysis.
Books: Bioinformatics–Sequence, Structure and Databanks, Higgins, D., Taylor, W., Pub: Oxford University Press, Incorporated. Bioinformatics: A practical guide to the analysis of genes and proteins, Baxevanis, A. D., Ouellette, B.F.F., Pub: John Wiley and Sons Inc. Bioinformatics: Sequence and Genome Analysis, Mount, D.W., Pub: Cold Spring Harbor Laboratory Press. Structural Bioinformatics, Ed: Bourne, P. E., Weissig, H., Pub: Wiley-Blackwell.

BIO704

Bioinformatics Essentials

3.00

Graduate

Bioinformatics Essentials

CHY451

Bioinorganic Chemistry

2.00

Undergraduate

Bioinorganic Chemistry

BIO310

Biology of Infectious Diseases

3.00

Undergraduate

Biology of infectious diseases. History of infectious diseases, basic concepts of disease dynamics, parasite diversity, evolution & ecology of infectious diseases Emergence of diseases: The basic reproductive number, critical community size, epidemic curve, zoonosis, spill over, human / wildlife interface, climate change, hot zones, pathology. Spread of diseases: transmission types (droplets, vectors, sex), super spreading, diffusion, social networks, nosomical transmission, manipulation of behavior. Control of diseases: drug resistance, vaccination, herd immunity, quarantines, antibiotics, antivirals, health communication, ethical challenges of disease control. The future of infectious diseases: Evolution of virulence, emergence of drug resistance, eradication of diseases, medicine & evolution, crop diseases & food security, digital epidemiology. Diseases in developing countries: Malaria, HIV, Cholera, Dengue, Tuberculosis.
Recommended books: Understanding infectious disease, Ellner, P. L., Neu, H. C., Pub: Mosby Year Book. Expert Guide to Infectious Diseases, Tan, J. S., File, T. M., Salata, R. A., Tan, M. J., Pub: ACP Press. The Biologic and Clinical Basis of Infectious Diseases, Shulman, S. T., Pub: Saunders. A practical approach to infectious diseases. Reese, R. E., Betts, R. F., Pub: Little Brown and Company.

MAT670

Biomathematics

4.00

Graduate

Biomathematics

BIO209

Biophysics

3.00

Undergraduate

Introduction: Definition of biophysics, why to study, examples.
Thermodynamics: Entropy, Enthalpy, The free energy of a system, Chemical potential, Redox potential, Bioenergetics
Biophysical properties: Surface tension, Diffusion & Brownian motion, Osmosis, Dialysis, Colloids.
Application of Radiation to Biological system: Introduction, particles and radiations of significance, physical and biological half-lives, macroscopic absorption of radiation, activity and measurements, units of dose, relative biological effectiveness and action of radiation at molecular level.
Experimental methods in biophysics:
(a) Microscope: Light characteristics, microscopes- compound, phase contrast, polarization, fluorescent and electron microscopes – Transmission Electron Microscope, Scanning Electron Microscope, and Scanning tunneling electron microscope, Atomic Force Microscopy
(b) Spectroscopy: Interaction of EM radiation with matter Ultraviolet & Visible spectroscopy-Beer Lamberts law- spectrophotometer. Infrared spectroscopy, Raman spectra, Circular Dichroism, Fluorescence spectroscopy, NMR spectroscopy.
Recommended books: Intermolecular and surface forces by J. Israelachvilli (Elsevier, 2011) Molecular & Cellular Biophysics by M. B. Jackson Biophysics, V. Pattabhi & N. Gautham (Narosa Publishing House) Biophysics by R. Glaser (Springer, 2004)

PHY570

BIOSENSORS: General principles and advanced sensing techniques

3.00

Graduate

This course covers the basic sensor terminologies (linearity, sensitivity, selectivity, response time, etc.), analyte surface interactions, Bio-MEMS, concepts of microfluidic devices, and various advanced detection techniques such as, fluorescence, surface plasmon resonance (SPR), impedance spectroscopy, scanning probe microscopy (SPM), surface enhanced Raman spectroscopy (SERC), and electrochemical methods.

MAT685

Business Statistics

3.00

Graduate

Business Statistics

MAT101

Calculus I

4.00

Undergraduate

Core course for B.Sc. (Research) programs in Mathematics, Physics and Economics. Optional course for B.Sc. (Research) Chemistry.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII mathematics or MAT 020 (Elementary Calculus)
Overview: This course covers one variable calculus and applications. It provides a base for subsequent courses in advanced vector calculus and real analysis as well as for applications in probability, differential equations, optimization, etc. One of the themes of the course is to bring more rigour to the formulas and techniques students may have learned in school.
Detailed Syllabus: Real Number System: The axioms for N and R, mathematical induction. Integration: Area as a set function, integration of step functions, upper and lower integrals, integrability of bounded monotone functions, basic properties of integration, polynomials, trigonometric functions. Continuous Functions: Functions, limits, continuity, Intermediate Value Theorem, Extreme Value Theorem, integrability of continuous functions, Mean Value Theorem for integrals. Differentiation: Tangent line, rates of change, derivative as function, algebra of derivatives, implicit differentiation, related rates, linear approximation, differentiation of inverse functions, derivatives of standard functions (polynomials, rational functions, trigonometric and inverse trigonometric functions), absolute and local extrema, First Derivative Test, Rolle's Theorem, Mean Value Theorem, concavity, Second Derivative Test, curve sketching. Fundamental Theorem of Calculus: Antiderivatives, Indefinite Integrals, Fundamental Theorem of Calculus, Logarithm and Exponential functions, techniques of integration. Polynomial Approximations: Taylor polynomials, remainder formula, indeterminate forms and L'Hopital's rule, limits involving infinity, improper integrals. Ordinary Differential Equations: 1st order and separable, logistic growth, 1st order and linear.
References: Calculus, Volume I, by Tom M Apostol, Wiley. Introduction to Calculus and Analysis I by Richard Courant and Fritz John, Springer Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition. Calculus with Analytic Geometry by G F Simmons, McGraw-Hill
Past Instructors: Amber Habib, Debashish Bose

MAT102

Calculus II

4.00

Undergraduate

Core course for B.Sc. (Research) programs in Mathematics, Physics. Optional course for B.Sc. (Research) Chemistry.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 101 (Calculus I)
Overview: The first part is an introduction to multivariable differential calculus. The second part covers sequences and series of numbers and functions. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering.
Detailed Syllabus: Differential calculus in several variables: Functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2nd derivative test Sequences and Series: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, Abel and Dirichlet tests, power series, Taylor series, Fourier Series.
References: Calculus, Volume II, by Tom M Apostol, Wiley. Essential Calculus – Early Transcendentals by James Stewart, Cengage, India Edition. Calculus and Analytic Geometry by G B Thomas and R L Finney, 9th edition, Pearson. Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1st edition, Springer (India), 2011. Calculus by Ken Binmore and Joan Davies, 1st edition, Cambridge, 2010.
Past Instructors: Amber Habib, Debashish Bose

BIO703

Cancer And Its Therapies

3.00

Graduate

Cancer And Its Therapies

BIO309

Cancer Biology

3.00

Undergraduate

Course description not available.

BIO312

Cancer Biology

3.00

Undergraduate

Description: Basic understanding of Biochemistry, Cell and Molecular Biology is prerequisite for this course offered to students in the final year of their degree program. This is designed to provide a comprehensive overview of the Chemistry, Biology and Pathology of cancer. Students opting for this course will be considered of having a specialization in modern cancer biology and therapeutics. The course is divided into two broad parts. The first part will focus on the genetic and molecular basis of cancer, while the second half will discuss the interface between cancer and medicine. The students will also be introduced to the concepts of anti-cancer drug resistance and the ever-growing need to implement personalized anti-cancer therapeutics in clinic. The use of genomics, proteomics and metabolomics tools for identification of diagnostics, predictive and prognostic cancer biomarkers will be presented. Pharmaceutical approach of anti-cancer drug discovery and concepts of clinical trials will also be discussed. Biology: Definition and pathology of cancer. Cancer is a slow growing disease. War against cancer. Cancer is a multistep process: evolution of cancer. Eight hallmarks of cancer. Inflammation and genomic instability as causes of cancer. Carcinogens/mutagens. Tumor heterogeneity. Tumor suppressors, oncogenes/oncogene addiction theory. Cancer cell signaling: PI3K and MAPK signaling. Apoptosis, autophagy, senescence and their roles in cancer. Cancer stem cells
Therapeutics: Chemo, targeted, immuno and stem-cell therapies. Anti-cancer drug resistance. Biomarkers: Diagnostic, prognostic and predictive. Personalized therapies: concept, experimental tools. 2 Cancer Genomics. Functional genomics. Synthetic lethality. Clinical trials.

BIO608

Cancer Biology

3.00

Graduate

Cancer Biology

BIO201

Cell Biology and Genetics

3.00

Undergraduate

Cell as a basic unit of living systems, broad classification of cell types: bacteria, eukaryotic microbes, plant and animal cells; cell, tissue, organ and organisms, Cell organelles: Ultrastructure of cell membrane and function, Chromosomes: Structural organisation of chromosomes, nucleosome organization, euchromatin and heterochromatin. Cell division and cell cycle, Cell–cell interaction, apoptosis, necrosis and autophagy, Cell differentiation.
History, scope and significance of Genetics. Mendelian laws of inheritance. Lethality and interaction of genes. Linkage and crossing over. Mapping of genes. Basic microbial genetics, Genetic mapping. Classical and modern concept of gene, Mutations, Chromosomal aberrations. Genetic disorders in humans. Sex determination in plants and animals. Non disjunction as a proof of chromosomal theory of inheritance. Sex linked, sex influenced and sex limited inheritance. Extra chromosomal inheritance; cytoplasmic inheritance, Mitochondrial and Chloroplast inheritance. Principles of Population genetics; Hardy-Weinberg equilibrium law, Gene and genotype frequencies.
Recommended Books: An Introduction to the Molecular Biology of the Cell, Alberts, B., Bray, D., Johnson, A., Lewis, J., Roff, M., Robert, K., Walter, P., Roberts, K., Pub: Garland Publishing Company. Cell and Molecular Biology, Sheelar, P., Bianchi, D. E., Pub: John Wiley. Molecular Cell Biology, Lodish, H., Berk, A., Zipursky, S.L., Matsudaura, P., Baltimore, D., Danell, J., pub; W.H. Preeman and Company. Principles of Genetics, Gardner, E. J., Pub; John Wiley & Sons Inc.

BIO526

Cell Signal. & Neuro

3.00

Graduate

BIO313

Cell Signalling and Neurosciences

3.00

Undergraduate

Molecular and cellular basis of brain development:
Brain structure and its origins and cognitive functions, including learning, memory and
perception, Human embryonic brain development, Induction of neuronal differentiation and
neuronal patterning, Structure of neurons, Axon guidance, Glial cell lineage development,
Generation of neurodevelopmental stages in vitro using induced pluripotent stem cells
(iPSCs).
Cell signaling:
Biochemistry of neurotransmitters and receptors, Signaling via second-messengers including
cAMP, Ca++ and lipids. Synaptic vesicle trafficking and exocytosis in neurons,
Membrane channels in signaling, Action potential and synaptic transmission in neuronal
circuitry formation.
Seminar Series/ Group discussion: To facilitate learning and concept building
on neuronal signaling associated to neurological diseases, molecular and cellular basis of
syndromic and idiopathic neurological disease.
Tutorials/ Demonstration:
Transcriptomics and metabolomics in brain, Cellular and molecular imaging in brain cells and
Brain imaging technologies including, Electroencephalogram (EEG), functional Magnetic
resonance imaging (fMRI), Magnetic Resonance spectroscopy (MRS).
Practicals:
Basic methods in neural cell culture, Generation of primary neurons and glial cells, Cytokines
and small molecules in neuronal development, Basic methods in molecular neurobiology.
Recommended books:
Fundamental Neuroscience by Larry R. Squire
Cell Signaling by John Hancock
Dynamics of cyclic nucleotides signaling in Neurons by Pierre Vincent

PHY573

Characterization Of Materials

3.00

Graduate

Characterization Of Materials

PHY575

Characterization of Materials II

3.00

Graduate

This course covers the basic interaction of matter with electrons, neutrons, ions, energetic particles, elastic and non–elastic scatterings, and characterization techniques: Optical microscopy, Transmission electron microscopy (TEM), Scanning electron microscopy (SEM), Scanning probe microscopy (SPM), Atomic force microscopy (AFM), X-ray diffraction, Energy dispersive X-ray analysis. X- Ray photoelectron spectroscopy (XPS), Secondary ion mass spectrometry (SIMS).

CHY212

Chemical Applications of Group Theory

2.00

Undergraduate

Symmetry operations and symmetry elements, Concepts and properties of a group, group multiplication Tables, Similarity transformation, Class, Determination of symmetry point group of molecules, Matrix representation of groups, reducible and irreducible representations, Great orthogonality theorem, Character tables, Direct Product and Spectroscopic selection rule, Molecular Vibrations, Normal coordinates, Symmetry of normal mode vibrations, Symmetry Adapted Linear Combination, Infrared and Raman active vibrations, Molecular orbitals, LCAO MO approach, HMO method, Hybrid orbitals, Free ion configuration, terms and states, splitting of levels and terms in a chemical environment, correlation diagrams, spectral and magnetic properties of the transition metal complexes.
Course outline: Introduction: Importance of Group Theory in Chemistry Symmetry elements and symmetry operations: Use molecular models to identify symmetry elements of different molecules. Understanding of the interrelation of different symmetry elements present in a molecule, product of symmetry operations. Point Groups: Concepts and properties of a group, group multiplication Tables, Similarity transformation, Class, Determination of symmetry point group of molecules. Matrix representations and Character Tables: Matrix representation of groups, reducible and irreducible representations, Great orthogonality theorem, character tables. SALC, direct product, Molecular vibrations: Direct Product and Spectroscopic selection rule, Molecular Vibrations, Normal coordinates, Symmetry of normal mode vibrations, Symmetry Adapted Linear Combination, Infrared and Raman active vibrations. Molecular orbital Theory, Hybrid orbitals: Molecular orbitals, LCAO MO approach, HMO method, Hybrid orbitals. Terms and states, Transition metals chemistry: Free ion configuration, terms and states, splitting of levels and terms in a chemical environment, correlation diagrams, spectral and magnetic properties of the transition metal complexes.

CHY311

Chemical Binding

4.00

Undergraduate

Quantum mechanics provides the microscopic basis for a fundamental understanding of chemistry, molecular structure, bonding, and reactivity. This course and the associated computer lab provide a comprehensive treatment of valence bond and molecular orbital theories, post Hartree-Fock wave function and density functional methods. Students will learn to compute molecular structures, spectra, and thermochemical parameters for molecules in the gas-phase and for condensed-phase systems.
COURSE CONTENT: Postulates of Quantum Mechanics Atomic Orbitals and Basis Sets The Born-Oppenheimer approximation and the molecular Hamiltonian The Concept of the Potential Energy Surface Geometry Optimization and Frequency Analysis Semi-empirical and ab initio Quantum Mechanics Variation and Perturbation Theory Valence Bond and Molecular Orbital theories Independent-Particle Models: the Hartree method Spin, statistics and the Pauli principle The Hartree-Fock Self-Consistent Field equations Electron Correlation, Density Matrices and Natural Orbitals Density Functional Theory Periodic systems Implicit and explicit solvent methods QM/MM and ONIOM
RECOMMENDED BOOK(S): Frank Jensen: Introduction to Computational Chemistry (Wiley) Henry Eyring, John Walter and George E. Kimball: Elementary Quantum Chemistry (John Wiley) J. N. Murrell, S. F. A. Kettle, J. M. Tedder: Valence Theory [ELBS & John Wiley] Richard P. Feynman, Robert B. Leighton & Matthew Sands: The Feynman Lectures on Physics, Vol.III (Addison Wesley Longman) James B. Foresman, AEleen Frisch, Exploring Chemistry With Electronic Structure Methods: A Guide to Using Gaussian (Gaussian, Inc.) Errol G. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics (Kluwer Academic Publishers, 2003) N. Sukumar, ed. A Matter of Density: Exploring the Electron Density Concept in the Chemical, Biological, and Materials Sciences (John Wiley, Hoboken, NJ, 2013)
Prerequisites: Chemical Principles, Calculus, Linear Algebra, physics, CS.
Co-requisite: Molecular Spectroscopy.

CHY211

Chemical Equilibrium

5.00

Undergraduate

In this course, we adopt a case studies approach to understanding thermodynamic principles already familiar to students from earlier courses. In class we will explore real chemical questions involving equilibrium, acid base chemistry, electrochemistry, surface phenomena and solution chemistry by reading and discussing research papers.
COURSE CONTENT:
Entropy and Information Absolute temperature Shannon Entropy
Thermodynamics & Thermochemistry First, second and third laws of thermodynamics and their applications in chemistry Enthalpy change and its impact on material science and biology Enthalpies of formation and reaction enthalpies Internal energy, entropy, Gibbs free energy Ideal Gas Law Kinetic Theory of Gases Design of an air bag Maxwell-Boltzmann Distribution
Phase Equilibria Phase diagrams and impact on material sciences Phase transitions Chemical equilibrium and its impact on technology and biochemistry Changes in equilibria with temperature and pressure Colligative properties Raoult's Law Ideal and non-ideal mixtures
Acid-base equilibria Open systems Soil Equilibria & Acid Rain
Chemical Kinetics Determination of rate, order and rate laws Impact of Chemical Kinetics on Biochemistry Oxidation of glucose in biological systems
Catalysis Activation energy Arrhenius equation Kinetics; Mechanisms; Enzymes Reducing Air Pollution from Automobiles
Diffusion across membranes Osmosis and reverse osmosis Design of a water filter Adsorption and Chromatography Ion Exchange columns and water purification
Electrochemistry in biology Nernst Equilibrium Potential Voltage-gated ion channels Photosynthesis and solar cells
Protein-ligand binding Binding free energy Force fields Empirical potentials Conformational freedom Docking & scoring computer lab
Statistical Thermodynamics Microcanonical, Canonical and Grand Canonical Ensembles Partition function Molecular Dynamics computer lab Monte Carlo simulations computer lab Membrane Protein Simulations computer lab
Molecular Reaction Dynamics Transition State Effect of translational and vibrational kinetic energy
RECOMMENDED BOOK(S): Physical chemistry by Peter Atkins, Julio De Paula. Edition: 9th ed. South Asia Edition. Publisher: UK Oxford University Press 2011 Physical chemistry by Gilbert W. Castellan, Edition: 3rd ed. Publisher: New Delhi. : Narosa Publishing House, 1985, 2004 Basic Physical Chemistry: The Route to Understanding by E. Brian Smith ISBN:978-1-78826-293-9 Publisher: World Scientific Elements of Classical Thermodynamics for Advanced Students of Physics by A. B. Pippard [Paperback] ISBN:9780521091015 A Farewell to Entropy: Statistical Thermodynamics Based on Information by Arieh Ben-Naim ISBN:978-1-270-706-2 Publisher: World Scientific Physical Chemistry by Thomas Engel, Philip Reid. Publisher: New Delhi Pearson 2006
Other reading materials will be assigned as and when required.
Prerequisites: Chemical Principles (CHY111).

CHY111

Chemical Principles

5.00

Undergraduate

This course will focus on introductory chemical principles, including periodicity, chemical bonding, molecular structure, equilibrium and the relationship between structure and properties. Students will explore stoichiometric relationships in solution and gas systems which are the basis for quantifying the results of chemical reactions. Understanding chemical reactivity leads directly into discussion of equilibrium and thermodynamics, two of the most important ideas in chemistry. Equilibrium, especially acid/base applications, explores the extent of reactions while thermodynamics helps us understand if a reaction will happen. The aim of the laboratory will be to develop your experimental skills, especially your ability to perform meaningful experiments, analyze data, and interpret observations. This is a required course for Chemistry majors, but also satisfies UWE requirements for non-majors.
COURSE CONTENT: Atomic structure, Periodic table, VSEPR, Molecular Orbital theory, and biochemistry: Introduction: why chemistry in engineering? Concept of atom, molecules, Rutherford’s atomic model, Bohr’s model of an atom, wave model, classical and quantum mechanics, wave particle duality of electrons, Heisenberg’s uncertainty principle, Quantum-Mechanical Model of Atom, Double Slit Experiment for Electrons, The Bohr Theory of the Hydrogen atoms, de Broglie wavelength, Periodic Table. Schrodinger equation (origin of quantization), Concept of Atomic Orbitals, representation of electrons move in three-dimensional space, wave function (Y), Radial and angular part of wave function, radial and angular nodes, Shape of orbitals, the principal (n), angular (l), and magnetic (m) quantum numbers, Pauli exclusion principle. Orbital Angular Momentum (l), Spin Angular Momentum (s), spin-orbit coupling, HUND’s Rule, The aufbau principle, Penetration, Shielding Effect, Effective Nuclear Charge, Slater’s rule. Periodic properties, Ionization Energies of Elements, Electron affinities of elements, Periodic Variation of Physical Properties such as metallic character of the elements, melting point of an atom, ionic and covalent nature of a molecule, reactivity of hydrides, oxides and halides of the elements. Lewis structures, Valence shell electron pair repulsion (VSEPR), Valence-Bond theory (VB), Orbital Overlap, Hybridization, Molecular Orbital Theory (MO) of homo-nuclear and hetero-nuclear diatomic molecules, bonding and anti-bonding orbitals. Biochemistry: Importance of metals in biological systems, Fe in biological systems, Hemoglobin, Iron Storage protein - Ferritin]
2. Introduction to various analytical techniques:
UV-Visible Spectroscopy, IR Spectroscopy, NMR spectroscopy, X-Ray crystallography
Spectroscopy: Regions of Electromagnetic Radiation, Infra-Red (IR) Spectroscopy or Vibrational Spectroscopy of Harmonic oscillators, degree of freedom, Stretching and Bending, Infrared Spectra of different functional groups such as OH, NH2, CO2H etc., UV-Vis Spectroscopy of organic molecules, Electronic Transitions, Beer-Lambert Law, Chromophores, principles of NMR spectroscopy, 1H and 13C-NMR, chemical shift, integration, multiplicity,
X-ray crystallography: X-ray diffraction, Bragg’s Law, Crystal systems and Bravais Lattices The Principles of Chemical Equilibrium, kinetics and intermolecular forces: Heat & Work; State Functions Laws of thermodynamics Probability and Entropy Thermodynamic and Kinetic Stability Determination of rate, order and rate laws Free Energy, Chemical Potential, Electronegativity Phase Rule/Equilibrium Activation Energy; Arrhenius equation Catalysis: types; kinetics and mechanisms Electrochemistry Inter-molecular forces
4. Introduction to organic chemistry, functional group and physical properties of organic compounds, substitution and elimination reaction, name reactions and stereochemistry
Texts & References: Chemical Principles - Richard E. Dickerson, Harry B. Gray, Jr. Gilbert P. Haight Valence - Charles A. Coulson [ELBS /Oxford Univ. Press] Valence Theory - J. N. Murrell, S. F. A. Kettle, J. M. Tedder [ELBS/Wiley] Physical Chemistry - P. W. Atkins [3rd Ed. ELBS] Physical Chemistry - Gilbert W. Castellan [Addison Wesley, 1983] Physical Chemistry: A Molecular Approach -Donald A. McQuarrie, J.D . Simon Inorganic Chemistry: Duward Shriver and Peter Atkins. Inorganic Chemistry: Principles of Structure and Reactivity by James E. Huheey, Ellen A. Keiter and Richard L. Keiter. Inorganic Chemistry: Catherine Housecroft, Alan G. Sharpe. Atkins' Physical Chemistry, Peter W. Atkins, Julio de Paula. Strategic Applications of Named Reactions in Organic Synthesis, Author: Kurti Laszlo et.al Classics in Stereoselective Synthesis, Author: Carreira Erick M & Kvaerno Lisbet Molecular Orbitals and Organic Chemical Reactions Student Edition, Author: Fleming Ian Logic of Chemical Synthesis, Author: Corey E. J. & Xue-Min Cheng Art of Writing Reasonable Organic Reaction Mechanisms /2nd Edn., Author: Grossman Robert B. Organic Synthesis: The Disconnection Approach/ 2nd Edn., Author: Warrer Stuart & Wyatt Paul
Other reading materials will be assigned as and when required.
Prerequisite: None.

CHY503

Chemistry and Biology of Glycoconjugates

3.00

Graduate

Introduction of glycocongugates, Structure and function of Glycoproteins, proteoglycans and
glycosaminoglycans; Glycopeptides. glyco-amino-acids and glycosyl-amino-acids and Peptidoglycans.
Inter- and intra-cellular communication and “Glycocode”, The need for homogeneity and pure, welldefined
conjugates. Glycocongugate assembly and vaccine development.

CHY400

Chemistry Colloquium

1.00

Undergraduate

Eminent speakers from around the world (and possibly from the department) present seminars about current topics at the forefront of chemical research. Students are expected to participate actively in these seminars by asking questions. This course serves to introduce undergraduate students to the range of research opportunities in chemistry.

CHY222

Chemistry of Carbonyl Compounds

4.00

Undergraduate

Nucleophilic Addition: (a) Reactivity of carbonyl groups (b) Cyanide as nucleophile- cyanohydrin formation (c) Oxygen/sulfur as nucleophile - Acetals, Ketals and Hydrates (d) Hydride as the nucleophile - Reduction reactions (e) Carbon as nucleophile - Organometallics (Grignard and alkyl lithiums) (f) Nitrogen as nucleophile - Imine and hydrazones. (g) Nucleophilic addition to carbonyl analogs Nucleophilic Substitution: (a) Reactivity of carboxylic acid family (b) Oxygen/sulfur as nucleophile – Esters and carboxylic acids (c) Nitrogen as nucleophile – Amides (d) Acyl halides and anhydrides (e) Hydride as the nucleophile - Reduction reactions (f) Carbon as nucleophile - Organometallics (Grignard and alkyl lithium) (g) Enantiomer resolution (h) Nucleophilic Substitution at sulfuric and phosphoric acids The alpha carbanion – nucleophilic-electrophilic reactivity of carbonyls (a) Enols and enolate anions (b) Addition-dehydration – The aldol reaction (c) Ester condensation (d) Fragmentation of Beta-dicarbonyl compounds (e) Alkylation of enolate anions (f) Other stabilized carbanions and carbon nucleophiles Nucleophilic additions and substitutions in Synthesis (a) Available reactions (b) Experimental considerations (c) The strategy of synthesis (d) Synthesis examples
Prerequisites: Basic Organic Chemistry-I (CHY122), Basic Organic Chemistry-II (CHY221).

CHY140

Chemistry of Colour and Art

3.00

Undergraduate

This inter-disciplinary course will introduce students to the basic principles of optics, colour theory and the chemical principles behind the colours of gemstones, pigments and nanomaterials. Absorption, scattering and emission of light, changes associated with chemical reactions, thermal radiation, colour vision, colours of bulk materials and at the nanoscale will be discussed and demonstrated. Topics covered include spectroscopy, art forensics, colour theory in art, colour spaces, colour in culture, introduction to photography, drawing and painting. Students will also explore how artists through the ages have used and exploited colour, and will have the opportunity to discover for themselves the fundamentals of colour photography, painting and art. Lab and studio sessions will be conducted during alternate weeks. Field trips to natural locations, art galleries and museums will be included to provide opportunities for creating individual works of art.
RECOMMENDED BOOK(S): Colour Chemistry by Robert M. Christie, RSC Publishing, Cambridge, 2015. BRAIN AND ART, Editors: Idan Segev, Luis M. Martinez, Robert J. Zatorre, Frontiers in Human Neuroscience, December 2014 http://journal.frontiersin.org/researchtopic/104/brain-and-art The Dimensions of Colour, by Dr David. J.C. Briggs, Julian Ashton Art School and National Art School, Sydney, Australia: http://www.huevaluechroma.com/index.php
Additional reading assignments will be given from multiple sources.

CHY342

Chemistry of Solids and Surfaces

3.00

Undergraduate

In this course the students will get to know the chemistry behind the formation of solids and on their surfaces, the kind of bonding involved and the available techniques to characterize them. Through this course students will also learn how to interpret various chemical structures of solids and their surfaces. Students will further understand crystallographic terminology, selected diffraction theory, nomenclature at surfaces, reconstruction and relaxations at surfaces and how to determine the surface structure. They will also realize the wide range of chemical information available from diffraction based techniques. Further the students will learn about different surface phenomena such as adsorption, catalysis, work function, and basics of the electronic, magnetic, and optical properties, and their relevance to nanomaterials. This is a required course for Chemistry majors, but also satisfies UWE requirements for non-majors.
COURSE CONTENT: INTRODUCTION TO SOLID STATE CHEMISTRY CRYSTAL CHEMISTRY Introduction to Crystallography Unit cells and Crystal Systems Symmetry, Lattice, Lattice spacing Crystal Densities and Packing Crystallographic Notations BONDING IN SOLIDS Overview on Bonding Ionic, Covalent, Metallic, van der Waals and Hydrogen Bonding Born-Haber Cycle The Shapes of Molecules Intermolecular Forces CRYSTALLINE MATERIALS Properties of X-Rays X-Ray Emission & Absorption X-Ray Diffraction Techniques Point, Line, Interface & Bulk Defects AMORPHOUS MATERIALS Introduction to Glasses Glass Properties INTRODUCTION TO THE CHEMISTRY of SURFACES Surface structure
Nomenclature
Surface unit cell
Relaxation and reconstruction at surfaces and its relevance to nanomaterials
How to characterize atomic structure at surfaces Basics of different phenomena at surfaces
Surface energy
Electronic structure, 2D Brillouin zone, photoemission
Work function
Magnetic properties and relevance to nanomaterials
Optical properties
Adsorption and catalysis
Two dimensional structures
Recommended reading: 1. P. Atkins and J. dePaula, Atkins' Physical Chemistry A. R. West, Basic Solid State Chemistry.L. Smart and E. Moore, Solid State Chemistry An Introduction J. P. Glusker, K. N. Trueblood, Crystal Structure Analysis W. Clegg, Crystal Structure Determination J.M. Blakely, Introduction to the properties of Crystal Surfaces, New York, Plenum Press 1973. G A Somarjai, Chemistry in Two Dimensions: Surfaces, Ithaca, New York, Cornell University Press 1981. A. Zangwill, Physics at Surfaces, New York: Cambridge University Press 1988. Surface Science, An Introduction, John B. Hudson, 1992, Butterworth-Heinemann. Solid Surfaces, Interfaces and Thin Films – Springer, by H Lüth. Modern Techniques of surface Science, Second Edition D.P. Woodruff and T A Delchar, Cambridge University Press 1994.
Prerequisites: Chemical Principles (CHY111), Physics (PHY101/102 or PHY103/104).

PHY502

Classical Dynamics

3.00

Graduate

Classical Dynamics

PHY303

Classical Electrodynamics

4.00

Undergraduate

Overview: This course is one step ahead towards understanding some oldest phenomena of nature that mankind has ever sought after since Benjamin Franklin’s “lightning” experiment in early eighteenth century. The course begins with discussion on basic theoretical framework of electrodynamics, the Maxwell’s equations and new phenomena with respect to field theoretical questions (energy, momentum of the field) and its application to establish optics as well as in sector of practical applications (wave guides and resonant cavities) are investigated thereon.
Unit 1: Review of Maxwell’s equations, The Poynting vector, The Maxwellian stress tensor. Unit-2: Electromagnetic waves in vacuum, Polarization of plane waves, Electromagnetic waves in matter, frequency dependence of conductivity, frequency dependence of polarizability, frequency dependence of refractive index. Laws of Reflection and Refraction of Electromagnetic waves, Wave guides, boundary conditions, classification of fields in wave guides, phase velocity and group velocity, resonant cavities.
Unit-3: Moving charges in vacuum, gauge transformation, the time dependent Green function, The Lienard-Wiechert potentials, Lienard-Wiechert fields, application to fields- radiation from a charged particle, Antennas, Radiation by multipole moments, Electric dipole radiation, Complete fields of a time-dependent electric dipole, Magnetic dipole radiation.
Unit-4: Lorentz transformations, Four vectors and four tensors, The field equations and the field tensor, Maxwell’s equations for covariant notation. Relativistic covariant Lagrangian formalism, Covariant Lagrangian formalism for relativistic point charges, The energy-momentum tensor, Conservation laws.

PHY411

Classical Field theory and general relativity

3.00

Undergraduate

The first part of this course reformulates classical electrodynamics as a field theory and the second part introduces general theory of relativity.

PHY301

Classical Mechanics

4.00

Undergraduate

Introduction to dynamical systems, degree of freedom, time evolution
Lagrangian formulation of mechanics
Noether's Theory: Symmetry and conservation laws
Hamiltionian formulation of mechanics
Phase space and Liouville's theorem: applications to statistical mechanics
Poisson Bracket: Symmetry, rotation generators
Small Oscillations: normal modes, normal coordinates, vibration of molecules
Rotation and rigid body motion: Euler angles and applications

PHY501

Classical Mechanics

3.00

Graduate

Classical Mechanics

PHY402

Classical Theory of Fields

3.00

Undergraduate

This course has two parts. The first part reformulates classical electrodynamics as a field theory. The second part introduces general theory of relativity.

MAT544

Combinatorial Design Theory

4.00

Undergraduate

(a) Introduction to Design Theory: Basic deﬁnitions and properties, Incidence matrices, Fisher’s Inequality.
(b) Symmetric BIBD’s
i. Intersection Property, Residual and Derived BIBD’s, Projective planes and Geometries ii. The Bruck-Ryser-Chowla Theorem
(c) Diﬀerence Sets and Automorphisms: Quadratic residue diﬀerence sets, Singer diﬀerence sets.
(d) Hadamard Matrices and Designs An equivlance between Hadamard matrices and BIBD’s, Conference matrices and Hadamard matrices, Bent Functions
(e) Latin Squares: Steiner Triple systems, Orthogonal Latin Squares, MOL’s, Orthogonal arrays
(f) PBIBD’s: Connection of PBIBD’s to Association Schemes and Distance regular graphs.
(g) Applications of Combinatorial Design Theory: Medicine, Agriculture, Visual cryptography, Information Security, Statistical designs.

MAT246

Combinatorics

4.00

Undergraduate

Course description not available.

MAT341

Commutative Algebra

4.00

Undergraduate

Major Elective for BSc (Research) Mathematics. Available as UWE.
Prerequisites: MAT240 Algebra I

MAT646

Commutative Algebra

4.00

Graduate

Commutaive Algebra

MAT424

Complex Analysis

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 221 Real Analysis II
Overview: This course covers the basic principles of differentiation and integration with complex numbers. Topics will be taught in a computational and geometric way. Knowledge of topology of euclidean space and calculus of several real variables will be assumed.
Detailed Syllabus: Algebraic properties of complex numbers, modulus, complex conjugate, roots of complex numbers, regions. Functions of a complex variable, limits, continuity. Differentiation, Cauchy-Riemann equations, harmonic functions, polar coordinates. Exponential function, logarithm, branch and derivative of logarithm, complex exponents, trigonometric functions, hyperbolic functions, inverse hyperbolic functions. Derivatives of curve w(t) in complex plane, Definite integral of functions w(t), Contours, Contour Integrals, Antiderivatives, Modulus of Contour integrals, Cauchy Goursat theorem. Simply and multiply connected domain, Cauchy Integral Formula and applications, Liouville's theorem, maximum modulus principle. Convergence of series, Power Series, Laurent series, Residues, Cauchy's Residue theorem, Singularities, Zeroes of analytic functions, Behaviour of function near singularities.
References: James W Brown and Ruel V Churchill, Complex Variables and Applications, 8th edition, Tata McGraw-Hill, 2009. H A Priestley, Introduction to Complex Analysis, 2nd edition, Oxford University Press. 2003. J Bak and D J Newman, Complex Analysis, 2nd edition, Springer, 2008. M J Ablowitz and A S Fokas, Complex Variables: Introduction and Applications, 2nd edition, Cambridge University Press India, 2006.

MAT624

Complex Analysis

4.00

Graduate

Core course for M.Sc. Mathematics
Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 621 (Analysis I). Undergraduates not allowed.
Overview: A graduate course of one variable complex analysis.
“The shortest path between two truths in the real domain passes through the complex domain” – Jacques Hadamard.
Detailed Syllabus: The complex number system: The field of Complex numbers, the complex plane, Polar representation and roots of complex numbers, Line and Half planes in the Complex plane, the extended plane and its Stereographic representation. Metric spaces and Topology of complex plane. Open sets in Complex plane, Few properties of metric topology, Continuity, Uniform convergence Elementary properties of Analytic functions. Analytic functions as mapping. Exponential and Logarithm Complex Integration: Basic review of Riemann-Stieltjes integral (without proof), Path integral, Power series representation of an analytic function, Liouville’s theorem and Identity theorem, Index of a closed curve, Cauchy theorem and Integral Formula, Open mapping theorem. Singularities: Removable singularity and Pole, Laurent series expansion, Essential singularity and Casorati-Weierstrass theorem Residues, Solving integral, Argument Principle, Rouche’s Theorem, Maximum modulus theorem. Harmonic Functions: Basic properties, Dirichlet problem, Green function.
References: Functions of One Complex Variable by John B Conway, 2nd edition, Narosa. Complex Analysis by Lars Ahlfors, 3rd edition, McGraw Hill Education India. Introduction to Complex Analysis by H A Priestley, Oxford University Press. Complex Function Theory by D Sarason, 2nd edition, TRIM Series, Hindustan Book Agency. Complex Analysis by T W Gamelin, Springer. Complex Variables by M J Ablowitz and A S Fokas, 2nd edition, Cambridge University Press.

PHY569

Complex Fluids

3.00

Graduate

Complex Fluids

MAT742

Complex Networks

4.00

Graduate

Complex Networks

MAT804

Complex Networks

4.00

Graduate

Complex Networks

PHY563

Comptnl. & Numerical Analysis

3.00

Graduate

This course develops the basic programming skills to perform numerical analysis of various physical phenomenon by emphasizing on the algorithms and their implementation in the FORTRAN program language.

PHY414

Computational and Numerical Analysis

3.00

Undergraduate

Numeric and computational techniques to calculate roots of polynomials and other nonlinear functions; determinants, eigenvalues, and eigenvectors, solutions to differential equations; applications of FFT, finite difference expressions, interpolation and approximation, numerical differentiation and integration, by emphasizing on the algorithms and their implementation in the FORTRAN program language.

BIO616

Computational Biology

2.00

Graduate

Computational Biology

CHY622

Computational Chemistry

3.00

Graduate

Classical Force Field Methods; Molecular Mechanics Postulates of Quantum Mechanics and measurement The Born-Oppenheimer approximation and the Molecular Hamiltonian The Concept of the Potential Energy Surface Semiempirical and ab initio Quantum Mechanics Variation and Perturbation Theory Independent-Particle Models: the Hartree method Spin and statistics in non-relativistic quantum mechanics The Hartree-Fock Self-Consistent Field equations Basis Sets and Relativistic Pseudopotentials Geometry Optimization Techniques and Frequency Analysis Valence Bond Methods Electron Correlation and Configuration Interaction Density Functional Theory - Hohenberg-Kohn theorems, v- and N-representability DFT - Fremi hole, Exchange-Correlation potential and Kohn-Sham method Conceptual DFT Density Matrices and Natural Orbitals Multi-configuration methods: MCSCF and CASSCF Diagrammatic Methods: Coupled Cluster Theory Wave Function Analysis Computation of Molecular Properties Periodic systems and theory of Insulators Basis Set Superposition Error and the Counterpoise method Introduction to Classical Statistical Mechanics Continuum (Implicit) solvent and Explicit solvent methods Protein Simulations QM/MM and ONIOM methods Introduction to TDDFT Carr-Parinello molecular dynamics
Textbooks: Frank Jensen: Introduction to Computational Chemistry (Wiley) Frank L. Pilar: Elementary Quantum Chemistry (McGraw Hill) Errol G. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics (Kluwer Academic Publishers, 2003) James B. Foresman, AEleen Frisch, Exploring Chemistry With Electronic Structure Methods: A Guide to Using Gaussian (Gaussian, Inc.) P. A. M. Dirac: The Principles of Quantum Mechanics (Clarendon Press; Oxford,1981) J. N. Murrell, S. F. A. Kettle, J. M. Tedder: Valence Theory [ELBS & John Wiley] Richard P. Feynman, Robert B. Leighton & Matthew Sands: The Feynman Lectures on Physics, Vol.III (Addison Wesley Longman) N. Sukumar, ed. A Matter of Density: Exploring the Electron Density Concept in the Chemical, Biological, and Materials Sciences (John Wiley, Hoboken, NJ, 2013)

MAT682

Computational Economics

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites:
Overview: This is a joint offering with Department of Economics. The objective of the course is to introduce graduate students to computational approaches for solving mathematical problems and economic models. The first half of the course will be devoted in learning (i) the core of the Python programming language, including the main scientific libraries, (ii) a number of mathematical topics central to economic modeling, such as finite and continuous Markov chains, filtering and state space models, Fourier transforms and spectral analysis and (iii) related numerical analysis methods like function approximation, numerical optimization, simulation based techniques and Monte Carlo, recursion. The second half of the course will be devoted in applying these techniques to solve economic problems like growth models, optimal savings problem, and optimal taxation problems. We will pay particular attention to methods for solving dynamic optimization problems.
Detailed Syllabus:
(a) Programming .Basics of Python: Input and output statements, formatting output, copy and assignment, arithmetic operations, string operations, lists and tuples, control statements, user defined functions, call by reference, variable number of arguments, one dimensional arrays, two dimensional arrays, random number generation. The NUMPY and SCIPY packages: Numpy numerical types, data type objects, character codes, dtype constructors. Mathematical libraries, plotting 2D and 3D functions, ODE integrators, charts and histograms, image processing functions, solving models involving difference equations, differential equations, finding limit at a point, approximation using Taylor series, interpolation, definite integrals.
(b) Numerical analysis. Solution of equations in one variable and two variables - Bisection, Newton-Raphson, General iterative scheme, Solution of systems of linear equations – Gauss-Jordan, LU decomposition, QR factorization, Lagrange and Hermite interpolation, Orthogonal polynomials, Gaussian quadrature.
(c) Deterministic dynamic programming. Understanding the fundamentals of dynamic programming and applying to solve the models for equipment replacement, Shortest path, and resource allocation.
(d) Growth Models. As an application we will study the neoclassical growth model.
(e) Other Applications. Other applications that we may study include the optimal savings problem, heterogeneous agents problem, etc.
References:
[1] John Stachurski and Thomas J. Sargent, Quantitative Economics, http://quant-econ.net.
[2] John Stachurski, Economic Dynamics: Theory and Computation, MIT Press, 2009.
[3] M. Miranda and P. Fackler, Applied Computational Economics and Finance, MIT Press, 2002.
[4] K. Judd, Numerical Methods in Economics, MIT Press.
[5] N. L. Stokey and R. E. Lucas with E. C. Prescott, Recursive Methods in Economic Dynamics, Harvard University Press, 1989.
[6] J. Adda and R. Cooper, Dynamic Economics: Quantitative Methods and Applications, MIT Press, 2003.
[7] S. E. Dreyfus, and A. M. Law, The Art and Theory of Dynamic Programming, Academic Press, 1977.
[8] John Zelle, Python Programming: An Introduction to Computer Science, Franklin, Beedle & Associates Inc., 2010.
[9] Ivan Idris, Numpy 1.5 Beginner’s Guide, Packt Publishing, 2011.
[10] Hans Petter Langtangen, A Primer on Scientific Programming on Python, Springer, 2011.
[11] E. Sulli, and D. Mayers, Introduction to Numerical Analysis, Cambridge University Press, 2003.

MAT590

Computational Finance

4.00

Graduate

Course description not available.

MAT433

Computational Fluid Dynamics

4.00

Undergraduate

Outline: Many physics laws like laws of motion, mass conservation law, energy conservation law,
when applied to engineering problems, come in form of Partial Differential Equations (PDE).
There are several softwares available for solving PDEs but they all require enough human
intervention to make if necessary to understand background theory. In this course we will learn
about Finite Volume Method (FVM), the most common method of solving PDEs computationally.
Though the course is titled based on Fluid Dynamics but materials discussed here should be
accessible to and useful for any audience who deals with PDE.
Learning objectives:
• Software: OpenFOAM (http://openfoam.org/)
• Physics to PDE: derivation of PDEs
• Finite Volume Method (FVM): PDEs to linear algebraic equations
• Implementations of FVM on OpenFOAM: C++ programming
References:
• The Finite Volume Method in Computational Fluid Dynamics An Advanced Introduction
with OpenFOAM and Matlab by F Moukalled, L Mangani, and M Darwish
• OpenFOAM user and programmer guide
Pedagogy: This course will be problem/project driven. This means that for each learning objectives
we will pose a list of small projects. Using the given references and internet, students will need to
figure out solutions on their own. The instructor will function as mentor and the contact hours will
be spent only on discussion, and not too much instructions.
Prerequisites:
Mathematics : Multi-variable Calculus,
Physics : Newton's laws of motion, work, energy, momentum
Computers : C++
Other courses (helpful but not mandatory):
ODE, PDE, Numerical Analysis, Linear Algebra, Fluid Dynamics
Assessment: Entirely on project reports (written and oral)

MAT434

Computational PDE

4.00

Undergraduate

Major Elective for BSc (Research) Mathematics. Available as UWE.
Prerequisites: MAT330 PDE.

MAT683

Computational Stat. using R

4.00

Graduate

Computational Statistics using R

MAT110

Computing

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics. Optional for B.Sc. (Research) Economics. Not available for B.Tech. students. Others may credit it as UWE with permission from Department of Mathematics. Does not count towards Minor in Mathematics.
Credits (Lec:Tut:Lab)= 3:0:1 (Three lecture hours and two lab hours weekly)
Prerequisites: Class XII Mathematics
Overview: This course aims to empower the students in data abstraction, algorithm design and performance estimation. In the process they shall learn the art of programming – a pretty useful skill to have! Programming in C and Matlab will be taught.
Detailed Syllabus: Basic programming constructs: conditional statements, functions, loops, arrays, structures, pointers. Linear data structures: Linked list, queue, stack Trees and Graphs: basic operations Searching and Hashing: Linear search, Binary search, tree search, hash tables Sorting: Insertion sort, bubble sort, merge sort, heap sort Introduction to MATLAB programming.
References: B. Kolman, R. Busby, and S. Ross, Discrete Mathematical Structures, PHI, 2012 Jeri R.Hanly, Eklliot B.Koffmain, Problem Solving and Program Design in C,Pearson,2009 A. Aho, J. Hopcroft, D. Ullman, Data structures and Algorithms, Addison-Wesley, 1983 A. Aho, and D. Ullman, Foundations of Computer Science, Comp. Sci. Press, 1992 T. Cormen and C. Leiserson, Introduction to Algorithms, MIT Press, 2009 N. Kalicharan, Data Structures in C, CreateSpace Independent Publishing, 2008 A. Tenenbaum, Data Structures using C, PHI, 2003
Past Instructors: Charu Sharma, Niteesh Sahni

PHY304

Condensed Matter Physics

4.00

Undergraduate

1. Invitation to Condensed Matter Physics
2. Geometrical Description of Crystals and Scattering
3. The Sommerfeld Free Electron Theory of Metals
4. One Electron Theory and Energy Bands
5. Lattice Dynamics of Crystals : Phonons

BDA496

Convex Optimization

4.00

Undergraduate

Course description not available.

MAT588

Convex Optimization

4.00

Undergraduate

Course description not available.

CHY533

Coordination and Bio-Inorganic Chemistry

2.00

Graduate

Coordination and Bio-Inorganic Chemistry

CHY553

Coordination and Bio-inorganic Chemistry

3.00

Graduate

Metals ions play important role in many biological processes. Their function can range from simple structural roles in which they hold a protein in a specific conformation, to more complex roles in which they are involve in multiple electron transfer processes and in bond cleavage and formation. Understanding of the biological functions of metal ions lies at the heart of bio-inorganic chemistry. This course will focus on the biologically important metal ions and their binding sites, and the techniques used to probe these sites (e.g.IR, UV-VIS, NMR, EPR, Mossbauer and CV). A more in-depth look at several key metalloenzymes and the functional role of the metal ions therein will also be taken.
Text Books: Inorganic Chemistry; Principles of Structures and Reactivity: James E. Huheey; Allen A. Keiter;Richard L. Keiter, Pearson Edition. Principles of Bioinorganic Chemistry: Stephen J. Lippard, Jeremy M. Berg, University Science Books, 1994. Physical Methods in Bioinorganic Chemistry: Spectroscopy and Magnetism: Lawrence Que, University Science Books, 1999.
Reference Materials: Other reading materials will be assigned as and when required.

CHY242

Coordination Chemistry

4.00

Undergraduate

Metals ions play important role in producing colour in coordination complexes. Understanding of the coordination complexes lies at the heart of coordination chemistry. This course will focus on the basic concept of coordination chemistry and their quantification in photophysical and magnetic properties. Students will synthesize interesting colour compounds and perform reactions to promote the understanding of common reactions. Intensive use of analytical and spectroscopic techniques to interpret extent of reaction, purity of product and photophysical property particularly colour of the coordination complexes will be involved.
COURSE CONTENT: Introduction and structures of complexes: Meaning of metal coordination and use of metal coordination in formation of color complex. Coordination number, bonding of organic ligands to transition metals, coordination number, linkage isomerism, electronic effects, steric effects, the chelate effect, fluxional molecules. Crystal field theory: application and limitation Molecular orbital theory: Application in pi-bonding, electronic spectra including MLCT, LMCT d-d transition, and magnetic properties of complexes. Inorganic substitution reaction; Types; Base catalyzed hydrolysis; Linear free energy relationship. Reaction and kinetics: Nucleophilic substitution reactions, rate law, mechanism of reactions, trans effect, ligand field effect, inner sphere and outer sphere reactions.
Text Books: Inorganic Chemistry; Principles of Structures and Reactivity: James E. Huheey; Allen A. Keiter;Richard L. Keiter, Pearson Edition. Inorganic Chemistry by Shriver & Atkins, 5th edition. Inorganic chemistry by Miessler, Gary L. Tarr, Donald A . Concise Inorganic Chemistry by J. D. Lee Application of physical methods to inorganic and bio-inorganic chemistry by scot Robert A.; Lukehart, Charles M.
Prerequisites: Chemical Principles (CHY111) and Chemical equilibrium (CHY211). .

MAT542

Cryptography

4.00

Undergraduate

Cryptography

MAT492

Data Mining & its Applications

4.00

Undergraduate

Course description not available.

PHY481

Data Mining & its Applications

4.00

Undergraduate

Course description not available.

BDA483

Data Science & Comput.Thinking

4.00

Undergraduate

Course description not available.

MAT494

Deep Learning

4.00

Undergraduate

Course description not available.

MAT630

Differential Equations

4.00

Graduate

Core course for M.Sc. Mathematics
Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 230/430 ODE (for undergraduates)
Overview:
Detailed Syllabus
(a) Review of Solution Methods for first order and second order linear equations.
(b) Existence and Uniqueness of Initial Value Problems: Lipschitz and Gronwall's inequality, Picard’s Theorem, dependence on initial conditions, continuation of solutions and maximal interval of existence.
(c) Higher Order Linear Equations and Linear Systems: fundamental solutions, Wronskian, variation of constants, matrix exponential solution, behaviour of solutions.
(d)* Two Dimensional Autonomous Systems and Phase Space Analysis: critical points, proper and improper nodes, spiral points, saddle points, Limit cycles, and periodic solutions.
(e)* Asymptotic Behavior: Stability (linearized stability and Lyapunov methods).
(f) Sturm-Liouville Boundary Value Problems: Sturm-Liouville problem for 2nd order equations, Green's function, Sturm comparison theorems and oscillations, eigenvalue problems.
Sections (d) and (e) will also be explored by computer implementation using MATLAB or other software.
References: M. Hirsch, S. Smale and R. Devaney, Differential Equations, Dynamical Systems and Introduction to Chaos, Academic Press, 2004. L. Perko, Differential Equations and Dynamical Systems, Texts in Applied Mathematics, Vol. 7, 2nd edition, Springer Verlag, New York, 1998. G. F. Simmons and S. G. Krantz, Differential Equations, Theory, Technique, and Practice, 4th edition, McGraw Hill Education, New Delhi, 2013. William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems. Wiley, New York, 1992.
Past Instructors: Ajit Kumar, Samit Bhattacharyya

MAT634

Differential Geometry

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 621 (Analysis I) or MAT 332/432 (Geometry of Curves and Surfaces)
Overview: Differential Geometry generalizes the calculus of several variables on Euclidean spaces to `differential manifolds’. This enables the use of analysis and linear algebra to study geometry. The two highlights of this course are the study of Lie groups and of differential forms, with the latter leading to the general Stokes’ theorem in integration.
Detailed Syllabus:
Part 1: Calculus in Rn
Rn as a normed linear space, derivative, chain rule, mean value theorem, directional derivatives, inverse mapping theorem, implicit function theorem, immersions and submersions, integration, higher derivatives, maxima and minima, existence of solutions of ODE.
Part 2: Differential Manifolds and Lie Groups
Differential manifolds, smooth maps and diffeomorphisms, Lie groups, tangent spaces, derivatives, immersions and submersions, submanifolds, vector fields, Lie algebras, flows, exponential map, Frobenius theorem, Lie subgroups and subalgebras.
Part 3: Differential Forms and Integration
Multilinear algebra, exterior algebra, tensor fields, exterior derivative, Poincare lemma, Lie derivative, orientable manifolds, integration on manifolds, Stokes' theorem.
References: An Introduction to Differentiable Manifolds and Riemannian Geometry, by William M Boothby, 2nd edition, Academic Press. A Course in Differential Geometry and Lie Groups, by S Kumaresan, TRIM Series, Hindustan Book Agency. Analysis on Manifolds, by James Munkres, Addison-Wesley. Calculus on Manifolds, by Michael Spivak, Addison-Wesley.

MAT644

Discrete Mathematics

4.00

Graduate

Discrete Mathematics

MAT140

Discrete Structures

4.00

Undergraduate

Major elective course for B.Sc. (Research) Mathematics. Not open to B.Tech. Computer Science majors or any other student who has taken CSD205.
Credits: 3:0:1 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics
Overview: This course offers an in-depth treatment of Lattice theory which will be used in areas of algebra and analysis in the subsequent semesters. Special kinds of lattices known as Boolean algebras are studied in reasonable detail and their importance is demonstrated through real life applications involving digital circuits. This course builds on the Foundations course taken by the first year students and it provides an exposure to formal proof writing.
Detailed Syllabus: Theory of Relations: Types of relations, Matrix representation of relations, Equivalence classes, Operations on relations, Closure of relations, Importance of transitive closure, Warshall’s algorithm. Lattice Theory: Posets, Chains, Hesse diagram, Extremal elements in a poset, Meet and Join operations, Lattices, General properties of lattices, isomorphism, modular lattice, distributive lattice, complements, atoms in a lattice, Boolean algebras. Finite Boolean algebras: Functions on Boolean algebras, Karnaugh maps, Logic gates, Digital circuits.
References: Thomas Donnellan, Lattice Theory, Pergamon Press, Oxford. J.E. Whitesitts, Boolean Algebra and Its Applications, Addison-Wesley Publications. G. Birkhoff, Lattice Theory, American Mathematical Society, 2nd Edition. E. Mandelson, Schaum’s Outline of Boolean Algebra and Switching Circuits, McGraw Hill. Bernard Kolman, Robert Busby, Sharon C. Ross, Discrete Mathematical Structures, Pearson Education, New Delhi. Kenneth H. Rosen, Discrete Mathematics and its Applications, Tata McGraw-Hill, New Delhi. C. L. Liu, D. P. Mohapatra, Elements of Discrete Mathematics, Tata McGraw-Hill, New Delhi. J.P. Tremblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, 1st edition, Tata McGraw-Hill, New Delhi, 2001.
Past Instructors: Niteesh Sahni

MAT490

Discrete Time Finance

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial/lab weekly)
Prerequisites: MAT 184 Probability (MAT 390 Introduction to Mathematical Finance is recommended but is not a compulsory requirement.)
Overview: This course serves two purposes. On the one hand, it introduces various theoretical notions in the simpler setting of discrete time and sets the stage for continuous time finance. On the other, it has a strong computational aspect and the student learns to implement models using Excel or Matlab.
Detailed Syllabus: Binomial pricing models Conditional expectation, Martingales, Markov Processes Risk-neutral probability measure American derivatives Random Walks Interest rate models and derivatives Implementation of models in Excel/Matlab
References: Steven E Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer 2004. Les Clewlow and Chris Strickland, Implementing Derivatives Models, Wiley 1998. John C Hull, Options, Futures and Other Derivatives, 8th edition, Pearson, 2013. Rudiger Seydel, Tools for Computational Finance, 5th edition, Springer, 2012.
Past Instructors: Sunil Bowry

MAT386

Dynamical Systems

4.00

Undergraduate

Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 102 Calculus II or MAT 103 Mathematical Methods I. And MAT 104 Mathematical Methods II or MAT 160 Linear Algebra I.
Overview:
Detailed Syllabus:
Basic Concepts: Discrete and continuous dynamical systems. Linear and nonlinear systems and principle of superposition. Linear and nonlinear forces. Concepts of evolution, iterations, orbits, fixed points, periodic and aperiodic (chaotic) orbits. Basics of Linear Algebra: Symmetric & Skew-symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Canonical forms; simple and non-simple canonical systems. System of Equations.
Stability Analysis:
Stability of a fixed point and classification equilibrium states (for both discrete and continuous systems). Concept of bifurcation and classification of bifurcations. Concepts of Lyapunov stability & Asymptotic stability of orbits. Phase Portraits of various Linear and Nonlinear systems. Hopf bifurcation. Concept of attractors and repellers, limit cycles and torus.
Phenomena of Bifurcation:
Definition of bifurcation. Bifurcations in one, two and higher dimensional systems. Hopf, Period doubling, Saddle node, Transcritical bifurcations. Feigenbaum’s number. Local and Global bifurcations. Homoclinic & Hetero-clinic points and orbits. Poincaré-Bendixson Theorem. Conservative and Dissipative Systems.
Investigation Tools & Chaos Theory:
Time Series and Phase Plane Analysis, Poincaé Map & Section. Lyapunov Characteristic Exponents. Hamiltonian Systems and concept of iIntegrability and non-integrability. Concept of Chaos and Chaotic evolution of a Dynamical System. Measure of Chaos. Routs to Chaos.
Applications:
Applications of Dynamical Systems, (to Physics, Biology, Economics with Examples). Mathematical Models. Population Dynamics. Investigation of Evolutionary Phenomena in Logistic Map, Lotka-Volterra System, Duffing Oscillator, Oscillation of Nonlinear Pendulum, Predator-Prey Systems etc.
Tutorial:
Drawing orbits of a system for given initial values. Clear Demonstration of Linear and Nonlinear Systems. Calculation of fixed points for given system and examine their stabilities (discrete and continuous). Drawing time series graphs, phase portraits for regular and chaotic systems. Cobweb Plots. Calculations of Eigenvalues and Eigenvectors corresponding to any fixed point. Plotting Bifurcation diagrams of 1 and 2 dimensional systems. Calculations of Lyapunov exponent.
Software such as MATHEMATICA / MATLAB will be used as needed.
References: Nonlinear Systems, by P. G. Drazin, Cambridge University Press India. An Introduction to Chaotic Dynamical Systems by R. L. Devaney, Addison Wesley, 1989. Chaos in Dynamical Systems, by Edward Ott, Cambridge University Press, 2002 Chaotic Dynamics – An Introduction, by G. L. Baker and J. P. Gollub, Cambridge University Press, 1996. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, by J. Guckenheimer and P. Holmes, Springer, 1983.
Past Instructors: L M Saha

MAT786

Dynamical Systems

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 621 for graduate students, MAT 320 for undergraduates.
Overview:
Detailed Syllabus: Introduction: Definition of Dynamical Systems, Discrete and Continuous Systems, Fixed points, Iterations, Classification of orbits, Stability of a fixed point, Classification of fixed points. Bifurcation Analysis: Definition of bifurcation, Classification of bifurcation, Period doubling phenomena, Hopf bifurcation. Chaos Theory: Definition of chaos, Regular and chaotic evolution, How chaos appears in a system. Tools for identification of regular and chaotic motions: Time series, Phase plot, Poincarè map, surface of section. Applications: Applications of Dynamical Systems to Population Dynamics, Predator-Prey evolution, Spread of Epidemic, Food Chain systems and in other areas. Use of Software MATHEMATICA or MATLAB for exploring above topics.
References: R. L. Devaney: Introduction to Chaotic Dynamical Systems. Benjamin – Cummings, 1986 R. L. Devaney : A First Course in Chaotic Dynamical Systems: Theory and Experiment. Westview Press, 1992 P. G. Drazin: Nonlinear Systems. Cambridge Texts in Applied Mathematics, 1992 Stephen Lynch: Dynamical Systems with Applications using MATHEMATICA. Birkhäuser, 2007 D. K. Arrowsmith and C. M. Place: An Introduction to Dynamical Systems. Cambridge University Press, 1990

BIO104

Ecology and Environmental Sciences

3.00

Undergraduate

Introduction to Ecology, Community and Ecosystem (Inter-relationships between living world and environment, Biosphere, ecosystem and its components (abiotic and biotic). Environment related concepts and laws (theory of tolerance, laws of limiting factors). Community characteristics- organization and concept of habitats and niche. Bioenergetics. Biogeochemical cycles, Hydrologic cycle. Concept of habitat and niche.
Population and Community Ecology Population attributes, density, natality, mortality, age ratio, sex ratio, dispersal and dispersion of population, exponential and logistic growth, life history strategies, population interactions, predation-types, predator-prey system, functional and numerical response, host-parasite interactions, social parasitism, symbiosis. Biogeography Phytogeography, Phytogeographic realms, major plant communities of the world, Vegetation of India, Zoogeography: Zoogeographic realms, Threatened species of animals. Principles of wildlife management, wildlife sanctuaries, parks and biosphere reserves in India, endangered and threatened species of plants and animals in India, germplasm banks. Environmental Issues, Policies and Regulation. Impact of urbanization and industrialization, EIA-Environmental Impact Assessment (Global, National and Local), restoration of degraded ecosystems, bioremediation, environmental pollution, global climatic change.
Recommended Books: Basics of Environmental Science, Allaby, M., Pub: Taylor and Francis group. Elements of Ecology (1st ed.) Smith, T. M., Smith, R. L., Pub: Pearson Benjamin Cummings. Environmental Science (11th ed.), Miller, G. T., Pub: Brooks/Cole.

CHY241

Electrochemistry

3.00

Undergraduate

Electrical dimensions and unit, Faraday’s laws of electrolysis, Theory of electrolytic dissociation, van’t Hoff factor and degree of dissociation, Specific Conductance, Equivalent conductance, Equivalent conductance at infinite dilution, Variation of equivalent conductance with concentration for strong and weak electrolytes, Conductance ratio and degree of dissociation, Equivalent conductance minima, Influence of dielectric constant on conductance, Kohlrausch’s law, Application of ion conductance, Ionic mobility, Influence of temperature on ionic conductance, Ion conductance and viscosity, Drift Speed, Variation of ionic mobility with ionic size and hydrodynamic radius, factors affecting the ionic mobility for strong electrolytes, Ionic Atmosphere, relaxation effect or asymmetry effect, Electrophoretic effect, partial molar quantities (briefly), partial molar free energy and chemical potential, Electrolytes as a non-ideal solution, activity coefficient, mean ionic activity, mean ionic molality, mean ionic activity coefficient, Outline of Debye-Hückel theory, Debye-Hückel’s limiting law, variation of activity coefficient with ionic strength, Nernst equation. General discussion about oxidation and reduction, electron transfer vs atom transfer, oxidation no. Concept of electrochemistry, Definition: Electrochemical cell, electrodes, salt bridge and its function etc. Battery; types of cell: Electrolytic cell vs Galvanic cell; concentration cell vs chemical cell, construction of a voltaic cell. Definition: Electrode potential, Std. potential and Formal potential; Physical significance of electrode potential. Types of electrodes: (i) metal electrode, advantage of amalgam electrode; (ii) non-metal electrode, e.g. hydrogen gas electrode, glassy carbon electrode. What is glassy carbon electrode? What is the difference between glassy carbon and graphite electrode? Factors affecting the electrode potential: (i) effect of concentration, (ii) effect of pH e.g. formation of insoluble hydroxide and (iii) effect of precipitation and complexation. Application of electrode potential; Periodic trend of the reduction potential; Pourbaix diagram. Electroanalytical techniques: Potentiometry, Coulometry, Voltammetry and Amperometry. Measurement of electrode potential; 3 electrode system: working electrode, reference electrode and counter electrode; comparison between three and two electrode system; linear sweep voltammetry, Cyclic voltammetry (CV), Differential pulse voltammetry (DPV) etc. Bulk electrolysis.
Prerequisite: Chemical Principles (CHY111)
Co-requisites: Chemical Equilibrium (CHY211).

CHY316

Electrochemistry

3.00

Undergraduate

1. General discussion about oxidation and reduction, electron transfer vs atom transfer, oxidation no.
2. Concept of electrochemistry, Definition: Electrochemical cell, electrodes, salt bridge and its function etc. Battery; types of cell: Electrolytic cell vs Galvanic cell; concentration cell vs chemical cell, How to construct a voltaic cell?
3. Electrical dimensions and unit, Mechanism of electrolysis (Grotthuss vs Faraday), Theory of electrolytic dissociation, Ostwald dilution law, Faraday’s laws of electrolysis, Significance of faraday’s laws, Specific Conductance, Equivalent conductance, Equivalent conductance at infinite dilution, Application of ion conductance, Kohlrausch law, Outline of Debye Huckel theory, Nernst equation and Concept of free energy.
4. Definition: Electrode potential, Std. potential and Formal potential; Physical significance of electrode potential.
5. Types of electrodes: (i) metal electrode, advantage of amalgam electrode; (ii) non-metal electrode, e.g. hydrogen gas electrode, glassy carbon electrode. What is glassy carbon electrode? What is the difference between glassy carbon and graphite electrode?
6. Factors affecting the electrode potential: (i) effect of concentration, (ii) effect of pH e.g. formation of insoluble hydroxide and (iii) effect of precipitation and complexation.
7. Application of electrode potential; Periodic trend of the reduction potential; Pourbaix diagram.
8. Electroanalytical techniques: Potentiometry, Coulometry, Voltammetry and Amperometry.
9. How to measure electrode potential?; 3 electrode system: working electrode, reference electrode and counter electrode; comparison between three and two electrode system; Linear sweep voltammetry, Cyclic voltammetry (CV), Differential pulse voltammetry (DPV) etc.
10. Bulk electrolysis.

PHY307

Electronics - II

4.00

Undergraduate

Overview Digital Electronics is an advanced course for students in which rigorous scientific approach driven hands-on training is provided on handling and designing basic components in digital electronic devices. The pre-requisite for this course is well-versed understanding of analog electronic systems as offered through courses like PHY206, PHY104 etc. At the end of this course, students are expected to demonstrate competency in handling and designing digital devices. Detailed Syllabus Introduction of Digital Systems comparing Analog Systems, Logic Levels: Introduction to Number System: Binary, Decimal and BCD, Logic Gates and discussion up to 3/4 input, Truth Table, Boolean Algebra, Boolean Circuit simplifications using algebra, Handling an unknown digital circuit through Truth table, De Morgan’s Theorems, Sum of Products (SOP) & POS, Introduction of Karnaugh Map: Need beyond Truth Table, Circuits simplification through K-map, Parity Checker, K-map working examples, K-map simplification using Max terms, Don’t care condition using Max terms/Min terms, Comparator and Gate circuit as memory: NOT gate Latch, S-R Latch, Clock Input and Clocked S-R Latch as Flip-Flop, D-Flip Flop & J-K Flip-Flop, Multiplexer and Demultiplexer, Synchronous counters, Shift Register, Examples of comparative circuits between Synchronous counters and shift
register, Difference between systematic and non-systematic counting: Introduction to Ripple Counter, Ripple counter concludes, Examples of Ripple and Synchronous Counters, D/A converter with examples, A/D converter with examples, Logic family: TTL and CMOS

PHY206

Electronics I

4.00

Undergraduate

Review from Fundamentals of Physics-II, Galvanometer to Ammeter and Voltmeter, Meaning of Network, Voltage and Current dividers, Voltage and Current source, Impedance Matching. Network Theorems. Thermionic Emission: Richardson’s equation, Child-Langmuir Law, Brief introduction on Valves, deflection sensitivity in electric and magnetic fields, Cathode Ray Oscilloscope, Lissajous figures.
Basic concepts of semiconductors, conduction and doping, PN junction, diode characteristics, forward bias, reverse bias, static and dynamic resistance, junction capacitance, equivalent circuit, Zener and avalanche breakdown, Heterojunction; Diode circuits - Rectifiers half wave and full wave efficiency and ripple factor, Voltage multiplier, clipper and clamper circuits.
Bipolar Junction transistor, the transistor action, transistor current components, Modes of operation, common base, common emitter and common collector configurations, Current voltage characteristics of CB, CE, CC configuration, current gain , and Early effect, DC load line, Q-point, saturation and cut-off regions;
Transistor biasing - Base bias, Emitter bias, Transistor switch, Voltage divider bias, Self bias, Collector feedback bias. Stability factor. Field Effect Transistors, MOSFET, HEMT and MOSFET as Capacitor. AC Models - ac resistance of the emitter diode, ac input impedance, ac load-line, ac-equivalent circuits - T- model, π-model.
Amplifier: types with uses, Transistor as an amplifier using h-parameters, comparison of amplifier configurations, simplified h-model; Voltage amplifiers voltage gain, DC, RC, transformer coupled amplifiers, frequency response of RC coupled amplifiers, cascading CE & CC amplifiers, Darlington pair. Feedback: Positive and negative feedback-advantages of negative feedback-input and output resistances-voltage series and current series feedback-frequency response of amplifiers with and without feedback. Power amplifiers - Class A, Class B, Class C amplifiers, Push pull amplifiers. Oscillators, Wien bridge oscillator, Colpitt oscillator, phase shift oscillator, resonant circuit oscillators, crystal oscillator.
Operational Amplifier: characteristics, applications like adder, differentiator, integrator, and voltage comparator.

MAT020

Elementary Calculus

4.00

Undergraduate

Core course for B.Sc. (Research) Biotechnology. Only available as UWE with prior permission of Department of Mathematics. Does not count towards a Minor in Mathematics.
Credits (Lec:Tut:Lab): (3:1:0)
Overview: This course is targeted at undergraduates who did not take Mathematics at +2 level in school, and now need to quickly acquire basic calculus skills in order to satisfy their major requirements. For example, the purpose may be to enable them to take a Probability course which requires basic concepts from calculus. The course will emphasize geometric meaning rather than formal proof.
Students who need greater rigour, as well as more computational skills, should take MAT101 Calculus I.
Detailed Syllabus: Functions: Real line and its subsets, real functions, graphs, polynomials, rational functions, real powers, trigonometric functions, roots, boundedness, monotonicity, composition of functions, inverse functions. Limits and Continuity: Algebra of limits, left and right limits, limits involving infinity, continuity, left and right continuity, types of discontinuity. Differentiation: Rates of change, tangents to graphs, first and higher derivatives, algebra of differentiation, chain rule, exponentials and logarithms. Applications of differentiation: Exponential growth and decay, intervals of increase and decrease, first and second derivative tests, curve sketching. Integration: Definite and indefinite integrals, Fundamental Theorem of Calculus, substitution, integration by parts, trigonometric integrals, improper integrals. First-Order Differential Equations: Separable differential equations, logistic growth.
References: Short Calculus, by Serge Lang, Springer. Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.
Past Instructors: L M Saha

MAT440

Elementary Number Theory

4.00

Undergraduate

Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics
Overview: This introductory course to Number Theory is also the entry point to the specialization in applications of algebra.
Detailed Syllabus: Divisibility: Definition and properties of Divisibility, Division Algorithm, Greatest Common Divisor, Least Common Multiple, Euclidean Algorithm, Linear Diophantine Equations. Primes and their Distribution: Sieve of Eratosthenes, Euclid's Theorem, Prime Number Theorem (statement only), Goldbach Conjecture, Twin Primes, Fermat Primes, Mersenne Primes, The Fundamental Theorem of Arithmetic, Euclid's Lemma, Divisibility, gcd and lcm in terms of prime factorizations, Dirichlet's Theorem on primes in arithmetic progressions (statement only). Theory of Congruences: Residue Classes, Linear congruences in one variable, Euclid's algorithm Chinese Remainder Theorem, Wilson's Theorem, Fermat's Theorem, Pseudoprimes and Carmichael Numbers, Euler's Theorem, Primality Testing, The Pollard Rho Factoring Method, Complete residue system. Applications of Congruences: Divisibility tests, Modular Designs, Check Digits, The p-Queens Puzzle, Round-Robin Tournaments, The Perpetual Calendar. Arithmetic Functions: Multiplicative Functions, Moebius function, Moebius inversion formula, The number-of-divisors and sum-of-divisors functions, Euler phi function, Greatest Integer Function, Carmichael conjecture,Perfect numbers, characterization of even perfect numbers, Dirichlet product, Riemann Zeta function. Group of Units and Quadratic Residues: Primitive roots, Group of units, Quadratic Residues and Non-Residues, Legendre symbol, Euler's Criterion, Gauss' Lemma, Law of Quadratic Reciprocity. Sums of Squares: Sums of Two squares, Sums of Three squares and Sums of Four squares.
References: David M. Burton Elementary Number Theory, Tata McGraw-Hill. Gareth A. Jones and J. Mary Jones Elementary Number Theory, Springer Undergraduate Mathematics Series. Thomas Koshy Elementary Number Theory with Applications, 2nd Edition, Academic Press. Kenneth Rosen Elementary Number Theory and its Applications, 5th Edition, McGraw Hill. G. H. Hardy and E. M. Wright An Introduction to the Theory of Numbers, 5th edition, Oxford University Press.
Past Instructors: A Satyanarayana Reddy

EVS510

Environment Science

4.00

Graduate

Environment Science

CHY334

Environmental Chemistry

2.00

Undergraduate

Environmental chemistry is an interdisciplinary science that includes atmospheric, aquatic and soil chemistry. During this course chemistry of the air, water, and soil, and how anthropogenic activities affect this chemistry on planet Earth will be covered. Specifically, sources, reactions, transport, effects, and fates of chemical species in air, water, and soil environments, and the effects of technology thereon will be examined. This course is divided into 5 major parts that reflect the most pressing issues in Environmental Chemistry today.
1.Fundamental concepts;
2.Introduction to Environmental Chemistry: Chemistry and the atmosphere, hydrosphere and soil, the role of chemistry in environmental studies;
3.The Hydrosphere: Fundamentals of aquatic chemistry, speciation and redox equilibria in natural waters, gases in water, organic matter in water, metals in water, environmental colloids, water pollution and waste water treatment, microplastics chemical aspects of the nitrogen and phosphorus cycles;
4.The Atmosphere: Introduction to the nature and composition of the atmosphere, the greenhouse effect and global warming, the case against global warming, Energy production and global warming, Climate Change and Energy.
5. The Biosphere: Nitrogen and food production, pest control

MAT543

Error Correcting Codes

4.00

Undergraduate

Error Correcting Codes

BIO113

Essentials of Biology

3.00

Undergraduate

Unit I: Basic Cell, Molecular Biology and Genetics
Prokaryotes and Eukaryotes, Introduction to Microbiology, Cell organelles, Biochemistry of macro molecules (Carbohydrates, Lipids, Proteins and Nucleic acids), Principles of Genetics (mendelian inheritance, concept of gene, Mutation, chromosomal abberations), Cell cycle, Cell division.
Central Dogma of Molecular Biology (Replication,Transcription,Translation and Gene expression), Introduction to Genomics, Transcriptomics and Proteomics, Basics of cloning, Cancer, Biosensors, Bio artificial organs. Applications of engineering in biology. Instrumental techniques: Microscopy, Centrifugation, PCR, Gel Electrophoresis

MAT791

Evolutionary Game Theory

4.00

Graduate

Evolutionary Game Theory

MAT811

Evolutionary Game Theory and A

4.00

Graduate

Evolutionary Game Theory and Applications

PHY562

Experimental Techniques in Particle Physics

3.00

Graduate

This course is intended to give an in-depth study of detector, data analysis and other experimental techniques used in particle physics. Modern particle detectors such as micro-pattern gaseous detectors, drift chambers, silicon detectors, calorimeters, Cherenkov detectors and others are discussed along with advanced statistical methods and data analysis techniques to extract results.

PHY599

Explorations in Research

3.00

Graduate

Explorations in Research

MAT591

Field Theory

4.00

Undergraduate

Course description not available.

MAT681

Finite Volume method

4.00

Graduate

Finite Volume method

MAT713

Formal Lang. & Automata Th II

4.00

Graduate

Formal Languages and Automata Theory II

MAT100

Foundations

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics. Not available as UWE.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: None
Overview: Introduction to modern mathematical language and reasoning: Sets and Logic, Proof strategies, Functions, Induction.
Detailed Syllabus: Sentential Logic: Deductive reasoning, negation of a sentence, conjunction and disjunction of sentences, equivalence of sentences, truth tables, logical connectives. Sets: Operations on sets, Venn diagrams, cartesian product, quantifiers. Proof Strategies: Direct proofs, proofs involving negations, conditionals, conjunctions, and disjunctions, existence and uniqueness proofs, proofs involving equivalence. Relations and Functions: Ordered pairs, equivalence relations, equivalence classes, partitioning of a set, functions as many-one relations, graphs of functions, one-one functions, onto functions, inverse of a function, images and inverse images of sets. Mathematical Induction: Division algorithm, principle of mathematical induction, well ordering principle, strong induction, principle of recursive definition. More on Sets: Finite and infinite sets, countable and uncountable sets.
References: Book of Proof by Richard Hammack, 2nd edition, Richard Hammack. Mathematical Thinking by Keith Devlin, Lightning Source. How to Prove It by Daniel J. Velleman, Cambridge University Press. Mathematical Writing by Franco Vivaldi, Springer. Proofs and Fundamentals by Ethan D. Bloch, Springer. Introduction to Logic and to the Methodology of Deductive Sciences, Alfred Tarski, Oxford University Press.
Past Instructors: Amber Habib, Priyanka Grover

MAT522

Fourier Analysis

4.00

Undergraduate

Fourier Analysis

MAT232

Fractal Geometry

4.00

Undergraduate

Course description not available.

MAT732

Fractal Geometry

4.00

Graduate

Fractal Geometry.

MAT528

Frame Theory

4.00

Undergraduate

Major Elective for BSc (Research) Mathematics. Available as UWE.
Prerequisites: MAT360 Linear ALgebra II
Overview: The course is an introduction to finite frames. Frames play a fundamental role in signal processing, image processing, data compression, sampling theory and more.
Detailed Syllabus:
1. Linear Algebra Review: Vector spaces, bases of a vector space, linear operators and matrices, rank of a linear operator and a matrix, determinant and trace of a matrix, inner products and orthonormal bases, orthogonal direct sum.
2. Finite-Dimensional Operator Theory: Linear functionals and dual spaces, Riesz representation theorem and adjoint operators, self-adjoint and unitary operators, the Moore-Penrose inverse, eigenvalues of an operator, square roots of a positive operator, trace of operators, the operator norm, the spectral theorem.
3. Introduction to Finite Frames: ????-frames, Parseval frames, reconstruction formula, frames and matrices, similarity and unitary equivalence of frames, frame potential.

MAT626

Functional Analysis

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 621 for graduate students, MAT 231/320 and MAT 360 for undergraduates.
Overview: This course introduces the tools of Banach and Hilbert Spaces, which generalize linear algebra and geometry to infinite dimensions. It is a prerequisite for advanced topics like Spectral Theory, Operator Algebras, Operator Theory, Sobolev Spaces, and Harmonic Analysis. Functional Analysis is a vital component of applications of mathematics to areas like Quantum Physics and Information Theory.
Detailed Syllabus: Banach Spaces Spaces: Some inequalities, Banach Spaces, finite dimensional spaces, compactness and dimension, quotient spaces, bounded operators, sums of normed spaces. Theorems: Baire Category Theorem, Open Mapping Theorem, Closed Graph Theorem, Principle of Uniform Boundedness. Spaces: Hahn-Banach Theorem, Spaces in Duality, Adjoint operator. Topologies: Weak topology induced by seminorms, weakly continuous functionals, Hahn-Banach separation theorem, weak*-topology, Alaouglu's Theorem, Goldstine's Theorem, reflexivity, extreme points, Krein-Milman Theorem. Hilbert Spaces Inner products: Inner product spaces, Hilbert spaces, orthogonal sum, orthogonal complement, orthonormal basis, orthonormalization, Riesz Representation Theorem. Operators on Hilbert spaces: Adjoint operators and involution in B(H), Invertible operators, Self adjoint operators, Unitary operators, Isometries. Spectrum: Spectrum of an operator, Spectral mapping theorem for polynomials.
Main References: E. Kreyszig: Introductory Functional Analysis with Applications, Wiley India. G. F. Simmons: Topology and Modern Analysis, Tata McGraw-Hill, 2004. Gert K. Pedersen: Analysis Now, Springer, 1988. John B. Conway: A Course in Functional Analysis, Springer International Edition, 2010. V. S. Sunder: Functional Analysis - Spectral Theory, Hindustan Book Agency, 1997. S. Kesavan: Functional Analysis, Hindustan Book Agency, 2009. G. Bachman and L. Narici: Functional Analysis, 2nd edition, Dover, 2000. Sterling K. Berberian: Lectures in Functional Analysis and Operatory Theory, Springer, 1974.

BDA605

Fundamentals of Computer Sc.

2.00

Graduate

Fundamentals of Computer Science

BIO101

Fundamentals of Computers

3.00

Undergraduate

Course Summary
IT has changed the Biologists thought process, revolutionary processing speed and advancement in data storage and mining methods has completely changed the Biotechnology and new branches emerged like “-Omics” technologies. The class is hands-on, project-oriented to give better understanding of IT applications in Biology. The course is designed to introduce the most important and basic computer concepts. It also involves case studies and applications in which Bioinformatics tools and algorithms can be used. The course will introduce students to altogether a new world of Biology which includes many new terminologies and concepts in Bioinformatics. This course will enable student aware of programming methods in Perl and linux which they can use in Bioinformatics analysis.
Detailed Contents
Introduction to computers:Overview and functions of a computer system, Computer generations with characteristic features, computer organization, CPU, ALU, memory hierarchy, registers, I/O devices, storage devices. Types of Processing: Batch, Real-Time, Online, Offline. Introduction to operating systems: Operating System concept, Variants of Unix, Linux operating system and command line applications. Computer Networking: Introduction to networking: Associated hardware devices, gadgets (Router, Switch etc.), Network Topologies and Protocols LAN, WAN and MAN, World Wide Web (WWW) Network security: fire walls. Concepts in text-based searching Medline, bibliographic databases.
Algorithms, Flowcharts & Programming concepts: Algorithms: Concepts & definitions, Converting algorithms to flowcharts, Comparing algorithms, flowcharts & programs, Algorithms solving Biological problems, Basic PERL Programming. Computers in Biology: Nature of Biological data, Biological Databases, pubmed, Overview of Bioinformatics, sequence alignment, Major Bioinformatics Resources: NCBI, EBI & ExPASY.
References Introduction to Bioinformatics- Attwood Bioinformatics -David Mount Developing Bioinformatics Computer Skills- Cynthia Gibas Introduction to Bioinformatics- Arthur M Lesk Fundamentals of Computers, -V Rajaraman, PHI. Introduction to computers - Peter Norton Computer Fundamentals – P.K. Sinha

CHY545

Fundamentals of Crystallography

3.00

Graduate

Crystallography in combination with X-ray or neutron diffraction yields a wealth of three-dimensional structural information unobtainable through other methods. The course has been designed to give an overview of crystallography, in general. This basic course will cover the topics such as symmetry in crystallography, crystals systems, Bravais lattices, crystal symmetry, crystallographic point groups and space groups, Miller indices, theory of X-ray diffraction, data collection, data reduction, structure factors and Fourier syntheses, electron density, phase problem, direct methods, Patterson method, crystal structure refinement etc. The course will also highlight the application of single crystal and powder X-ray diffraction techniques and will include hands on training on crystal growth, mounting, structure solution, refinement and analysis. Further, training on the use of database for structural search will also be provided. Introduction - Introduction on Crystallography and discussion on course structure Crystallographic Symmetry - Concept of 1D and 2D symmetry and lattices, notations of symmetry elements, space groups in 2D, 3D lattices, 32 point groups and their notations, stereographic projections, Laue symmetry; glide planes, screw axes and their notations, space groups, equivalent points, space group symmetry diagrams etc. Miller Indices, crystallographic planes and directions, close pack structures, linear density, planar density, Miller-Bravais indices for hexagonal systems. Theory of X-ray diffraction - What is X-ray, generation and classification of X-ray, X-ray sources, diffraction of X-rays, Bragg’s law, the reciprocal lattice, reciprocal relationship, Bragg’s law in reciprocal space, Ewald’s sphere, Laue Method, Oscillation, rotation and precession methods. Data reduction - L-P corrections, structure factor, scaling, interpretation of intensity data, temperature factor, symmetry from intensity statistics, structure factor and Fourier synthesis, Friedel’s law; exponential, vector and general forms of structure factor, determination of systematic absences for various symmetry or lattice centering, FFT, Anomalous scattering. The Phase Problem - Definition, Direct Methods, structure invariants and semi invariants, probability methods, Phase determination in practice, Patterson Methods, Patterson Symmetry, completion of structure solution, F synthesis. Refinement of Crystal Structures - Refinement by Fourier synthesis, refinement by F synthesis, Refinement by least squares method, weighting functions, Goodness-Of-Fit (GOF) parameter, treatment of non-hydrogen atoms, and treatment of hydrogen atoms. Powder X-ray diffraction (PXRD) - Methodology, geometrical basis of powder X-ray diffraction, applications of PXRD (determination of accurate lattice parameters, identification of new/unknown phases, applications in pharmaceutical industry, structure solution from PXRD etc.), Reitveld method for structure refinement, indexing of PXRD, handling of PXRD using DASH. Neutron and Electron Diffraction - Basics of neutron, synchrotron and electron diffraction and their applications. Practical - Crystal growth, selection, indexing of crystals, data collection, data reduction, space group determination and structure refinement using SHELXS97, SIR and SHELXL97, introduction to International Tables for Crystallography and crystallographic packages (e.g. WinGx, PLATON, OLEX-2), IUCr validation of the structure and use of Cambridge Structural Database for structural search.
Text Book:
X-ray structure determination: A Practical Guide (2nd Ed.) by George H. Stout and Lyle H Jensen, Wiley-Interscience, New York, 1989.
Reference Books: Fundamentals of Crystallography (2nd Ed.) by C. Giacovazzo, Oxford University Press, USA, 2002. X-ray analysis and The Structure of Organic Molecules (2nd Ed.) by Jack D. Dunitz, Wiley-VCH, New York, 1996. Chemical Applications of Group Theory (3rd Ed.) by F. A. Cotton, Wiley-India Edition, India, 2009. International Table of Crystallography.

PHY588

Fundamentals of Ion-Solid Interactions

3.00

Graduate

Introduction to ion beam processes, ion implanter and applications, interatomic potential, Thomas-Fermi statistical model, classical two-particle scattering theory, differential scattering cross-section, energy-loss process in solid, Fermi-teller model, ZBL universal scattering function, ion range & distribution, Straggling, radiation damage in solid, Thermal spikes, Mono-Carlo simulation, diffusion in solid, sputtering, applications of ion beam, ordering-disordering, alloying, Hume-Rothery rules, ion-mixing, phase transition, doping semiconductors, location of dopants via Rutherford backscattering and ion channeling.

MAT605

Fundamentals of Mathematics

2.00

Graduate

Fundamentals of Mathematics

BIO206

Fundamentals of Molecular Biology

3.00

Undergraduate

Nature of genetic material, organization of genetic material in prokaryotes and eukaryotes. Structure of chromatin, fine structure of the gene. Different kinds of genes- split genes, overlapping, assembled, polyprotein & nested genes. Gene amplification and polytene chromosome. C - Value paradox, mitochondrial & plastid genomes.
DNA replication – Types of DNA polymerases. Mechanism of DNA replication. Enzymes and accessory proteins involved in DNA replication. Replication of telomeres and its significance. Differences in prokaryotic and eukaryotic DNA replication and regulation. DNA damage and repair.
Transcription in prokaryotes and eukaryotes. Mechanism of transcription, Types of RNA polymerases and promoter-polymerase interactions. Transcriptional factors. Processing of mRNA, tRNA and rRNA. RNA editing and transport.
Translation in prokaryotes and eukaryotes: Genetic code, translational machinery, mechanism of initiation, elongation and termination. Regulation of translation, co and post translational modifications. Leader sequences & protein targeting.
Regulation of gene expression in prokaryotes and eukaryotes- the operon concept, negative & positive control and attenuation. Role of enhancers, cis-trans elements, DNA methylation and chromatin remodeling in gene expression. Environmental regulation of gene expression. RNAi and gene silencing.
Recommended Books: Biochemistry (5th ed.), Stryer, L., Pub: freeman-Toppan. Genes VIII, Lewin, B., Pub: Oxford. Cell and Molecular Biology (7th ed.), De Roberties, E,D.P., De Robertis, E. M. F., Pub: Saunders College publisher. Molecular Biology, Frefielder, D., Pub: Narosa Publishing House Pvt. Limited, Molecular Biology of the Gene, Watson, J. D., et. al., Pub: Benjamin. Molecular Biology, Weaver, R. F., Pub: McGraw-Hill.

PHY103

Fundamentals of Physics I

5.00

Undergraduate

This is an introductory course for students majoring in physics or those who are planning to take physics as their minor. It will provide an introduction to Newtonian mechanics, Lagrangian Methods, and to the Special Theory of Relativity.
Physics and its relation to other sciences.
Time and Distance. Frames of reference and the inertial frames of reference.
Vector Analysis, Coordinate systems, Dimensional Analysis
Newton’s laws of motion in one dimension.
Rotational invariance. Newtons’s laws of motion in three dimension
Conservation of energy and momentum.
Oscillations.
The Lagrangian method.
Rotation in two dimensions. Rotation in three dimensions.
Central forces
The Special Theory of Relativity. Space-Time and four vectors.
Accelerating frames of reference

PHY104

Fundamentals of Physics II

5.00

Undergraduate

Vector Analysis
Electrostatics: Electric Field, Divergence and Curl of Electrostatic Fields, Electric Potential, Work and Energy in Electrostatics, Conductors
Potentials: Laplace's Equation, Method of Images, Multipole Expansion
Electric Fields in Matter: Polarization, Field of a Polarized Object, Electric Displacement, Linear Dielectrics
Magnetostatics: Lorentz Force Law, Biot-Savart law, Divergence and Curl of Magenetic Field, Magnetic Vector Potential
Magnetic Fields in Matter: Magnetization, Field of a Magnetized Object, Auxiliary Field, Linear and Nonlinear Media
Electrodynamics: Electromotive Force, Electromagnet Induction, Maxwell's Equations
Conservation Laws: Charge and Energy, Momentum, Work
Electromagnetic Waves: Waves in One Dimension, Electromagnetic Waves in Vacuum, Electromagnetic Waves in matter

PHY201

Fundamentals of Thermal Physics

4.00

Undergraduate

1. The Kinetic Theory of Gases Macroscopic and microscopic description of matter, thermodynamic variables of a system, State function, exact and inexact differentials, Basic assumptions of the kinetic theory, Ideal gas approximation, deduction of perfect gas laws, Maxwell’s distribution law, root mean square and most probable speeds. Collision probability, Mean free path from Maxwell’s distribution. Degrees of freedom, equipartition of energy. Nature of intermolecular interaction : isotherms of real gases. van der-Waals equation of state.
2. Transport Phenomena Viscosity, thermal conduction and diffusion in gases. Brownian Motion: Einstein’s theory, Perrin’s work, determination of Avogardo number.
3. Thermodynamics of Photon Gas Spectral emissive and absorptive powers, Kirchoff’s law of blackbody radiation, energy density, radiation pressure. Stefan-Boltzmann law, Planck’s law
4. First Law of Thermodynamics Zeroth law and the concept of temperature. Thermodynamic equilibrium, internal energy, external work, quasistatic process, first law of thermodynamics and applications including magnetic systems, specific heats and their ratio, isothermal and adiabatic changes in perfect and real gases.
5. The Second Law of Thermodynamics and its Statistical Interpretation (a) Second law of thermodynamics: different formulations and their equivalence (b) Entropy: The statistical postulate. (c) Equilibrium of an isolated system: Temperature (d) Illustration: The Schottky defects. (e) Equilibrium of a system in a heat bath: Boltzmann distribution; Kinetic interpretation of the Boltzmann distribution.
6. Thermodynamic Functions Enthalpy, Helmholtz and Gibbs’ free energies; Chemical potential, Maxwell’s relations; thermodynamic equilibrium and free energies.
7. Change of State Equilibrium between phases, triple point, Gibbs’ phase rule and simple applications. First and higher order phase transitions, The phase equilibrium and the ClausiusClapeyron equation,. JouleThomson effect, third law of thermodynamics
8. Applications of Thermodynamics. (a) Heat engines and Refrigerators: Derivation of limits on efficiency from the laws of thermodynamics; Carnot cycle; realistic cycles for internal combustion engines, steam engines, and refrigeration (b) Thermodynamics of rubber bands: Gibbs free energy, Entropy (c). Paramagnetism: A paramagnetic solid in a heat bath. The heat capacity and the entropy. An isolated paramagnetic solid. Negative temperature.

BDA656

Game Theory

3.00

Graduate

Course description not available.

MAT491

Game Theory

4.00

Undergraduate

Course description not available.

MAT790

Game Theory

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 660 Linear Algebra
Overview:
Detailed Syllabus: Simple Decision Models: Ordinal Utility, Linear Utility, Modelling Rational Behaviour, Modelling Natural Selection, Optimal Behaviour, Strategic Behaviour, Randomizing Strategies, Optimal Strategies Strategic Games: Interactive Decision Problems, Describing Static Games, Games in Normal Form, Describing Strategic Games, Solving Games Using Dominance, Nash Equilibrium in Strategic Games, Existence of Nash Equilibria, The Problem of Multiple Equilibria, Classifying Games, Two- Player Zero-Sum Games, Mixed Strategies in Finite Games, Matrix and Bimatrix Games, Games with n-Players Infinite Dynamic Games: Repeated Games, The Iterated Prisoner’s Dilemma, Folk Theorems Population Games: Evolutionary Game Theory, Evolutionarily Stable Strategies, Games against the Field, Pairwise Contest Games
References: K. Binmore Playing for Real: A Text on Game Theory, Oxford University Press. J. N. Webb Game Theory, Decisions, Interaction and Evolution, Springer. J. G-Diaz, I. G-Jurado, M. G.F-Janeiro An Introductory Course on Mathematical Game Theory, Graduate Studies in Mathematics 115, American Mathematical Society.

MAT721

General Measure Theory

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 623 Analysis II
Overview:
Detailed Syllabus: Measure and Integration Measure Spaces Measurable functions Integration – Fatou’s Lemma, Monotone Convergence Theorem, Lebesgue Convergence Theorem. General Convergence Theorems Signed Measures – Hahn Decomposition Theorem, Jordan decomposition of a measure, Radon-Nikodym Theorem, Lebesgue Decomposition Theorem. The Lp spaces – Riesz Representation Theorem. Measure and Outer Measure Outer measure and measurability The extension theorem – Caratheodory Theorem The Lebesgue-Stieltjes Integral Product measures – Fubini’s Theorem, Tonelli Theorem, Lebesgue Integral on Rn, change of variable. Inner Measure Measure and Topology Baire sets and Borel sets Regularity of Baire and Borel measures Construction of Borel Measure Positive linear functionals and Borel Measures – Riesz Markov Theorem (Dual of Cc(X)). Bounded linear functionals on C(X) – Riesz Representation Theorem
References: Real Analysis by H. L. Royden and P. Fitzpatrick. 4th edition, Prentice-Hall India, 2010. Measure Theory and Integration by G. de Barra, New Age International, reprint 2006. Real Analysis: Modern Techniques and their Applications by G. B. Folland, Wiley, 2nd edition, 1999. Measure Theory by Paul Halmos, Springer, 1974.

PHY413

General Theory of Relativity

3.00

Undergraduate

We begin with an overview of special theory of relativity and proceed to give the definitions of tensor, connection, parallel transport and covariant differential with the aim of providing the description of gravity as arising from a curve space. From Riemann geometry and the Christoffel symbols we move to geodesic equations and to Riemann tensor outlining its various properties. We explain how one can formulate Einstein equations from fundamental principles. We also derive the Einstein equations from the least action principle applied to the Einstein-Hilbert action. We define the energy-momentum tensor for matter and show that it obeys a conservation law. We take up the study of the black hole type solution and derive the one for Schwarzschild black hole. We touch upon the Birkhoff theorem and explain the important differences between energy-momentum conservation laws in the absence and in the presence of the dynamical gravity. We discuss gravitational waves and give an introduction to cosmology including cosmic microwave background radiation, dark matter and dark energy.

BIO600

Genomics, Proteo.-Metabolomics

3.00

Graduate

Comparative Genomics, Proteomics and Metabolomics

BIO305

Genomics, Proteomics & System Biology

3.00

Undergraduate

Introduction and scope of proteomics; Protein separation techniques: ion exchange, size-exclusion and affinity chromatography techniques; Polyacrylamide gel electrophoresis; Isoelectric focusing (IEF); Two dimensional PAGE for proteome analysis; Image analysis of 2D gels; Introduction to mass spectrometry; Strategies for protein identification; Protein sequencing; Protein modifications and proteomics; Applications of proteome analysis to drug; Protein-protein interaction (Two hybrid interaction screening); Protein engineering; Protein chips and functional proteomics; Clinical and biomedical application of proteomics; Proteome database; Proteomics industry.
Methods of preparing genomic DNA; DNA sequence analysis methods: Sanger Dideoxy method and Fluorescence method; Gene variation and Single Nucleotide Polymorphisms (SNPs); Expressed sequenced tags (ESTs); Gene disease association; Recombinant DNA technology: DNA cloning basics, Polymerase chain reaction, DNA fingerprinting, Human genome project and the genetic map.
Introduction to systems Biology. Terms and definitions. Dynamical systems, linear stability and bifurcation analysis. Limit cycles, attractors. Genetic and biochemical networks, chemical kinetics, deterministic and stochastic descriptions. Other network types: Regulatory (e.g. fly), Signal transduction (e.g. MAP Kinase cascade in yeast), Metabolic (E coli), Neural network. Topology of genetic and metabolic networks.
Software for systems biology. SBML, and open source programs eCell, Virtual Cell, StochSim, BioNets. Quantitative models for E Coli: lac operon and lambda switch. The chemotactic module in E. Coli. Pathways and pathway inference. DAVID. Gene Ontologies. § Pathway Miner and similar Software. SNPs and complex diseases.
Recommended Books: Genomics: The Science and Technology Behind the Human Genome Project, Cantor, C. R., Smith, C. L., Pub: John Wiley & Sons. Introduction to Genomics, Lesk, A. M., Pub: Oxford University Press. Handbook of Proteomic Method, P. M. Conn, Pub: Humana Press. Biochemistry, Berg, J. M., Tymoczko, J. L., Stryer, L., Pub: W. H. Freeman.

MAT632

Geometry

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 360 Linear Algebra II for undergraduates, MAT 660 Linear Algebra for graduate students
Overview: This course provides a bridge to modern geometry. It provides a unified axiomatic approach leading to a coherent overview of the classical geometries (affine, projective, hyperbolic, spherical), culminating in a treatment of surfaces that sets the stage for future study of differential geometry.
Detailed Syllabus: Affine geometry – finite planes, planes over fields, affine transformations, collineations, affine coordinates, triangles and parallelograms, classical theorems of Menelaus and others. Projective geometry – finite planes, projective completion of affine planes, homogeneous coordinates, projective transformations, collineations, projective line, poles and polars. Conics – affine and projective classifications, group actions. Euclidean geometry – isometries, triangles, parallelograms, length minimizing curves, geometry of plane curves. Hyperbolic geometry – Poincare upper half plane, Poincare metric, distance function, triangles and area, two-point homogeneity. Spherical geometry – Sphere, tangent space, great circles, triangles and area, two-point homogeneity Surfaces – Level surfaces, parametrized surfaces, curvature, Gauss theorem, introduction to manifolds.
References: An Expedition to Geometry by S Kumaresan and G Santhanam. Hindustan Book Agency, 2005. Geometry by M. Audin. Springer International Edition, Indian reprint, 2004. Geometry by David A. Brannan, Matthew F. Esplen and Jeremy J. Gray. Cambridge University Press, 2nd edition, 2012. Geometry by Roger A Fenn, Springer International Edition, 2005.

MAT332

Geometry of Curves & Surfaces

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 102 Calculus II or MAT 103 Mathematical Methods I. And MAT 160 Linear Algebra I.
Overview: This course combines the traditional approach to learn the basic concepts of curves and surfaces with the symbolic manipulative abilities of Mathematica. Students will learn and study the classical curves/surfaces as well as more interesting curves/surfaces using computer methods. For example, to see the effect of change of parameter, the student will explore and observe with the help of Mathematica and then the mathematical proof of the observation will be developed in the class.
Detailed Syllabus:
1- Curves in the plane: Length of a curve, Vector fields along curves. Famous plane curves: cycloids, lemniscates of Bernoulli, cardioids, catenary, cissoid of Diocles, tractrix, clothoids, pursuit curves.
2- Regular curve, curvature of a curve in a plane, curvature and torsion of a curve in R3. Determining a plane curve from given curvature.
3- Global properties of plane curves: Four vertex theorem, Isoperimetric inequality.
4- Curves on Sphere. Loxodromes on spheres, animation of curves on a sphere.
5- Review of calculus in Euclidean space.
6- Surfaces in Euclidean spaces: Patches in R3, local Gauss map, Regular surface, Tangent vectors.
7- Example of surfaces: Graphs of a function of two variables, ellipsoid, stereographic ellipsoid, tori, paraboloid, seashells.
8- Orientable and Non-orientable surfaces. Mobius strip, Klein Bottle.
9- The shape operator, normal curvature, Gaussian and mean curvature, fundamental forms.
10- Surfaces of revolution
References: Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition by Elsa Abbena, Simon Salamon, Alfred Gray. Elementary Differential Geometry by A.N. Pressley, Springer Undergraduate Mathematics Series. Differential Geometry of Curves and Surfaces by Manfredo DoCarmo.
Past Instructors: Pradip Kumar

MAT432

Geometry of Curves & Surfaces

4.00

Undergraduate

Geometry of Curves and Surfaces

MAT640

Graduate Algebra I

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: Linear Algebra, Group Theory
Overview: An overview of graduate algebra with an emphasis on commutative algebra. The instructor may choose 3 or 4 topics from the following, depending on the background and interest of the students.
Detailed Syllabus: Group Actions: Orbit-stabilizer theorem, Centralizers, Normalizers, Class Equation, Sylow Theorems. Rings: Homomorphisms and ideals, quotient, adjunction, integral domains and fraction fields, maximal ideals, factorization, unique factorization domains, principal ideal domains, Euclidean domains, factoring polynomials. Modules: Submodules, quotient modules, homomorphisms, isomorphism theorems, direct sums, simple and semisimple modules, free modules, finitely generated modules, Schur’s Lemma, Jordan-Holder Theorem, Modules over a matrix algebra. Fields: Algebraic and transcendental elements, degree of field extension, adjunction of roots, finite fields, function fields, transcendental extensions, algebraic closure. Galois Theory: Galois group, Galois extension, cubic equations, symmetric functions, primitive elements, quartic equations, Kummer extensions, quintic equations. Homological Algebra: Categories, monomorphisms and epimorphisms, projective and injective modules, left/right exact functors, additive functors, the Hom functor, diagram chasing, push-outs and pull-backs, tensor product, natural transformations, adjoint functors, flat modules.
References: Algebra by M Artin, 2nd edition, Prentice-Hall India, 2011. Abstract Algebra by D S Dummit and R M Foote, 2nd edition, Wiley, 1999. Algebra by S. Lang, 3rd edition, Springer, 2005. Algebra by T. W. Hungerford, Springer India, 2005.

CHY615

Graduate Seminar

1.00

Graduate

Faculty members from the department (and possibly beyond) present seminars about their areas of interest, the proposed research in their respective groups and the experimental (or computational) techniques used in their field. Students will be expected to participate actively in these seminars by asking questions. This module serves to introduce new students to the possibilities for research, preparatory to selection of their research advisors.

MAT442

Graph Theory

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 160 Linear Algebra I
Overview: Graphs are fundamental objects in combinatorics. The results in graph theory, in addition to their theoretical value, are increasingly being applied to understand and analyze systems across a broad domain of enquiry, including natural sciences, social sciences and engineering. The course does not require any background of the learner in graph theory. The emphasis will be on the axiomatic foundations and formal definitions, together with the proofs of some of the central theorems. Few applications of these results to other disciplines would be discussed.
Detailed Syllabus:
Unit 1 Definitions of Graph, Digraph, Finite and Infinite Graph, Degree of a Vertex, Degree Sequence, Walk, Path, Cycle, Clique. Operations on graphs, Complement of a graph, Subgraph, Connectedness, Components, Isomorphism. Regular graph, Complete graph, Bipartite graph, Cyclic graph, Euler graph, Hamiltonian path and circuit, Tree, Cut set, Spanning tree.
Unit 2 Planar graph, Colouring, Covering, Matching, Factorization, Independent sets.
Unit 3 Graphs and relations, Adjacency matrix, Incidence matrix, Laplacian matrix, Spectral properties of graphs, Matrix tree theorem, Automorphism group of a graph.
Unit 4 DFS, BFS for minimal spanning tree, Kruskal, Prim and Dijkstra algorithms.
References: D. West, Introduction to Graph Theory, 2nd ed., PHI Learning, New Delhi, 2009. N. Deo, Graph Theory: With Application to Engineering and Computer Science, PHI Learning, New Delhi, 2012. C. D. Godsil and G. Royle, Algebraic Graph Theory, Springer, New Delhi, 2013. B. Kolman, R.C. Busby, S.C. Ross, Discrete Mathematical Structures, 6th ed., PHI Learning, New Delhi, 2012. F. Harary, Graph Theory, Narosa, New Delhi, 2012. J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New Delhi, 2013. R.J. Wilson, Introduction to Graph Theory, 4th ed., Pearson Education, New Delhi, 2003.
Past Instructors: Sudeepto Bhattacharya

MAT642

Graph Theory

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: For undergraduates: MAT 140 (Discrete Structures), MAT 360 (Linear Algebra II). For MSc students: MAT 660 (Linear Algebra)
Overview: Combinatorial graphs serve as models for many problems in science, business, and industry. In this course we will begin with the fundamental concepts of graphs and build up to these applications by focusing on famous problems such as the Traveling Salesman Problem, the Marriage Problem, the Assignment Problem, the Network Flow Problem, the Minimum Connector Problem, the Four Color Theorem, the Committee Scheduling Problem , the Matrix Tree Theorem, and the Graph Isomorphism Problem. We will also highlight the applications of matrix theory to graph theory.
Detailed Syllabus: Fundamentals: Graphs and Digraphs, Finite and Infinite graphs, Degree of a vertex, Degree Sequence, Walk, Path, Cycles, Clique, Operations on Graphs, Complement, Subgraph, Connectedness, Components, Isomorphism, Special classes of graphs: Regular, Complete, Bipartite, Cyclic and Euler Graphs, Hamiltonian Paths and Circuits. Trees and binary trees. Connectivity: Cut Sets, Spanning Trees, Fundamental Circuits and Fundamental Cut Sets, Vertex Connectivity, Edge Connectivity, Separability. Planar graphs, Coloring, Ramsey theory, Covering, Matching, Factorization, Independent sets, Network flows. Graphs and Matrices: Incidence matrix, Adjacency matrix, Laplacian matrix, Spectral properties of graphs, Matrix tree theorem, Automorphism group of a graph, vertex, edge and distance transitive graphs, Cayley graphs. Algorithms and Applications: Algorithms for connectedness and components, spanning trees, minimal spanning trees of weighted graphs, shortest paths in graphs by DFS, BFS, Kruskal's, Prim's, Dijkstra's algorithms.
References: D. West, Introduction to Graph Theory, Prentice Hall. Narsingh Deo, Graph Theory: With Application to Engineering and Computer Science, PHI, 2003. Chris D. Godsil and Gordon Royle, Algebraic Graph Theory, Springer-Verlag, 2001. Norman Biggs, Algebraic Graph Theory, 2nd edition, Cambridge Mathematical Library. Frank Harary, Graph Theory, Narosa Publishing House. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Addison Wesley. R. J. Wilson, Introduction to Graph Theory, 4th Edition, Pearson Education, 2003. Josef Lauri, Raffaele Scapellato, Topics in Graph Automorphisms and Reconstruction, London Mathematical Society Student Texts.

MAT687

Graph Theory and Complex Net.

4.00

Graduate

Graph Theory and Complex Networks

CHY402

Green Chemistry and Sustainability

3.00

Undergraduate

Green Chemistry and Sustainability

CHY554

Green Chemistry and Sustainability

3.00

Graduate

Since a decade, scientific community especially chemistry has been mobilized to develop new chemistries that are less hazardous to human health and the environment. Several steps were taken to protect both the nature and maintain ecological balance. But still such an effort is in nascent stage. Are we really protecting earth? Are we utilizing nature’s sources wisely? What are the hazards associated with one wrong step…and with several such steps? We are surrounded by chemistry since we wake up in morning till we sleep in night such as toothpaste, soap, cloth, perfume, medicine, plastic furniture, shoes etc. For those of us who have been given the capacity to understand chemistry and practice it as our day to day life, it is and should be expected that we should use it in a sustainable manner. With knowledge comes the burden of responsibility. We should not enjoy this luxury with ignorance and cannot turn a blind eye to the effects of the science in which we are engaged. We have to work hard and put brain waves together to develop new chemistries that are more benign, and safer to mother earth!! Green chemistry Lessons from past for a better future: Need, Limitations and Opportunities. Principles of Green Chemistry and their illustrations with examples: Scales of measurement such as Atom efficiency, E factors etc., homo vs. heterocatalysis, reaction efficiency, toxicity reduction etc. Green reactions: Green alternatives of starting materials, non-risky reagents, benign solvents (Aqueous medium, Ionic liquids, Supercritical fluids, Solvent free reactions, Flourous phase reactions), and reaction conditions (Nonconventional energy sources: Microwave assisted reaction, Ultrasound assisted reactions, Photochemical reactions), catalysis (heterogeneous catalysis, biocatalysis, phase-transfer catalysis), Replacement of Non-Green reactions with Green reactions (Real/Award cases) Safety for sustainable environment: Hazards assessment and mitigation in chemical industry Future trends in Green Chemistry: Green analytical methods, Redox reagents, Green catalysts; Green nano-synthesis, Green polymer chemistry, Exploring nature, Biomimetic, multifunctional reagents; Combinatorial green chemistry; Proliferation of solvent-less reactions; Non-covalent derivatization, Biomass conversion, emission control.
Reference Books: Green Chemistry: Theory and Practice. P.T. Anastas and J.C. Warner. Oxford University Press. Green Chemistry: Introductory Text. M. Lancaster Royal Society of Chemistry (London). Introduction to Green Chemistry. M.A. Ryan and M.Tinnesand, American Chemical Society (Washington). Real world cases in Green Chemistry, M.C. Cann and M.E. Connelly. American Chemical Society (Washington). Real world cases in Green Chemistry (Vol 2) M.C. Cann and T.P.Umile. American Chemical Society (Washington) Alternative Solvents for Green Chemistry. F.M. Kerton. Royal Society of Chemistry (London). Handbook of Green Chemistry & Technology. J. Clark and D. Macquarrie. Blackwell Publishing. Solid-Phase Organic Synthesis. K. Burgess. Wiley-Interscience. Eco-Friendly Synthesis of Fine Chemicals. R. Ballini. Royal Society of Chemistry (London) Green Polymer Chemistry: Biocatalysis and Biomaterials; Cheng, H., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2010.

MAT724

Hardy-Hilbert Spaces & Apps.

4.00

Graduate

Hardy-Hilbert Spaces and Applications

BIO607

Host Path. Int. & Vasc. Dys.

3.00

Graduate

Vascular Dysfunction: The primary structure, characteristics and function of Endothelial cells. Involvement of endothelial cells in inflammation and pathogenesis following pathogen attack and blood tumor barrier. Cell Signaling in primary cells.
Practical: Adhesion assay, Cell death and cell cycle in primary brain cells, immunofluorescence assays, Surface Plasmon Resonance and ELISA techniques.
Host Pathogen Interaction: Introduction to human diseases. Mechanism of pathogen adhesion and attack and entry into the human body. The mechanistic details and process of a few specific pathogens on primary brain cells.
Practical: Cell Culture of human pathogens, co-culture and growth assays, Live cell imaging.

BIO314

Host Pathogen Interaction and Vascular Dysfunction

3.00

Undergraduate

Vascular Dysfunction: The primary structure, characteristics and function of Endothelial cells. Involvement of endothelial cells in inflammation and pathogenesis following pathogen attack and blood tumor barrier. Cell Signaling in primary cells.Practical: Adhesion assay, Cell death and cell cycle in primary brain cells, immunofluorescence assays, Surface Plasmon Resonance and ELISA techniques.
Host Pathogen Interaction: Introduction to human diseases. Mechanism of pathogen adhesion and attack and entry into the human body. The mechanistic details and process of a few specific pathogens on primary brain cells.
Practical: Cell Culture of human pathogens, co-culture and growth assays, Live cell imaging.
References: Recent publications on Host pathogen Interaction and reviews will beprovided.

BIO207

Immunology

3.00

Undergraduate

Concepts of immune response. Innate immunity – barriers and role of toll like receptors in innate immunity. Cells of the immune system , Adaptive immunity – organization and structure of lymphoid organs. Antigens –immunogenicity, antigenicity, factors influencing the immunogenicity, haptens, adjuvants and mitogens. Super antigens, B & T cell epitopes.
Types of B cells, BCR, developmental stages of B cells, regulation of immune response. Classification, fine structure and functions of antibodies. Antigenic determinants on immunoglobulins – isotypes, allotypes and idiotypes. The generation of antibody diversity. Effector cell mechanism of humoral response. T cell ontogeny – Types of T cells, T cell development. T-cell maturation and activation. Structure of TCR. T-cell differentiation, Effector cell mechanism. Cell death and T-cell populations, Types of cell mediated immunity.
Cytokines – classes and their biological activities. Therapeutic uses of cytokines and their receptors. Complement system– mode of activation, classical, alternate and mannose binding pathway, biological functions and regulation. Major histocompatibility complex (MHC). Human leukocyte antigens (HLA), MHC restriction. MHC and disease susceptibility, regulation of MHC expression. APC’s and antigen processing and presentation.
Immunological techniques: Principle concepts of antigen–antibody interactions:
Agglutination, precipitation, gel diffusion: Ouchterlony double immuno diffusion and Mancini’s radial immuno diffusion, immunoelectrophoresis and complement fixation test. ELISA, RIA, Western Blot and FACS.
Recommended Books: Kuby Immunology (6th ed.), Kindt, T. J., Goldsby, R. A., Osborne, B. A., Pub: W. H. Freeman and Company. Roitt's Essential Immunology (12th ed.), Delves, P. J., Martin, S. J., Burton, D. R., Roitt, I. M., Pub: Wiley- Blackwell. Janeway's Immunobiology (8th ed.), Murphy, K., Pub: Garland Science. Fundamental Immunology (6th ed.), Paul, W. E., Pub: Lippincott Williams &Wilkins publishers.

BIO304

Industrial Biotechnology

3.00

Undergraduate

Introduction to fermentation, the fermentation industry, Production process batch and Continuous system of cultivation, Solid-state fermentation. Selection of industrial microorganisms, media for fermentation, aeration, pH, temperature and other requirements during fermentation, downstream processing and product recovery, food industry waste as fermentation substrate.
Production of compounds like antibiotics, enzymes, organic acids, solvents, beverages, SCP. Production of fermented dairy products, Immobilized enzymes systems, production and applications. Industrial application of microbes - Wine, Beer, Cheese, Yogurt.
Primary and secondary metabolites and their applications; preservation of food.
Biogas; bio-fertilizers and bio-pesticides. Use of microbes in mining: leaching of ores by microorganisms; microorganisms and pollution control-bioremediation; biosensors.
Biological waste treatment and in-plant sanitation - principle and use of biosensor- production of vitamins, amino acids, organic acids, enzymes and antibiotics, alcohols. Enzyme technology - production and recovery of enzymes, enzyme immobilization - application of enzyme in industries. Biosensors.
Recommended Books: Industrial Microbiology, Casida, L. E., Pub: Wiley. Principles of fermentation Technology, Stanbury, P. F., Whitaker, A., Hall, S. J., Pub: Pergamon. Fundamental Principles of Bacteriology, Salle, A. J., Pub: Lightening Source Incorporated.

CHY332

Informatics & Molecular Modelling

3.00

Undergraduate

This course and the associated computer lab deal with Molecular Modelling and Cheminformatics, applied to the search for new drugs or materials with specific properties or specific physiological effects (in silico Drug Discovery). Students will learn the general principles of structure-activity relationship modelling, docking & scoring, homology modelling, statistical learning methods and advanced data analysis. They will gain familiarity with software for structure-based and ligand-based drug discovery. Some coding and scripting will be required.
COURSE CONTENT: Introduction: Drug Discovery in the Information-rich age Introduction to Pattern recognition and Machine Learning Supervised and unsupervised learning paradigms and examples Applications potential of Machine learning in Cheminformatics & Bioinformatics Introduction to Classification and Regression methods Representation of Chemical Structure and Similarity: Sequence Descriptors Text mining Representations of 2D Molecular Structures: SMILES Chemical File Formats, 3D Structure Descriptors and Molecular Fingerprints Graph Theory and Topological Indices Progressive incorporation of chemically relevant information into molecular graphs Substructural Descriptors Physicochemical Descriptors Descriptors from Biological Assays Representation and characterization of 3D Molecular Structures Pharmacophores Molecular Interaction Field Based Models Local Molecular Surface Property Descriptors Quantum Chemical Descriptors Shape Descriptors Protein Shape Comparisons, Motif Models Molecular Similarity Measures Chemical Space and Network graphs Semantic technologies and Linked Data Mapping Structure to Response: Predictive Modelling: Linear Free Energy Relationships Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) Modeling Ligand-Based and Structure-Based Virtual High Throughput Screening 3D Methods - Pharmacophore Modeling and alignment ADMET Models Activity Cliffs Structure Based Methods, docking and scoring Model Domain of Applicability Data Mining and Statistical Methods: Linear and Non-Linear Models Data preprocessing and performance measures in Classification & Regression Feature selection Principal Component analysis Partial Least-Squares Regression kNN, Classification trees and Random forests Cluster and Diversity analysis Introduction to kernel methods Support vector machines classification and regression Introduction to Neural Nets Self-Organized Maps Deep Neural Networks Introduction to evolutionary computing Genetic Algorithms Data Fusion Model Validation Best Practices in Predictive Cheminformatics
RECOMMENDED BOOK(S): Johann Gasteiger, Thomas Engel,Chemoinformatics: A Textbook (Wiley-VCH, 2003) Jürgen Bajorath (Editor), Chemoinformatics and Computational Chemical Biology (Methods in Molecular Biology) (Humana Press, 2004) Leach & Gillet, An Introduction to Chemoinformatics
Prerequisites: Basic Organic chemistry/Biochemistry, Basic Statistics, Computer Programming.

CHY522

Informatics and Drug Discovery

3.00

Graduate

This course and the associated computer lab deal with Bioinformatics and Cheminformatics, applied to the search for new drugs with specific physiological effects (in silico Drug Discovery). Students will learn the general principles of structure-activity relationship modeling, docking & scoring, homology modeling, statistical learning methods and advanced data analysis. They will gain familiarity with software for structure-based and ligand-based drug discovery. Some coding and scripting will be required. At the end of the course, students will be expected to present a completed piece of software of significant utility and/or an analysis of experimental data from the published literature. Students will be encouraged to seek avenues for publication of their most significant results.
Syllabus: Introduction Drug Discovery in the Information-rich age Introduction to Pattern recognition and Machine Learning Supervised and unsupervised learning paradigms and examples Applications potential of Machine learning in Chem- & Bioinformatics Introduction to Classification and Regression methods, and types of classification and regression: KNN and Linear Discriminant analysis Representation of Chemical and Biochemical Structures Drug Discovery in the Information-rich age Sequence Descriptors Text mining Representations of Molecular Structures Characterizing 2D structures with Descriptors and Fingerprints Searching 2D Chemical Databases Chemical File Formats and SMARTS Topological Indices Substructural Descriptors Molecular Fingerprints Physicochemical Descriptors Descriptors from Biological Assays Representation and characterization of 3D Molecular Structures Calculation of Structure Descriptors Pharmacophores Molecular Interaction Field Based Models Local Molecular Surface Property Descriptors Quantum Chemical Descriptors Shape Descriptors Protein Shape Comparisons 3D Motif Models Representation of Chemical Reactions and Databases Analysis and Visualization Molecular Similarity Analysis Molecular Quantum Similarity Measures Cluster and Diversity analysis Network graphs from Molecular Similarity 3D visualization tools Self-Organized Maps Semantic technologies and Linked Data Mapping Structure to Response: Predictive Modeling Linear Free Energy Relationships Quantitative Structure-Activity Relationships (QSAR) Modeling Ligand-Based and Structure-Based Virtual High Throughput Screening 3D Methods - Pharmacophore Modeling and alignment ADMET Models Activity Cliffs Structure Based Methods, docking and scoring Site Similarity Approaches and Chemogenomics Model Domain of Applicability assessment
5. Data Mining and Statistical Methods Linear and Non-Linear Models Feature selection Partial Least-Squares Regression Introduction to Neural Nets, Bayesian Methods and Kernel Methods Support vector machines classification and regression and application to chemo & bioinformatics Random forest Principal Component analysis and SVD Data preprocessing and different performance measures in Classification & Regression Introduction to evolutionary computing Deep Learning and Convolutional Neural Nets Data Fusion Model Validation Interpretation of Statistical Models Best Practices in Predictive Cheminformatics
Textbooks: Johann Gasteiger, Thomas Engel,Chemoinformatics: A Textbook (Wiley-VCH, 2003) Jürgen Bajorath (Editor), Chemoinformatics and Computational Chemical Biology (Methods in Molecular Biology) (Humana Press, 2004) An Introduction to Chemoinformatics by Leach & Gillet

CHY556

Inorganic Reaction Mechanism

3.00

Graduate

General discussion about reaction kinetics, how to derive rate law and the ambiguity of mechanistic interpretations of rate laws Inorganic substitution Reaction for octahedral geometry vs square planar geometry, Trans effect, Redox reactions: Outer sphere ET vs. Inner sphere ET vs. Proton coupled ET (PCET) Organometallic reactions, mechanism and catalysis: Insertion, Oxidative addition, Reductive elimination C-H activation: Introduction, C-H functionalization vs. C-H activation, Importance, Classification, Organometallic C-H activation vs. biological C-H activation, Present research status C-C coupling reactions, mechanism, Present research status

CHY557

Intelligent Materials for Medicine

3.00

Graduate

Recent advances in field of medicine have resulted in designing and development of large number of novel synthetic architectures for target drug delivery in order to revolutionize the treatment and
prevention of disease. Advanced drug delivery and targeting can offer significant advantages to conventional drugs, such as increased efficiency, safety for drug delivery, convenience. However, such
potential is severely compromised by significant obstacles to delivery of these drugs in vivo. These obstacles are often so great that effective drug delivery and targeting is now recognized as the key to effective development of many therapeutics. This course will provide a comprehensive introduction to the vehicles for drug delivery, principles of advanced drug delivery and targeting, their current applications and potential future developments.
Books: Principles of Polymerization, George Odian, John Wiley & Sons, Inc., 3rd Ed., 1991. Chemistry of Nanocarbons, T. Akasaka, F. Wudl, S. Nagase, John Wiley & Sons, Inc.,1 st Ed., 2010. Contemporary Polymer Chemistry, Harry R Allcock, F W Lampe, J. E Mark, Pearson Publication Chemistry and Applications of Polyphosphazenes, Harry R. Allcock, John Wiley & Sons, Inc., 2003. Stem Cells: A Very Short Introduction, Jonathan Slack (Mar 24, 2012) Stem Cells for Dummies, Lawrence S.B. Goldstein and Meg Schneider (Feb 2, 2010) Essentials of Stem Cell Biology (2nd Edition, July 2009) by Robert Lanza, John Gearhart, Brigid Hogan and Douglas Melton. Scientific journals will be provided

BIO402

Internal Project Dissertation

9.00

Undergraduate

The students are advised to work under the supervision of any one of the faculty members in the department.

BIO406

Internal Project Dissertation

9.00

Undergraduate

Internal Project Dissertation

BIO610

Internal Project Dissertation

10.00

Graduate

Internal Project Dissertation

PHY419

Intro to Density Functional...

3.00

Undergraduate

Course description not available.

PHY255

Introduction to Biophysics

3.00

Undergraduate

1. Introduction: Definition of biophysics, why to study, examples.
2. Thermodynamics: Entropy, Enthalpy, The free energy of a system, Chemical potential, Redox potential, Bioenergetics
3. Biophysical properties: Brownian motion, Osmosis, Dialysis, Colloids
4. Membrane biophysics: Structure of bio-membrane. Structure-function relation.
5. Application of Radiation to Biological system: Introduction, particles and radiations of significance, physical and biological half-lives, macroscopic absorption of radiation, activity and measurements, units of dose, relative biological effectiveness and action of radiation at molecular level.
6. Experimental methods in biophysics: (a) Microscope: Light characteristics, microscopes- compound, phase contrast, polarization, fluorescent and electron microscopes – Transmission Electron Microscope, Scanning Electron Microscope, and Scanning tunneling electron microscope, Atomic Force Microscopy
(b) Spectroscopy: Electronic structure of atoms, Bond formation, hybridization of orbitals, Molecular orbitals, Bond energy, Ultraviolet & Visible spectroscopy-Beer Lamberts law- spectrophotometer. Infrared spectroscopy, Raman spectra, Circular Dichroism, Fluorescence spectroscopy, NMR spectroscopy.

PHY105

Introduction to Computational Physics I

3.00

Undergraduate

Introduction to Python: General information, Operators, Functions, Modules, Arrays, Formatting, Printing output, Writing a program
Approximation of a function: Interpolation, Least-squares Approximation
Roots of Equations: Method of Bisection, Method based on Linear Interpolation,
Newton-Raphson Method
Numerical Differentiation: Finite Difference Approximation
Numerical Integration: Trapezoidal Rule, Simpson's Rule
Ordinary Differential Equations: Taylor Series Method, Runge-Kutta Methods, Shooting Method

PHY106

Introduction to Computational Physics II

3.00

Undergraduate

1.Systems of Linear Algebraic Equations: Gauss Elimination Method, LU
decomposition, Choleski’s Decomposition Method, Symmetric and Banded Coefficient Matrices, Pivoting, Matrix Inversion, Iterative Methods
2.Symmetric Matrix Eigenvalue Problems: Jacobi Method, Power and Inverse Power Methods, Eigenvalues of Symmetric Tridiagonal Matrices, Computation of Eigenvectors
3. Two-Point Boundary Value Problems: Shooting Method
4. Solution of Partial Differential Equations: Separation of variables, Finite
Difference Method, The Relaxation Method, The matrix method for difference Equations.

MAT452

Introduction to Differential Manifolds

4.00

Undergraduate

Major elective for BSc (Research) Mathematics. Available as UWE.
Prerequisites: MAT332 Geometry of Curves and Surfaces or MAT221 Real Analysis II (These were previously numbered 432 and 420, respectively)
Overview
This course is an introductory course, which starts from several variable calculus and aimed to discuss classical integrability theorems for example Frobenius theorem etc. After these course, students will be able to do any next level course for example Riemannian geometry, Riemann surface, Complex geometry, Symplectic geometry etc.
Detailed Syllabus
1- Several variable calculus: Local immersion and submersion theorems, Inverse and Implicit function theorems.
2- Differential manifolds: Differential structure, Smooth functions on manifolds, critical points.
3- Tangent Bundle: Tangent space of R^n, Taylor theorem, Tangent space of an imbedded manifold, Tangent bundle. Vector field, orientation.
4- Vector field and flow: Integral curves, flow, one parameter group of diffeomorphism.
5- Introduction and particular cases of Frobenius theorem (integrability theorems)
Text Books
1- A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition by Michael Spivak
2- Foundations of Differentiable Manifolds and Lie Groups Authors: Warner, Frank W.
3- An Introduction to Differentiable Manifolds and Riemannian Geometry, Second Edition by William M. Boothby

PHY412

Introduction to Experimental Techniques in Particle Physics

3.00

Undergraduate

This course introduces the student to detectors, data analysis and other experimental techniques used in experimental particle physics.

PHY410

Introduction to High Energy Particle Physics

3.00

Undergraduate

This course introduces the experimental results and the theoretical concepts that lead to the formulation of the standard model of particle physics

MAT390

Introduction to Mathematical Finance

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics. Cross-listed as FAC201.
Credits (Lec:Tut:Lab): 3:0:1 (3 lectures and 1 two-hour lab weekly)
Prerequisites: MAT 184 Probability or MAT 205 Mathematical Methods III or CSD209.
Overview: Mathematical Finance is a modern study area where mathematical methods are used to create and add immense value in a practical environment. The aim of this course is twofold. First, to discuss the mathematical models that have driven the explosion of financial services and products over the last 30 years or so. Second, to use spreadsheet programs to work with actual data. This course is also the gateway to our Specialization in Mathematical Finance.
Detailed Syllabus: Basic concepts: Bonds and shares, risk versus profit, return and interest, time value of money, arbitrage. Fixed Income Securities: Net Present Value and Internal Rate of Return, price and yield of a bond, term structures, duration, immunization. Mean-Variance Analysis: Random returns, efficient portfolios, feasible set, Markowitz model, Two Fund and One Fund Theorems, Capital Asset Pricing Model and applications. Forwards, Futures and Swaps: Replicating portfolios, futures on assets without income, futures on assets with fixed income or dividend yield, hedging with futures, currency futures, stock index futures, forward rate agreements, interest rate swaps, currency swaps, equity swaps. Stock Price Models: Geometric Brownian Motion, Binomial Tree. Options: Call and put options, put-call parity, Binomial Options Pricing Model, dynamic hedging, risk-neutral valuation, Black-Scholes formula, trading strategies. Labs: Microsoft Excel and VBA.
References: Principles of Finance with Excel 2nd edition by Simon Benninga, Oxford University Press, 2010. Mathematics for Finance by M Capinski and T Zastawniak, Springer (International Edition), 2003. The Calculus of Finance by Amber Habib, Universities Press, 2011. Options, Futures and Other Derivatives 7th edition by John C Hull and Sankarshan Basu, Pearson 2009. Investment Science by David Luenberger, Oxford University Press (Indian Edition), 1997. An Elementary Introduction to Mathematical Finance 2nd edition by Sheldon Ross, Cambridge University Press (Indian Edition), 2005.
Past Instructors: Amber Habib, Charu Sharma, Sunil Bowry

PHY203

Introduction to Mathematical Physics I

3.00

Undergraduate

(a) Linear transformations of the plane
i. Affine planes and vector spaces
ii. Vector spaces and their affine spaces
iii. Euclidean and affine transformations
iv. Representing linear transformations by matrices
v. Areas and determinants
(b) Eigenvectors and eigenvalues
i. Conformal linear transformations
ii. Eigenvectors and eigenvalues
iii. Markov processes
(c) Linear differential equations in the plane
i. Functions of matrices
ii. Computing the exponential of a matrix
iii. Differential equation and phase portraits
iv. Applications of differential equations
(d) Scalar products
i. The Euclidean scalar product
ii. Quadratic forms and symmetric matrices
iii. Normal modes
iv. Normal modes in higher dimensions
v. Special relativity: The Poincare’ group and the Galilean group
(e) Calculus in the plane
i. The differential calculus and the examples of the chain rule: the Born approximation and Kepler motion
ii. Partial derivatives and differential forms.
iii. The pullback notation
iv. Taylor’s formula
v. Lagrange multiplier
(f) Double integrals
i. Exterior derivative
ii. Two-forms
iii. Pullback and integration for two-forms
iv. Two-forms in three space
v. Green’s theorem in the plane

PHY204

Introduction to Mathematical Physics II

3.00

Undergraduate

1. Functions of a complex variable
(a) Elementary properties of analytic functions
(b) Integration in the complex plane
(c) Analytic functions
(d) Calculus of residues: applications
(e) Periodic functions: Fourier series
(f) Gamma function
2. Differential Equations: analytical methods
(a) Linear differential equations and their power series solutions
(b) Legendre’s equation
(c) Bessel’s equation
(d) Hypergeometric equation
3. Hilbert Spaces
(a) Infinite-dimensional vector spaces
(b) Function spaces
(c) Fourier series
(d) Fourier integral and integral transforms
(e) Orthogonal polynomials
4. Partial differential equations
(a) Linear first-order equations
(b)The Laplacian and the Green function for Laplace’s equation
(c) Time-dependent partial differential equations: The diffusion
equation and the Schrödinger equation
(d) Nonlinear partial differential equations and solitons

PHY101

Introduction to Physics I

4.00

Undergraduate

The aim of this course is to bridge the gap between the various boards across the country at 10+2 level and bring everyone at the standard undergraduate level. All the engineering branches have their origin in the basic physical sciences. In this course we aim to understand the basic physical laws and to develop skills for application of various physical concepts to the science and engineering through problem solving. This will involve the use of elementary calculus like differentiation and integration.
Detailed Syllabus
Mechanics: The inertial reference frames, Newton’s laws of motion in vector notation, Conservation of energy, Application of Newton’s laws of motion, Dynamical stability of systems: Potential energy diagram, Collisions: Impulse, conservation of energy and linear, momentum, Conservation of angular momentum and rotation of rigid bodies in plane Thermal Physics: Averages, probability and probability distributions, Thermal equilibrium and macroscopic variables, Pressure of an ideal gas from Newton’s laws - the kinetic theory of gases. Maxwell’s velocity distribution, Laws of Thermodynamics and the statistical origin of the second law of thermodynamics, Application of thermodynamics: Efficiency of heat engines and air-conditioners, Thermodynamics of batteries and rubber bands

PHY102

Introduction to Physics II

5.00

Undergraduate

This is a continuation of PHY 101 and is meant for engineers and non-physics majors. The course will introduce students to Electricity and Magnetism, Maxwell’s equations, Light as an electromagnetic wave, and Wave optics.
Electrodynamics:
Vector calculus: Gradient, Divergence, Curl and fundamental theorems of vector calculus. Basic laws in electricity and magnetism, Classical image problem, displacement current and continuity equation, Maxwell’s Equations, electromagnetic wave equation and its propagation in free space, conducting media and dielectric medium, Poynting theorem, Electromagnetic spectrum.
Wave Optics:
Interference of light waves: Young’s double slit experiment, displacement of fringes, Interference in thin films
Diffraction: Fresnel’s and Fraunhofer’s class of diffraction, diffraction from single, double & N- Slits, Gratings.
Polarization: Concept of Polarization in electromagnetic waves, types of polarized waves.

PHY556

Introduction to Quantum Field Theory

3.00

Graduate

This course introduces the techniques of quantum field theory and its application to condensed matter physics and particle physics.

PHY202

Introduction to Quantum Mechanics

4.00

Undergraduate

1. Quantum and Classical Behavior
a) Experiments with bullet, waves and electrons
b) Probability Amplitude
c) The two-slit interference pattern
d) Identical particles
2. Base States
a) Filtering atoms with a Stern-Gerlach apparatus
b) Base states
c) Interfering amplitudes
d) Transferring to different bases
e) Base states of spin one-half particle
3. Dependence of Amplitude on Time
a) The Hamiltonian Matrix
b) The Ammonia Maser
c) Other Two State Systems: The Hydrogen Molecule, The Benzene Molecule, Neutrino
d) Oscillations
e) The Pauli spin matrices and the Hamiltonian of a spin-half particle in an external
f) magnetic field
g) Generalization to N-state system
4. Propagation in a Crystal Lattice
a) States for an electron in a one-dimensional lattice
b) An electron in a three-dimensional lattice
c) Scattering by imperfections in the lattice
d) Trapping by a lattice imperfection
e) Semiconductors and the transistor
5. Symmetry, Conservation Laws and Angular-Momentum
a) Symmetry and conservation
b) The conservation laws
c) Polarized light
d) The annihilation of positronium
e) Entangled states and Bell’s theorem
6. Dependence of Amplitude on Position
a) Amplitudes on a line
b) The wave function
c) The Schrödinger equation in one dimension

MAT283

Introduction to Statistics

4.00

Undergraduate

Course description not available.

PHY566

Introduction to String Theory

3.00

Graduate

The aim of this course is to introduce the basic concepts of string theory by applying quantum mechanics to a relativistic string. In this manner the student will deepen his or her understanding of quantum mechanics and will also be able to appreciate the diverse areas of physics in which the mathematical description of a string like object is useful.

PHY578

Introduction to Thin Films

3.00

Graduate

This course covers the crystals structure, defects, bonding, phase diagram, kinetics, diffusion, nucleation and growth, trapping, surface diffusion, growth models, vacuum techniques; thin film deposition techniques: thermal evaporation, e-beam evaporation, sputtering, molecular beam epitaxy, chemical vapor deposition, pulsed laser deposition; thin film properties: materials surface, structural, mechanical, optical, electrical, magnetic properties; thin film based devises and applications.

MAT384

Introductory Econometrics

4.00

Undergraduate

Introductory Econometrics

PHY589

Ion Beam Based Materials Characterization Techniques

3.00

Graduate

Ion accelerator, instrumentations, basic interaction of matter with ions, energy loss process, elastic and non–elastic scatterings, characterization techniques: Rutherford backscattering spectrometry (RBS), Ion channeling, Resonance channeling, Proton induced X-ray emission (PIXE), Elastic recoil detection analysis (ERDA), Nuclear reaction analysis (NRA), pitfalls in ion beam analysis, and radiation safety.

BIO321

IPR, Patent Laws & Bioethics

3.00

Undergraduate

IPR, Patent Laws & Bioethics

BIO307

IPR, Patent Laws and Bioethics

3.00

Undergraduate

Introduction to various Intellectual Property Rights with a special focus on Patent laws, role of IP in research and development, International framework for the protection of IP (TRIPS, PCT, Paris Convention etc.), application of patent law in the domain of biotechnology, patentability: requirements and non-patentable subject matter, statute and rules for the administration of Patent law in India, legal requirements and administrative steps for getting a patent for a biotechnological invention, process flow of grant of a patent, use of databases of (patent and non-patent) for retrieving information to conduct research before filing a patent, understanding the published patent document, interpreting and constructed a patent claim, challenging and revoking a granted patent , Enforcing a patent: remedies available.
Bioethics: ethical concerns of biotechnology research and innovation, other IPRs including, industrial designs, plant breeder’s rights/plant variety protection, IC layout designs, Trade Marks, Geographical indications and Trade Secrets etc. , managing IP assets, case studies and examples on successful grant of patents and study of important case laws involving biotechnological inventions/discoveries, Evaluation and case studies.
Bio-Ethics: General Bio-Ethical Considerations, Ethics in Stem cell research, Ethics in Genetic Engineering, Genetic Testing
Bio-Regulatory Affairs: Definition, History and Need, New Drug Development Process, Drug Regulatory Agencies: US, Europe and India, Regulatory Filing Process for New Drug and Marketing , Good Laboratory Practices (GLP), Good Manufacturing Practices (GMP), Good Clinical Practices (GCP)
Recommended books: Beier, F.K., Crespi, R.S. and Straus, T. Biotechnology and Patent protection-Oxford and IBH Publishing Co. New Delhi. Sasson A, Biotechnologies and Development, UNESCO Publications. Singh K, Intellectual Property rights on Biotechnology, BCIL, New Delhi Indian Patent Act, 1970 Manual of Patent Practice and Procedure, Indian patent Office Patents for Chemicals, Pharmaceuticals and Biotechnology- Fundamentals of Global Law, Practice and Strategy by Philip W. Grubb, Oxford University Press Beier, F.K., Crespi, R.S. and Straus, T. Biotechnology and Patent protection-Oxford and IBH Publishing Co. New Delhi. Sasson A, Biotechnologies and Development, UNESCO Publications. Singh K, Intellectual Property rights on Biotechnology, BCIL, New Delhi

MAT160

Linear Algebra

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics
Overview: Linear Algebra provides the means for studying several quantities simultaneously. A good understanding of Linear Algebra is essential in almost every area of higher mathematics, and especially in applied mathematics. A CAS such as Maxima/Matlab will be used throughout the course for computational purposes.
Detailed Syllabus: Matrices and Linear Systems Vector Spaces and Linear Transformations Inner Product Spaces Determinant Eigenvalues and Eigenvectors, Diagonalization Quadratic Forms and Positive Definite Matrices Applications chosen from: Numerical aspects, Difference equations, Markov matrices, Least squares.
References: Linear Algebra by Jim Hefferon Linear Algebra and its Applications by Gilbert Strang, 4th edition, Cengage. Linear Algebra and its Applications by David C. Lay, 3rd edition, Pearson. Linear Algebra: A Geometric Approach by S. Kumaresan, PHI, 2011. Elementary Linear Algebra by Howard Anton and Chris Rorres, 9th edition, Wiley. Linear Algebra: An Introductory Approach by Charles Curtis, Springer. Matrix Analysis and Applied Linear Algebra by Carl D Meyer, SIAM. Videos of lectures by Prof Gilbert Strang: 18.06 Linear Algebra, Spring 2010. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu

MAT260

Linear Algebra

4.00

Undergraduate

Linear Algebra provides the means for studying several quantities simultaneously. A good understanding of Linear Algebra is essential in almost every area of higher mathematics, and especially in applied mathematics. Detailed Syllabus: 1. Matrices and Linear Systems 2. Vector Spaces and Linear Transformations 3. Inner Product Spaces 4. Determinant 5. Eigenvalues and Eigenvectors 6. Positive definite matrices 7. Linear Programming and Game Theory Matlab will be used in tutorial for computational purposes. Main References: • Linear Algebra and its Applications by Gilbert Strang, 4th edition. • Algebra by Michael Artin, Second edition. Other References: • Linear Algebra: A Geometric Approach by S. Kumaresan, PHI, 2011. • Advance engineering Mathematics by E. Kreyszig, 10th Edition

MAT660

Linear Algebra

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: None. Not open to undergraduates.
Overview: The theory of vector spaces is an indispensable tool for Mathematics, Physics, Economics and many other subjects. This course aims at providing a basic understanding and some immediate applications of the language of vector spaces and morphisms among such spaces.
Detailed Syllabus: Familiarity with sets: Finite and infinite sets; cardinality; Schroeder-Bernstein Theorem; statements of various versions of Axiom of Choice. Vector spaces: Fields; vector spaces; subspaces; linear independence; bases and dimension; existence of basis; direct sums; quotients. Linear Transformations: Linear transformations; null spaces; matrix representations of linear transformations; composition; invertibility and isomorphisms; change of co-ordinates; dual spaces. Systems of linear equations: Elementary matrix operations and systems of linear equations. Determinants: Definition, existence, properties, characterization. Diagonalization: Eigenvalues and eigenvectors; diagonalizability; invariant subspaces; Cayley-Hamilton Theorem. Canonical Forms: The Jordan canonical form; minimal polynomial; rational canonical form.
References: Friedberg, Insel and Spence: Linear Algebra, 4th edition, Prentice Hall India Hoffman and Kunze: Linear Algebra, 2nd edition, Prentice Hall India Paul Halmos: Finite Dimensional Vector Spaces, Springer India Sheldon Axler: Linear Algebra Done Right, 2nd edition, Springer International Edition S. Kumaresan: Linear Algebra: A Geometric Approach, Prentice Hall India

MAT360

Linear Algebra II

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Linear Algebra I (MAT 160)
Overview: In MAT 260 we studied real and complex linear transformations up to the diagonalizability of symmetric operators. In this course we take up vector spaces over arbitrary fields and more advanced results on expressing linear transformations by simple matrices.
Detailed Syllabus: Linear Equations – Systems of linear equations, matrices, elementary row operations and row reduction. Vector spaces – Abstract vector spaces, subspaces, dimension, coordinates. Linear transformations – Matrix representations, change of basis, linear functionals and the double dual, transpose. Determinants – Commutative rings, determinant function, permutations, properties. Canonical Forms – Characteristic values, invariant subspaces, simultaneous diagonalization and triangulation, invariant direct sums, Primary Decomposition Theorem, cyclic subspaces, Rational Form, Jordan Form. Inner Product Spaces – Linear functionals and adjoints, unitary and normal operators, spectral theory.
References: Kenneth Hoffman and Ray Kunze, Linear Algebra, 2nd edition, PHI Learning. Friedberg, Insel and Spence, Linear Algebra, 4th edition, PHI Learning Sheldon Axler, Linear Algebra Done Right, 2nd edition, Springer International Edition Paul Halmos, Finite Dimensional Vector Spaces, 2nd edition, Springer International Edition Paul Halmos, Linear Algebra Problem Book, Mathematical Association of America, 1995.
Past Instructors: Neha Gupta

CHY899

Litterature Seminar

1.00

Graduate

Graduate students from the department present seminars based on current literature in their areas of interest. Other students will be expected to participate actively in these seminars by asking questions. Communicating research findings before an audience of peers is an integral component of a scientist’s career training. This module serves to introduce new students to the art of delivering presentations and hone their verbal communication skills.
The course will be conducted during 1hr each week with input from faculty so that real improvements may be effected.

BIO525

Machine Learning

2.00

Graduate

Machine Learning

MAT394

Machine Learning through R.

4.00

Undergraduate

Course description not available.

CHY351

Macromolecules

3.00

Undergraduate

In this course we will learn cellular macromolecules namely carbohydrates, nucleic acids, proteins and chemical synthesized polymers. As monomers are the key building blocks, we will discuss the chemistry associated with these monomers including nomenclature, stereochemistry, associated chemical reactions and their importance. Classes will be through a combination of lectures, presentations and assignments. Students participation in discussion is required. The assessment will be based on quiz, exams and presentation.
Course Aims
To provide students with basic understanding of macromolecules such as proteins, carbohydrates, nucleic acids, polymers and corresponding monomers To enable students gaining knowledge of cellular macromolecules and polymers in day to day life To see the biomolecules or polymers in the view of atomic level i.e. C, H, N, O To learn about macromolecules, not only from a structural but from an atomic point of view as well To develop students’ skills in chemistry, biochemistry to analyse in scientific way
Learning Outcomes On successful completion of the course, students will be able to: Gain the knowledges and the importance of macromolecules in daily life Formulate a strategy for solving the problems related to macromolecules Know the significance of chemical bonding and their structures which significantly tune the properties and functions Solve chemical problems competently and rationally estimate the solution Learn chemical understanding in biochemistry that will provide solid platform to know advanced biochemistry in next semester Improve presentation skill, innovative thinking,
Curriculum Content Introduction of Macromolecules and Polymers Carbohydrates Introduction Function and importance in chemistry and biology Class of Carbohydrates Monosaccharides: definitions and functions Nomenclature Fischer Projections and D/L notation Open chain and cyclic structure of pentose, hexose sugars Determination of configuration/ absolute, mutarotation Ascending and descending in Monosaccharides Chemical Reactions of Monosaccharides Oligosaccharides, Examples and functions Polysaccharides Homo and hetero Polysaccharides Examples and their functions (Starch, Glycogen, Dextran, Cellulose, Chitin, Alginates) Glycoconjugates: Proteoglycans, Glycoproteins and Glycolipids Structural and Functions of glycoproteins Nucleic Acids (DNA and RNA) Introduction Nucleic Acids Classes of Nucleic acids Building-Blocks Purine and Pyrimidine bases, Sugars and Phosphates Structures, Examples and functions of Nucleosides & Nucleotides Structures of Polynucleotides i.e. Nucleic acids Forces for Stabilities of Base-pairing Primary, secondary structure of DNA Watson and Crick's Model Minor and major grooves in DNA A, B and Z-DNA and their biological relevance DNA Transcription and DNA translation RNA: Basic structure and functions Summary of Nucleic acid Amino acids, peptide and proteins Amino Acids (name, structures, three letter code, one letter code) Common features of Amino acids (AA) Number of carbons in amino acids D, L classification and configurations of amino acids Classification of AA side chains by chemical properties (Polar, non-polar, ionic amino acids) Acid base properties of amino acids (pKa calculations) Ionization of AAs (Zwitter ion, isoelectric point and electrophoresis) Peptide, oligopeptides structures and proteins Reaction of amino acids N terminus and C terminus Ester of carboxylic group, Acetylation of amino group, Complexation with Cu+2 ions Ninhydrin test Post translational modifications (phosphorylation, glycosylation etc.) Preparation of amino acids Strecker synthesis Gabriels phthalimide synthesis Protein Structure and quick overview of primary, secondary, tertiary and quaternary structure Structure determination of peptides N-terminal analysis by Edmann degradation C-terminal (thiohydantoin and carboxypeptidase). Synthesis of simple dipeptides by N-protection (t-butoxycarbonyl and phthaloyl) C-activating group and Merrifield solid phase synthesis. Thermodynamics and Kinetics of Proteins, Protein Evolution Summary of Proteins Polymers Basic concepts in Polymer Chemistry Nomenclature Classification Structure and properties of Polymers Natural Occurring Polymers/synthetic polymers Polymer synthesis Step-growth polymerization Chain Growth Polymerization Free Radical Ionic (Cationic and Anionic) Molecular weight determination Number average and weight average MW Measurement of Number average MW Polymer morphology Amorphous state and rheology Glass transition temperature Crystallinity Liquid crystallinity Polymer properties (Structure property correlation) Mechanical Properties Thermal Stability Polymer degradation Chemical resistance Molecular weight and intermolecular force Physical and chemical crosslinking Non-linear optical properties Applications of polymers
Prerequisites: CHY221.

CHY142

Main Group Chemistry

3.00

Undergraduate

The s–block elements and the noble gases: The s–block elements of Gr – I, Gr – II, their general electronic configuration, trends in I. P., ionic radii; reaction with H, O, N, C, and hydrolytic behaviour of the products. General metallurgical consideration of these elements. Differences of Li and Be from other members of their groups (the diagonal relationship). Isotopes of H, industrial preparation of deuterium, its properties, reactions and uses; ortho–para – hydrogen. Separation and uses of the noble gases; compounds of Kr and Xe – preparation, properties, structures.
The p–block elements: Gr. III. (a) The general group properties * (b) Boron Chemistry – preparation, properties of boranes; Structure and bonding of diborane, Boranine Boron nitrides; electron deficient nature of hydrides, halides and their polymerisation. Gr. IV (a) The general group properties * (b) Aspects of C and Si chemistry the difference of C and P from the rest of the group elements. Preparation, properties, u ses of the fluoroecarbons, the silanes and the silicones. Gr. IV (a) The general group properties * (b) N and P – Chemistry: The presence of lone pair and basicity of trivalent compounds; trends in bond angles of hydrides, halides, preparation, properties, structures and bonding of hydrazine, hydroxylamine, hydrazoic acids, the oxides and oxyacids of N, P; d – orbital participation in P–compounds. Gr. VI (a) The general group properties * (b) S–Chemistry – Preparation, properties, structures and bonding of the oxides, oxyacids (including the thionous, thionic and per–acids), halides, oxy–halides and poly sulphides; d–orbital participation in S–Compounds. Gr. VII (a) The general group properties * (b) The halogen hydrides, their acidity; Preparation, properties, structures and bonding of the oxides and oxy acids; the inter halogen compounds including polyhalides, the pseudohalides – including their preparation, properties, structures. The cationic compounds of iodine.
* Note : General group properties : – For each group this includes discussion, on a comparative basis, of major physical and chemical properties, e.g. – i) Physical properties – the electronic configuration; ionisation potential / electron affinity; m.p. – b.p. ; ionic/covalent radii etc. ii) Chemical properties – Various oxidation states and their relative stability (redox behaviour in solution, wherever applicable), higher stability of the higher oxidation states for the heavier members; gradual changes of the ionic/covalent character of the compounds from lighter to heavier members; the relative acidity, amphoteric, basic characteristics of the oxides and formation of oxocations (wherever applicable); examples of compounds in all the oxidation states, in particular, the unusual (rare) oxidation states being stabilised through coordination; hydrides, halides (including the halo complexes) and their hydrolytic behaviour; dimerization and/or polymerization through halogen bridges (wherever applicable) etc. iii) Common natural sources of the elements.
Acid-Base / Ionic Equilibrium / Non-aqueous solvents, reduction.
BOOKS: Inorganic Chemistry: Duward Shriver and Peter Atkins. Inorganic Chemistry: Principles of Structure and Reactivity by James E. Huheey, Ellen A. Keiter and Richard L. Keiter. Inorganic Chemistry: Catherine Housecroft, Alan G. Sharpe. Atkins' Physical Chemistry, Peter W. Atkins, Julio de Paula. Cotton F.A. and Wilkinson, G. Advanced Inorganic Chemistry Sharpe, A.G. Inorganic Chemistry Douglas, B.; McDaniel, D.H.; Alexander, J.J. Concepts and Models of Inorganic Chemistry Greenwood, Norman, and A. Earnshaw. Chemistry of Elements. Oxford, UK: Elsevier Science, 1997. ISBN: 9780750633659
Other reading materials will be assigned as and when required.
Prerequisite: Chemical Principles (CHY111).

PHY451

Materials Characterization Techniques

3.00

Undergraduate

This course covers the interaction of matter with photons, electrons and charge particles, and the related characterization techniques. The fundamentals of each technique will be discussed with suitable examples.

PHY574

Materials Characterization Techniques I

3.00

Graduate

This course covers the basic interaction of matter with photons, elastic and non–elastic scatterings, characterization techniques: Ultra-violet photoelectron spectroscopy (UPS), Raman spectroscopy, Extended X-ray absorption fine structure (XAFS), X-ray fluorescence, Fourier transform infrared spectroscopy (FTIR), UV- Visible spectroscopy, Photoluminescence (PL), Electroluminescence (EL) and Cathode luminescence (CL).

MAT601

Mathematical Computing

3.00

Graduate

Mathematical Computing

MAT202

Mathematical Methods

3.00

Undergraduate

Mathematical Methods

MAT103

Mathematical Methods I

4.00

Undergraduate

Core course for all B.Tech. Optional for B.Sc. (Research) Chemistry. Not open as UWE.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics.
Overview: In this course we study multi-variable calculus. Concepts of derivatives and integration will be developed for higher dimensional spaces. This course has direct applications in most engineering applications.
Detailed Syllabus: Review of high school calculus. Parametric curves (Vector functions): plotting, tangent, arc-length, polar coordinates, derivatives and integrals. Functions of several variables: level curves and surfaces, differentiation of functions of several variables, gradient, unconstrained and constrained optimization. Double and triple integrals: integrated integrals, polar coordinates, cylindrical and spherical coordinates, change of variables. Vector fields, divergence and curl, Line and surface integrals, Fundamental Theorems of Green, Stokes and Gauss.
References: A Banner, The Calculus Lifesaver, Princeton University Press. James Stewart, Essential Calculus – Early Transcendentals, Cengage. G B Thomas and R L Finney, Calculus and Analytic Geometry, Addison-Wesley. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley.
Past Instructors: Ajit Kumar, Sneh Lata

MAT201

Mathematical Methods I

4.00

Undergraduate

Mathematical Methods I
COURSE DESCRIPTION :
In this course we study multi variable calculus. Concepts of derivatives and integration will be developed for higher dimensional space. This course has direct applications in most of engineering applications.
ASSESSMENT SCHEME :
• Midterm 1 (20 %)
• Midterm 2 (20 %)
• End term ( 30 % )
• Tutorial quizzes ( 20 %)
• HW 10 %

MAT104

Mathematical Methods II

4.00

Undergraduate

Core course for all B.Tech. Programs. Optional for B.Sc. (Research) Chemistry. Not available as UWE.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII Mathematics
Overview: We will study Ordinary Differential Equations which are a powerful tool for solving many science and engineering problems. This course also covers some basic linear algebra which is needed for systems of ODEs.
Detailed Syllabus: First order ODEs: separable, exact, linear Second order ODEs: homogeneous and nonhomogeneous linear, linear with constant coefficients, Wronskian, undetermined coefficients, variation of parameters Laplace transform: definition and inverse, linearity, shift, derivatives, integrals, initial value problems, time shift, Dirac’s delta function and partial fractions, convolution, differentiation and integration of transform Matrices: operations, inverse, determinant, eigenvalues and eigenvectors, diagonalization Systems of ODEs: superposition principle, Wronskian, constant coefficient systems, phase plane, critical points, stability
References: James Stewart, Essential Calculus – Early Transcendentals, Cengage. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley.
Past Instructors: Ajit Kumar, Neha Gupta

MAT203

Mathematical Methods II

4.00

Undergraduate

Mathematical Methods II

MAT205

MATHEMATICAL METHODS III ? Probability and Statistics

3.00

Undergraduate

Core course for B.Tech. except Computer Science. Not available as UWE.
Credits (Lec:Tut:Lab)= 3:0:0 (3 lectures weekly)
Prerequisites: MAT 103 (Mathematical Methods I)
Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course introduces you to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions.
Detailed Syllabus: Probability: sample space and events, classical and axiomatic probability, permutations and combinations, conditional probability, independence, Bayes’ formula Random Variables: discrete and continuous probability distributions, mean and variance, binomial and Poisson, normal, joint distributions, covariance, correlation and regression (linear) Mathematical Statistics: exploring data, random samples, point estimation, Central limit theorem, Maximum likelihood, chi-square, t and F-distributions, confidence intervals, hypothesis testing
References: Advanced Engineering Mathematics by Erwin Kreyszig, Wiley. Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross, 2nd edition, Harcourt Academic Press. Theory and Problems of Beginning Statistics by L. J. Stephens, Schaum’s Outline Series, McGraw-Hill John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011.
Past Instructors: Charu Sharma, Niteesh Sahni, Suma Ghosh

MAT150

Mathematical Modelling

4.00

Undergraduate

Mathematical modeling is the science and art of addressing real-world problems many other scientific disciplines. The practice of mathematical modeling inherently captures the interdisciplinary nature of the real-world phenomena, and thus appropriate for students from all disciplines. This course is designed to introduce students to fundamental concepts and methods of mathematical modeling, through a hands on, project-oriented approach. The applications studied will motivate the mathematics covered, contrary to traditional math courses.
Core course for B.Sc. (Research) programs in Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Class XII mathematics

MAT686

Mathematics for Data Analytics

5.00

Graduate

Mathematics for Data Analytics

MAT725

Matrix Analysis

4.00

Graduate

Matrix Analysis

MAT620

Measure and Integration

4.00

Graduate

Measure and Integration

MAT420

Measure and Probability

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 220 Real Analysis I. And one of MAT 184 Probability or MAT 205 Mathematical Methods III or CSD209.
Overview: This sequel to an introductory course on probability provides a rigourous look at the subject which opens up many more applications, especially to stochastic processes. This course is compulsory for students opting for the Specialization in Mathematical Finance.
Detailed Syllabus: Introduction to measures and probability triples Random variables: independence, limit events, expectation Inequalities and convergence, Laws of large numbers Distributions, change of variables Limit Theorems, Differentiation of expectation, Moment generating functions, Fubini’s theorem Weak convergence Characteristic functions, Central Limit Theorem and generalizations, Method of Moments Lebesgue and Hahn decompositions Conditional probability and expectation
References: A First Look at Rigorous Probability Theory by J S Rosenthal, 2nd edition, World Scientific Publishing, 2006. Measure, Integral and Probability by M Capinski and E Kopp, 2nd edition, Springer. Probability and Random Processes by G R Grimmett and D R Stirzaker, 2nd edition, Oxford University Press.
Past Instructors: Debashish Bose

CHY324

Medicinal Chemistry

3.00

Undergraduate

CHY 324, Spring 2019
Instructor: Dr. Goutam Chowdhury
3 Credits
In this course we will address various issues regarding drugs and its role inside a cell. We will learn what are drugs and their different types? How do drugs work? What causes side effects? How do drugs become resistance? These and other questions will be considered in this course. We will learn the chemistry and biochemistry necessary to understand the mechanism of drug action and the process of drug discovery and development. Students will investigate what is known about active ingredients in natural remedies. Social, ethical and economic issues related to drugs will be addressed. Instruction will be through a combination of group discussions, reading assignments, projects, video presentations and lectures. Students are expected to do library research, read papers, and present discussion in class.
Course Evaluation
2 Take Home Quizzes: 10%
1 Assignment & 1 Presentation: 10% each.
Content: Drugs and the body What are drugs? What are the common drug targets? Why do they work? How are drugs transported? Types of Drugs Drug Targets DNA Damaging agents Enzymes, mechanism based inhibitors, covalent inhibitors Receptors Drug Discovery and optimization Generation of lead compounds Lead Optimization Preclinical studies Clinical trials Drug Metabolism Phase I Cytochrome P450 Aldehyde dehydrogenase Monoamine oxidase Phase II GST UGT Transporters Drug toxicity Reactive intermediate Adverse effects Drug-drug interaction Polymorphism and its effect on drug action/toxicity Structure-activity relationships Mechanism of action Painkillers and opioids (e.g. morphine) Antidiabetic Antibiotics Anticancer NSAIDS Statins Blood Thinners Antacids/Proton pump inhibitors Antivirals Antidepressant/antipsychotic Synthesis and biosynthesis of drugs Combinatorial chemistry

CHY501

Medicinal Chemistry

3.00

Graduate

The objectives of the course are to give synthetic chemists, biochemists and pharmacologists a broad and balanced introduction to the background, general principle, concepts and tools of medicinal chemistry. The course will also highlight the new understanding of the factors governing modern drug discovery. Case histories of drug discovery will be explained with particular examples along with their biochemistry, pharmacology and toxicology, drug metabolism and disposition. Modern preclinical drug research is thus the focus of the course, which combines lectures, tutorials and practical work.
This course will cover the following main topics: Introduction to Medicinal Chemistry Biological Mechanisms Pharmacokinetics and Drug Metabolism Screening of New Compounds Molecular Biology in Medicinal Chemistry Exploiting a Chemical Lead Combinatorial Chemistry and Molecular Diversity Case Histories of Drug Discovery Toxicology in Drug Discovery Pharmaceutical Considerations in Drug Development Structure-guided Drug Design Diversity oriented synthesis (DOS) Fragment based drug design (FBDD) Physical Properties and Quantitative Structure-Activity Relationships Hints and Tips in Medicinal Chemistry
RECOMMENDED READING(S): An Introduction to Medicinal Chemistry (4th Ed, 2009) by Graham L. Patrick, Oxford University Press,.ISBN 978-0-19-923447-9. Fundamentals of Medicinal Chemistry (1st Ed, 2003) by Gareth Thomas, John Wiley & Sons Inc. ISBN 0-470-84307-1. The Organic Chemistry of Drug Design and Drug Action (2nd Ed, 2004) by Richard Silverman Academic Press. ISBN 0-12-643732-7. Analogue-Based Drug Discovery (1st Ed, 2006) by J. Fischer and C. R. Ganellin, Wiley-VCH. ISBN 3-527-31257-9. Contemporary Drug Synthesis (1st Ed, 2004) by J. Jack Li, Douglas S. Johnson, Drago R. Sliskovic and Bruce D. Roth. Wiley-Interscience.ISBN 0-471-21480-9.

MAT422

Metric Spaces

4.00

Undergraduate

Metric Spaces

BIO524

Microbial Technology

3.00

Graduate

Microbial Technology

BIO202

Microbiology

3.00

Undergraduate

History, evolution and development of microbiology. Diversity of microorganisms- scope and importance. Characterization and identification of bacteria based on morphology, physiology, biochemistry, ecology, chemotaxonomy and molecular systematics. Bergey’s manual – classification of bacteria, fungi, algae and archea.
The study of microbial structure by use of light, phase, fluorescent and electron microscopy. Preparation and staining of specimens. Microbial nutrition, nutritional types, requirements, design and types of nutrient media, microbial growth- principles, kinetics and methods. The influence of environmental factors on growth. Microbial control- definition, methods of sterilization, physical methods and chemical agents. Isolation of pure cultures- spread plate, streak plate and pour plate.
Classification of general features of cyanobacteria and importance of Spirulina, Rickettsia, Chlamydia, Mycoplasma, Archaebacteria. Methanogenic and Halophilic bacteria. General account and economic importance of algae and fungi. Clinically important bacteria and protozoans. Distribution of microbes in nature.
History and development of viruses. Nature, origin and evolution of viruses. Nomenclature, recent classification (ICTV) structure and characteristics of viruses. Isolation, cultivation and identification of viruses. Biological and chemical properties of viruses. Animal, plant and bacterial viruses and their interactions with hosts. Virus replication and genome expression. Process of infection- animal, plant and bacterial cells. Molecular mechanisms of viral pathogenesis with respect to poliovirus, rotavirus, herpes virus, retroviruses.
Transmission of viruses (Direct and Indirect) persistence of viruses and their mechanism. Purification and inactivation of viruses- physical and chemical methods. Virus ecology and epidemiology, scope and concepts of epidemiology. Bacterial recombination, transformation, conjugation and transduction. Mapping of prokaryotic genome and tetrad analysis, insertion sequences, transposons and mechanism of transposition, retro transposons, plasmids.
Recommended Books: Microbiology: Concepts and Applications, Pelczar, M. J., Chan, E. C. S., Krieg, N. R., Pub: Mcgraw hill International Book Company. Brock Biology of Microorganisms (9th edition), Brock, T. D., Madigan, M. T., Pub: Prentice Hall International. Introduction to Microbiology, Ross, Pub: Addison-Wesley Educational Publishers. Prescot’s Microbiology, Willey, J., Sherwood, L., Woolverton, C., Pub: MacGraw Hill. Microbiology: An Introduction, Oortora, G. J., Funke, B. R., Case, C. L., Pub: Pearson Benjamin Cummings.

CHY313

Molecular Spectroscopy

3.00

Undergraduate

In this course, Rotational, Vibrational, UV-Visible, Fluorescence, Mass and NMR spectroscopy methods will be taught. Chemists often adopt these techniques to identify the electronic and molecular structures of chemical and biochemical systems. Students will achieve a knowledge about the behaviour of molecular systems in presence of an external electromagnetic field in different frequency ranges. The principle along with comprehensive theories for each of the spectroscopy method will be discussed in the classes.
Course Aims
The main aim of this course is to provide students a concept about how these commonly used molecular spectroscopy techniques work, a theoretical knowledge of each of these methods and their usage in molecular and electronic structure determination.
Learning Outcomes
On successful completion of the course, students will be able to
(i) explain the behaviour of molecular systems in external electromagnetic field.
(ii) understand the principles and theories of rotational, vibrational, UU-Vis, Fluorescence, Mass and NMR spectroscopy methods.
(iii) interpret the molecular spectra and find molecular properties from molecular spectra.
Curriculum Content
Introduction: Meaning of spectroscopy and use of different spectroscopic tools to understand diverse applications.
Origin of a spectra: Revision of electromagnetic spectrum and Energy associated with them, factors affecting line broadening and intensity of lines, selection rules.
Rotational spectroscopy: Rotational spectroscopy of diatomic molecules, Effect of isotopic substitution, Non-rigid rotator, Application of rotational spectroscopy.
Vibrational spectroscopy: Vibrational spectroscopy, vibration-rotation spectrum, breakdown of Born-Oppenheimer Approximation, vibration of polyatomic molecules, applications.
UV-vis spectroscopy: Theory of UV-Vis/electronic spectroscopy: Lambert-Beer’s Law, Woodward-Fieser Rules, Chemical analysis by electronic spectroscopy.
Fluorescence spectroscopy: Introduction to fluorescence spectroscopy: Jablonski diagram, Frank-Condon principle, Stokes shift, solvent relaxation, solvatochromism, excimer and exciplex formation, quantum yield & life time. Spin-orbit coupling.
Mass spectroscopy: Introduction to mass spectroscopy: isotope effect, fragmentation patterns, applications.
Nuclear Magnetic Resonance (NMR): Theory of NMR, isotopes, Spinning nucleus, effect of an external magnetic field, precessional motion and precessional frequency, and the field strength, temperature effect, Boltzman distribution, origin of chemical shift and its implication in magnetic field strength, anisotropic effect, proton NMR spectrum, carbon NMR, concept of multi-dimensional NMR, influence of restricted rotation, fluxiaonal molecules, conformational dynamics, solvents used in NMR, solvent shift and concentration and temperature effect and hydrogen bonding, spin-spin splitting and coupling constants, chemical and magnetic equivalence in NMR, factors influencing the coupling constant, geminal coupling, vicinal coupling, heteronuclear coupling, deuterium exchange.
Tutorials: Basics of Spectroscopy. Origin of Spectra and factors affecting the spectral line and intensity. Rotational Spectroscopy. IR Spectroscopy tutorial (characteristic absorption of common classes of organic compounds) IR Spectroscopy tutorial (application of IR spectroscopy to isomerism, identification of functional groups) IR Spectroscopy tutorial (effects of water and hydrogen bonding) UV Spectroscopy tutorial (calculation of for conjugated organic compounds) UV Spectroscopy tutorial ( for α, β unsaturated organic compounds and solvent effects) Role of fragmentation and rearrangement reaction during mass spectroscopic analysis. Application of shielding and deshielding effects. Chemical shift and coupling constants of alkane. Chemical shift and coupling constants of alkenes and alkynes. Assignment of 1H and 13C NMR signals of aromatic compounds. How to determine enantiomeric excess by NMR spectroscopy. Interpretation of 2D NMR and it’s application for the characterization of organic molecules.
Recommended Books: Fundamentals of Molecular Spectroscopy (McGraw-Hill 1995) by C. N. Banwell and E.M. McCash Atkins' Physical Chemistry (Oxford University Press 2010) by Peter Atkins and Julio De Paula Spectrometric Identification of Organic Compounds (John Wiley & Sons 2005) by R. M. Silverstein and F. X. Webster. Basic One and Two – Dimensional NMR Spectroscopy (Wiley – VCH 2011) by Horst Friebolin. Organic Spectroscopy (Palgrave Macmillan 2008) by William Kemp. Organic Spectroscopy (Springer 2005) by L D S Yadav
Prerequisites: Physical Methods in Chemistry (CHY213); Chemical Applications of Group Theory (CHY212).
Co-requisite: Chemical Binding (CHY311).

CHY120

Molecules and Medicine

3.00

Undergraduate

Since the time of Hippocrates until modern days, human being has explored several means of alleviating pain and curing disease. There have been pathbreaking discoveries resulting in the development of medicines of immense benefit. Present day research of inventing novel molecules constantly adds to the repertoire of drugs available to counter ill-health.
We will begin with a short introduction (which discusses fundamental organic chemistry followed by development and testing of drugs). Next we will explore the discovery and development of a range of drugs and medicines that relieve pain, effect cures and reduce the symptoms of ill-health. We will discuss how drugs interact with and affect their target areas in the human body. There are online videos to help you to understand the three-dimensional structures and shapes of the molecules concerned and to develop an understanding of how the drugs work.
Books:
Scientific journals will be provided
Prerequisite: None.

CHY321

Named Organic Reactions and Mechanism

3.00

Undergraduate

C-C bond forming reactions and their mechanism focusing on Carbanion alkylation, Carbonyl addition and carbonyl substitution reactions, Conjugate addition reactions (1,2-addition & 1,4- addition), Reactions of alkene, alkynes and aromatics. C-N and C-O bond forming reactions and their mechanism. Glycosylation reactions. Oxidation and reduction reactions, Rearrangement reactions, Free radical reactions. Photochemical reactions and mechanism, Norrish type I and II reactions, Electrophilic substitution reactions. These types of reactions will be taught under
following name reactions. C-C Bond forming reactions and Mechanism - Grignard Reaction, Aldol Condensation, Diels Alder Reaction, Ring Closing Metathesis, Heck Reaction, Negishi Reaction, Suzuki Reaction, Benzoin condensation, Reformatsky reaction, Ugi reaction, Wittig reaction, Morita-Baylis-Hillmann Reaction. C-N Bond forming reactions and Mechanism - Ullmann reaction, Buchwald and Hartwig reaction, Metal free C-N bond formation reactions, Fisher Peptide synthesis, Hetero Diels Alder reaction, Click reaction. C-O Bond forming reactions and Mechanism - Allan-Robinson Reaction, Baeyer-Villiger Reaction, Fisher Oxazole synthesis, Ferrier Reaction, Glycosidation reaction, Sharpless asymmetric Epoxidation. Oxidation, Reduction reactions and Mechanism - Bayer-Villeger oxidation, Dess-Martin periodinane oxidation, Swern Oxidation, Corey–Kim oxidation, Jones Oxidation, Luche reduction, Birch reduction, Gribble reduction. Rearrangement Reactions and Mechanism - Benzilbenzilic acid rearrangement, Pinacol Pinacolone rearrangement, Fries rearrangement, Amadori rearrangement, Beckmann rearrangement, Demzanov rearrangement, Payne rearrangement, Wallach rearrangement, Ferrier rearrangement Conjugate addition reactions and Mechanism - 1,2-addition reaction, 1,4-addition reaction, Reformatsky reaction, Prins reaction, Michael reaction Photochemical reactions and Mechanism - Norish type I reaction, Norish type II reaction
Prerequisites: Basic Organic Chemistry-II (CHY221).

CHY542

Nano and Supramolecular Chemistry

3.00

Graduate

This course will help to understand the basic concept of supramolecular chemistry (non-covalent interactions) and their quantification in molecular recognition process. It will cover the area of non-covalent interaction, multiple hydrogen bonding (H-B) stems, self-assembly, acyclic receptors for neutral and charged guests, macrocycles and macrobicycle, cryptands and macropolycycles, cyclodextrin.
The chemistry of nanomaterials will deal with the basic understanding of the atomic and electronic structures of different nanomaterials such as clusters and nanoparticles of inorganic materials (metals and semiconductors), fullerenes, nanotubes, nanowires, and two dimensional systems such as graphene. Aspects related to optical, magnetic and vibrational properties of nanomaterials as well as the development of nanomaterials will be covered.
Text Book:
Supramolecular Chemistry Concept and Perspective: Jean-Marie Lehn, VCH, Weinheim, 1995
Reference Book:
Supramolecular Chemistry: J. W. Steed and J. L. Atwood, John Wiley and Sons, 2009
The references to nanomaterials will be original journal papers and review articles in journals and edited volumes.
Other reading materials will be assigned as and when required.

PHY551

NanoMaterial and NanoPhysics

3.00

Graduate

This is an interdisciplinary advanced level Ph.D. course in which various nanomaterials processing techniques, including chemical and physical vapor deposition, lithography, self-assembly, and ion implantation will be introduced. Tools commonly used to characterize nanomaterials will be introduced. The structural, mechanical, optical and electronic properties which arise due to nano-scale structure will be discussed from the point of view of nano-scale devices and application.

BDA690

Network Analytics

3.00

Graduate

Network Analytics

BIO520

NGS: Concepts, Methods & App.

3.00

Graduate

Next Generation Genomics: Concepts, Methods and Applications

MAT809

Non Negative Matrices

4.00

Graduate

Non Negative Matrices

PHY415

Non-linear dynamics

3.00

Undergraduate

Nonlinear dynamics will deal with fundamental properties of nonlinear systems and the question of non-integrability.
This course provides a broad introduction and familiarity to the field of nonlinear dynamics and chaos. It takes an intuitive approach and focuses on both the analytical and the computational tools that are important in the study of nonlinear dynamical systems.

MAT740

Number Theory

4.00

Graduate

Number Theory

MAT680

Numerical Analysis & Computer programming

4.00

Graduate

Credits: 4 (3 lectures and 2 lab hours weekly)
Prerequisites: None. Not open for undergraduates.
Overview: This course takes up the problems of practical computation that arise in various areas of mathematics such as solving algebraic or differential equations. The focus is on algorithms for obtaining approximate solutions, and almost half of the course will be devoted to their implementation by computer programs in MATLAB.
Detailed Syllabus: Solving equations: Iterative methods, Bisection method, Secant method, and Newton-Raphson method. Solving Linear systems: Gaussian Elimination and pivoting Computing eigenvalue and eigenvector: Jacobi method Curve fitting Solution of ODEs and systems: Runge-Kutta method, Boundary value problems, Finite Difference Method Solutions of PDEs
References: Numerical Methods using Matlab, by John H. Mathews and Kurtis D. Fink, 4th edition, PHI, 2009. An Introduction to Numerical Analysis, by E. Suli and D. Mayers, Cambridge University Press. Numerical Analysis, by Rainer Kress, Springer, 2010. Introduction to Numerical Analysis, by J. Stoer and R. Bulirsch, 3rd edition, Springer, 2009.

MAT280

Numerical Analysis I

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab) = 3:0:1 (3 lectures and 1 two-hour lab weekly)
Prerequisites: Class XII Mathematics
Overview: Numerical Analysis takes up the problems of practical computation that arise in various areas of mathematics, physics and engineering. The focus is on analyzing the numerical methods and algorithms for obtaining approximate solutions, error estimates and rate of convergence, and implementation of computer programs.
Detailed Syllabus: Solving Equations: Iterative methods, Bisection method, Secant method, Newton-Raphson method, Rates of convergence, Roots of polynomials. Interpolation: Lagrange and Hermite interpolation, Interpolating polynomials using difference operators. Numerical Differentiation: Methods based on interpolation, methods based on finite difference operators. Numerical Integration: Newton-Cotes formula, Gauss quadrature, Chebyshev’s formula. Systems of Linear Equations: Direct methods (Gauss elimination, Gauss-Jordan method, LU decomposition, Cholesky decomposition), Iterative methods (Jacobi, Seidel, and Relaxation methods) Labs: Computational work using C, Python or Matlab.
References: E. Suli and D. Mayers, Introduction to Numerical Analysis, Cambridge University Press, 2003. R.L. Burden and J.D. Faires, Numerical Analysis, Cengage Learning, 9th Edition, 2010. M.K. Jain, S.R.K. Iyengar, and R.K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Ltd., 1999. J.H. Mathews and K. Fink, Numerical Methods using Matlab, PHI Learning, 4th Edition, 2003.

MAT380

Numerical Analysis II

4.00

Undergraduate

Course description not available.

MAT782

Numerical Differential Equations

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 680 (MAT 280 for undergraduates)
Overview:
Detailed Syllabus: Review of numerical techniques for Linear System of equations, Review of Numerical Differentiation and Integration: Mid-point rule, Trapezoidal rule, Simpson's rule, Richardson improvement, variable steps, errors and convergence of above methods. Numerical ODE: Initial Value Problems (Euler methods, Heun's Method, Taylor Series Method, Runge Kutta method), Boundary value problems (Shooting Method). Numerical PDE: Finite difference methods for 2 dimension parabolic, hyperbolic, and elliptic PDEs. Eigenvalue Problems: Power Method, Jacobi's method, Householder's method Programming: Matlab, C++
References: Numerical Methods using Matlab, John H. Mathews and Kurtis D. Fink, 4th edition, PHI Learning, 2005. Introduction to Numerical Analysis, J. Stoer and R. Bulirsch, 3rd edition, Springer, 2002.

MAT692

Numerical Linear Algebra

4.00

Graduate

Numerical Linear Algebra

MAT694

Numerical PDE

4.00

Graduate

Numerical PDE

MAT689

Operations Research

3.00

Graduate

Operations Research

MAT785

Optimal control of systems gov

4.00

Graduate

Optimal control of systems governed by PDEs

MAT688

Optimization

4.00

Graduate

Optimization

MAT388

Optimization I

4.00

Undergraduate

A Major Elective for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 160 (Linear Algebra) or MAT 104 (Mathematical Methods II)
Overview: Optimization deals with the problem of establishing the best & worst cases for a given situation. This course deals mostly with the special case of linear programming, which is commonly applied to problems of business and economics as well as industrial problems in transportation, energy and telecommunication.
Detailed Syllabus: Mathematical modeling and optimization problem formulation Application of optimization (linear case) Geometry of linear optimization Simplex method Duality theory Sensitivity analysis Robust optimization Graphs and Network flow problems Discrete optimization or Integer programming formulations Non-linear optimization – introduction and applications
Main References: Linear Programming by G. Hadley, Narosa, 2000 Understanding and Using Linear Programming by J. Matousek and B. Gärtner, Springer, 2006 Introduction to Linear Optimization by D. Bertsimas and J. Tsitsiklis, Athena Scientific, 1997 Theory of Linear and Integer Programming by A. Schrijver, Wiley, 1998 Operations Research: An Introduction by H. Taha, Pearson, 2012
Past Instructors: Samit Bhattacharyya

MAT430

Ordinary Differential Eqns.

4.00

Undergraduate

Overview Ordinary Differential Equations are fundamental to many areas of science. In this course we learn how to solve large classes of them, how to establish that solutions exist in others, and to find numerical approximations when exact solutions can’t be achieved. Further, many phenomena which undergo changes with respect to time or space can be studied using differential equations. In this course we will also see many examples of mathematical modeling using differential equations.

MAT230

Ordinary Differential Equations

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 101 Calculus I or MAT 103 Mathematical Methods II
Overview: Ordinary Differential Equations are fundamental to many areas of science. In this course we learn how to solve large classes of them, how to establish that solutions exist in others, and to find numerical approximations when exact solutions can’t be achieved. Further, many phenomena which undergo changes with respect to time or space can be studied using differential equations. In this course, we will also see many examples of mathematical modeling using differential equations.
Detailed Syllabus: First Order ODEs: Modelling, Geometrical Meaning, Solution techniques Second and Higher Order Linear ODEs: Modelling, Geometrical Meaning, Solution techniques Numerical Techniques Existence of Solutions of Differential Equations Systems of ODEs: Phase Plane and Qualitative Methods Laplace Transforms Series Solutions
References: Erwin Kreyszig, Advanced Engineering Mathematics, 9th edition, Wiley India, 2012. G.F. Simmons and S. Krantz, Differential Equations: Theory, Technique, and Practice, McGraw Hill Publishing Company, 2006. J. Polking, D. Arnold, A. Boggess, Differential Equations, Pearson, 2005. C. Henry Edwards and David E. Penney, Differential Equations and Boundary Value Problems: Computing And Modeling, 3rd edition, Pearson, 2010. Hirsch, Morris W., Stephen Smale, and Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press, 2012.
Past Instructors: Ajit Kumar

CHY322

Organic Reaction and Synthesis

3.00

Undergraduate

COURSE CONTENT: Electrophilic addition to carbons Electrophilic aromatic substitution Common heterocycles and their reactions Electrophilic addition to carbon-carbon multiple bonds. Rearrangement reactions Migration to C, N, O and B Free radical rearrangements Anion rearrangement Sigmatropic rearrangements Oxidation and Reduction reactions Oxidation/Reduction of carbonyls Reductive elimination and fragmentation Olefin reduction Reductive deoxygenation of carbonyl groups Chemoselective oxidation and reduction reactions of functional groups Cycloaddition, unimolecular rearrangement and thermal eliminations Name reactions and mechanism Applications and limitations of the major reactions in organic synthesis Application in natural product synthesis Literature review Reaction involving transition metals Name reactions and mechanism, Applications and limitations of the major reactions in organic synthesis. Application in natural product synthesis Literature review
Each topic will end with a discussion section, where student participation is important.
Prerequisites: Basic Organic Chemistry-II (CHY221).

CHY421

Organic Synthesis

4.00

Undergraduate

a. Nucleophilic Reactions
i. Alkylation of nucleophilic carbon intermediates.
ii. Reaction of carbon nucleophiles with carbonyl group.
iii. Functional group interconversion by nucleophilic substitution.
b. Electrophilic addition to carbons
i. Electrophilic aromatic substitution,
ii. Electrophilic addition to carbon-carbon multiple bonds.
c. Reduction
i. Reduction of carbonyls.
ii. Reductive elimination and fragmentation.
iii. Olefin reduction
iv. Reductive deoxygenation of carbonyl groups
d. Cycloaddition, unimolecular rearrangement and thermal eliminations
i. Name reactions and mechanism,
ii. Applications and limitations of the major reactions in organic synthesis.
iii. Application in natural product synthesis
iv. Literature review
e. Reaction involving transition metals
i. Name reactions and mechanism,
ii. Applications and limitations of the major reactions in organic synthesis.
iii. Application in natural product synthesis
iv. Literature review
Note. Each topic will end with a discussion section, where student participation is important and will have direct implication in there grade

CHY323

Organometallic Chemistry

3.00

Undergraduate

The course will discuss various organometallic compounds involving Pd, Pt, Cr, Mo, Mn, their various complexes with several organic ligands and their application in the synthesis of heterocycles and natural products. The course will also cover all the name reactions involving organometallics. Since the advent of Pd as a suitable metal for C-C bond formation along with Ru-in Grubbs Metathesis the present pharmaceutical industry relies heavily on organometallics. Nearly 40% of the reactions in the lab involve organometallics. The intricacies of the reactions, the subtlety of the condition in the reactions involving organometallic compounds requires utmost understand of the mechanism of the reactions. Hence this course will provide an in-depth understanding of organometallic reactions and their applications.
Reference Books: The Organometallic Chemistry of the Transition Metals (6th Edition) by Robert H. Crabtree. Organotransition Metal Chemistry: From Bonding to Catalysis; 1st edition (10 February 2010) by John F. Hartwig. Basic Organometallic Chemistry: Concepts, Syntheses and Applications (Paperback) 2nd edition by B.D. Gupta, Anil J. Elias.

CHY558

Organometallic Chemistry

3.00

Graduate

Organometallic Chemistry

MAT330

Partial Differential Equations

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 102 Calculus II or MAT 103 Mathematical Methods I. MAT 230 Ordinary Differential Equations or MAT 104 Mathematical Methods II.
Overview: Many physics principles like conservation of mass, momentum, energy, when applied to real life scenarios, take the form of PDEs. In this course we will learn how basic physics concepts together with simple calculus translate into mathematical models of many engineering problems in the form of PDEs. We will learn some well-known techniques to solve these problems in simple settings. We will also learn approximation techniques which will be needed in cases where it is impossible to get analytical solutions.
Detailed Syllabus:
Essentially Chapters 1, 2, 4, 5, 6, and 8 of the book by Strauss. This material will be supplemented with exercises from other prescribed texts and Matlab exercises. The list of topics covered is: Definition of PDEs, well-posedness, initial value and boundary value problems Examples of PDEs, classification of PDEs Wave equation, diffusion equation Source terms Boundary conditions and their impact on solution Fourier Series and their use in solving PDEs Harmonic equations and their solution Numerical methods
References: Partial Differential Equations, an Introduction, Second Edition, by Walter A. Strauss Applied Partial Differential Equations by Paul DuChateau, David Zachmann Partial Differential Equations for Scientists and Engineers, by Stanley J. Farlow
Past Instructors: Ajit Kumar, Samit Bhattacharyya, Srinivas VVK

MAT431

Partial Differential Equations

4.00

Undergraduate

Partial Differential Equations

PHY315

Particle and Nuclear Physics

3.00

Undergraduate

Particle and Nuclear Physics

PHY560

Particle Physics Phenomenology

3.00

Graduate

Introduction, decay rates and cross Sections, the Dirac equation and spin, interaction by particle exchange, electron – positron annihilation, electron – proton scattering, deep inelastic scattering, symmetries and the quark model, QCD and color, V-A and the weak interaction, leptonic weak interactions, the CKM matrix and CP violation, electroweak unification and the W and Z, tests of the standard model, the Higgs Boson and beyond.

CHY213

Physical Methods in Chemistry

4.00

Undergraduate

Analyses of compounds are an integral aspect of chemistry. We get to know the structure, spatial orientation and purity of compounds we synthesize through analysis which helps us to advance in our investigation. To address this purpose a bevy of instruments ranging from UV spectroscopy, IR spectroscopy to High Pressure Liquid Chromatography are available. However accurately understanding the output from these instruments is an essential attribute for a successful chemist. The purpose of this course is to familiarize the students with the basic principles of spectroscopic and diffraction methods that are instrumental to the analysis of molecules and structures in the day-to-day life of a chemist. In this course, we will learn to interpret and understand working of various types of analytical instruments commonly used for analysis in a chemistry lab.
COURSE CONTENT:
UV-visible spectroscopy: Beer–Lambert law, types of electronic transitions, effect of conjugation. Concept of chromophore and auxochrome. Bathochromic, hypsochromic, hyperchromic and hypochromic shifts, Woodward–Fieser rules, Woodward rules, introduction to fluorescence.
Vibrational spectroscopy: Molecular vibrations, Hooke’s law, Modes of vibration, Factors influencing vibrational frequencies: coupling of vibrational frequencies, hydrogen bonding, electronic effects, The Fourier Transform Infrared Spectrometer, Calibration of the Frequency Scale, Absorbance and Transmittance scale, intensity and position of IR bands, fingerprint region, characteristic absorptions of various functional groups and interpretation of IR spectra of simple organic molecules, basic mention of Raman Spectroscopy including the mutual exclusion principle, Raman and IR active modes of CO2.
Nuclear Magnetic Resonance (NMR) spectroscopy: Spinning nucleus, effect of an external magnetic field, precessional motion and precessional frequency, precessional frequency and the field strength, chemical shift and its measurement, factors influencing chemical shift and anisotropic effect, proton NMR spectrum, influence of restricted rotation, solvents used in NMR, solvent shift and concentration and temperature effect and hydrogen bonding, spin-spin splitting and coupling constants, chemical and magnetic equivalence in NMR, Lanthanide shift reagents, factors influencing the coupling constant, germinal coupling, vicinal coupling, heteronuclear coupling, deuterium exchange, proton exchange reactions.
Electron Spin Resonance Spectroscopy: Derivative curves, g values, Hyperfine splitting
X-ray Diffraction: X-ray and diffraction of X-rays by atoms, Bragg’s law, lattice, crystal systems, planes and Miller indices, reciprocal lattice, crystal growth and mounting, diffractometer operation, recording diffraction pattern, reflection analysis and preliminary structure determination. ,
Mass spectrometry: Basic principles, basic instrumentation, electron impact ionization, separation of ions in the analyzer, isotope abundances, molecular ions and metastable ions, basic fragmentation rules, factors influencing fragmentation, McLafferty rearrangements, chemical ionization.
Data Analysis: Uncertainties, errors, mean, standard deviation, least square fit.
Books: Spectroscopy of organic compounds, 6th Edition by P. S. KALSI, New Age International Publishers. Spectrometric Identification of Organic Compounds, 6th Edition by R. M. Silverstein and F. X. Webster, Wiley Student Edition. Molecular Fluorescence: Principles and Applications. Bernard Valeur, Wiley-VCH X-ray structure determination: A Practical Guide (2nd Ed.) by George H. Stout and Lyle H Jensen, Wiley-Interscience, New York, 1989.
Prerequisites: Chemical Principles (CHY111), Basic Organic Chemistry-I (CHY122).

PHY108

Physics For Life

4.00

Undergraduate

It will provide an introduction to Newtonian mechanics, Fluids, Thermodynamics, Electricity & Magnetism and Wave Optics.
1. Introduction: Relation of Physics with other sciences, Estimation and Units, Dimensional analysis, Vector and scalar.
2. Mechanics: Newton’s laws of motion in one dimension, work & energy in one dimension, Motion in two dimensions, Momentum, Rotational motion.
3. Fluids: Ideal fluid, Viscous fluid, Surface tension
4. Thermodynamics: Temperature, laws of thermodynamics, entropy
5. Electricity & Magnetism: Electric force & field, Energy & potential, Magnetic force & field, Electromagnetic induction
6. Wave optics: Interference, diffraction, Diffraction gratings, Polarization

PHY568

Physics Of Semiconductor Materials And Devices

3.00

Graduate

The course covers the electric polarization and their types, dipoles, frequency and temperature dependence of polarization, local field and Clausius-Mossotti equation, dielectric constant, loss and breakdown; Applications of high-k materials, ferroelectricity, pyroelectricity and piezoelectricity, electrical memory/hysteresis loop, fatigue testing, pyro and piezo coefficients; Shape Memory alloys: types, working, properties, manufacturing and applications.

BIO302

Plant Biotechnology

3.00

Undergraduate

Plant tissue culture media, phytohormones, in vitro cultures- initiation and maintenance of callus, suspension cultures and single cell clones- organogenesis, somatic embryogenesis, cite differentiation and morphogenesis. Embryo culture, embryo rescue after wide hybridization, and its applications. Endosperm culture and production of triploids. Introduction to the processes of embryogenesis and organogenesis and their practical applications.
Micropropagation, axillary bud, shoot-tip and meristem culture. Haploids and their applications. Somaclonal variations and applications. Introduction to protoplast isolation, Principles of protoplast isolation and applications. Testing of viability of isolated protoplasts. Various steps in the regeneration of protoplasts. Introduction of somatic hybridization. Various methods for fusing protoplasts, chemical and electrical. Cybrids- definition and application. Use of plant cell, protoplasts and tissue culture for genetic manipulation of plants ,Introduction to A. tumefaciens. Tumor formation on plants using A.tumefaciens (Monocots vs. Dicots). Practical application of genetic transformation.
Methods of gene transfer in plants- PEG, particle guns and Agrobacterium mediated (Ti and Ri plasmids) gene transformation. Identification of transgenic plants, Molecular markers and their applications. RFLP, AFLP, simple sequence repeats. RAPD for molecular mapping and crop improvement. Stress- biotic and abiotic stress. Development of transgenic plants- herbicide tolerance, disease resistance, insect resistance, and stress tolerance. Protein and oil quality traits in seeds. Genetic manipulation of photosynthetic traits for improvement of crop yield. Edible vaccines and plantibodies.
Plant secondary metabolites - types and applications, Biofertilizers- organization of nif genes and their regulation, Rhizobium, Azotobacter, Azolla, cyanobacteria and their associations, Mycorrhizal biofertilizers and biopesticide production strategies.
Recommended Books: Plant Biotechnology, Slater, A., Scott, N. W., Fowler, M. R., Pub: Oxford University press. Biotechnology in Agriculture, Swaminathan, M. S., Pub: Mc. Millian India Ltd. Biotechnology and its applications to Agriculture, Copping, L. G., Rodgers, P., Pub: British Crop Projection. Plant Biotechnology, Kung, S., Arntzen, C. J., Pub: Butterworths. Agricultural biotechnology, Purohit, S. S., Pub: Agrobios. Experiments in Plant Tissue Culture, Dodds, J. H., Roberts, L. K., Pub: Cambridge University Press.

BIO105

Plant Sciences 2

3.00

Undergraduate

Structural organization of flower, initiation and differentiation of floral organs, structure and development of anther, microsporogenesis, structure and type of ovule, megasporogenesis, types of embryo sac.
Plant water relationship, mineral nutrition, Solute transport, Role of growth regulators. Photosynthesis-light and dark phases of photosynthesis. Role of ATP and NADPH in carbon dioxide assimilation, factors influencing photosynthesis, photosynthesis of CAM plants. Role of plants in converting radiant energy into chemical energy. Respiration of chlorophyllous tissues in C3 and C4 plants. Regulation of photorespiration, photo periodism and flowering.
Plant development: structure of plant body; fundamental differences between animal and plant development; embryogenesis – classical and modern views using Fucus and Arabidopsis as models; axis specification and pattern formation in angiosperm embryos; organization and homeostasis in the shoot and root meristems; patterning in vegetative and flower meristems; growth and tissue differentiation in plants; evolution of developmental mechanisms in plants.

BIO102

Plant Sciences I

3.00

Undergraduate

Course Content
Taxonomy: General principles of taxonomy, Hierarchy Systematics: Carolus Linnaeus Systematics. Outlines and relative studies on classification of angiosperms, Bentham & Hooker, Engler and Prantel and Hutchinson system. General characteristics of cyanobacteria, algae, fungi, lichens, bryophytes and pteridophytes. Range of thallus structure, types of reproduction. Economic importance of thallophytes. General characteristics of Gymnosperms and Angiosperms, classification distribution, morphological features, development and reproduction. Evolution of angiosperms and gymnosperms.
Recommended Books: Plant taxonomy and biosystematics, Stace, C. A., Pub: Cambridge University Press. Plant systematics: a phylogenetic approach, Judd, W. S., Pub: Sinauer Associates, Incorporated. Cell Biology, Genetics, Molecular Biology, Evolution and Ecology, Verma, P.S., Pub: S. Chand Limited.

BIO203

Plant Sciences II

3.00

Undergraduate

Structural organization of flower, initiation and differentiation of floral organs, structure and development of anther, microsporogenesis, structure and type of ovule, megasporogenesis, types of embryo sac.
Plant water relationship, mineral nutrition, Solute transport, Role of growth regulators. Photosynthesis-light and dark phases of photosynthesis. Role of ATP and NADPH in carbon dioxide assimilation, factors influencing photosynthesis, photosynthesis of CAM plants. Role of plants in converting radiant energy into chemical energy. Respiration of chlorophyllous tissues in C3 and C4 plants. Regulation of photorespiration, photo periodism and flowering.
Plant development: structure of plant body; fundamental differences between animal and plant development; embryogenesis – classical and modern views using Fucus and Arabidopsis as models; axis specification and pattern formation in angiosperm embryos; organization and homeostasis in the shoot and root meristems; patterning in vegetative and flower meristems; growth and tissue differentiation in plants; evolution of developmental mechanisms in plants.
Recommended books: Introduction to Plant Physiology, Hopkins, W. G., Huner, N.P.A., pub: Wiley. Integrative Plant Anatomy, Dickinson, W. C., Pub: Academic press. Principles of Developmental Biology, Hake, S., Wilt, F., Pub: WW. Norton and company Inc.

CHY552

Polymer Chemistry and Its Scope

3.00

Graduate

How do changing demands in society lead to polymer invention? How are monomers bonded in nature to form our body’s building blocks? How do scientists mimic nature in labs? How does the several-fold change in molecular weight from monomer to polymer result in different sets of properties? Most of the polymeric materials around us are synthesized in different ways, depending upon end usage. This course will help the students to understand the need and importance of polymers in today’s world. Interesting chemical aspects of synthesis of polymeric architectures from small molecules will be explored.
Course Outline:
1. Introduction to Polymers
Nomenclature, Classification, Molecular weight, Physical state, Applications
2. Step Growth Polymerization
Polyamide, Polyesters, Polycarbonates, Phenolic polymers, Epoxy resins, Polyethers, Polyurea, Polyurethanes, Carother’s equation
3. Chain Growth Polymerization
Free Radical polymerization: Initiators, Inhibitors and retarders, Mechanism, Kinetics and Thermodynamics, Polymerization processes (Bulk, Solution, Suspension, Emulsion), Copolymers
Ionic polymerization
Cationic and Anionic Polymerization: Mechanism, Ring Opening Polymerization (ROP)
Controlled/Living polymerizations: ATRP (Atom Transfer Radical Polymerization), RAFT (Reversible Addition Fragmentation Chain Transfer), GTP (Group Transfer Polymerization), Ziegler Natta Polymerization, Metathesis
4. Specialty Polymers
Conducting Polymers, Liquid Crystal Polymers, Organometallic Polymers, Green Polymers and their applications
5. Polymer Characterization (Molecular weight determination)
Number average molar mass, End group assay, Colligative Properties of Solutions, Osmometry, Light scattering (Dynamic Light Scattering), Viscometry, Gel Permeation Chromatography, MALDI (Matrix Assisted Laser Desorption/Ionization)
6. Polymers in Life
Proteins: Synthesis of amino acids and their reactions, Test reactions, Zwitter ion, Isoelectric point and Electrophoresis. Overview of Primary, Secondary, Tertiary and Quaternary Structure of proteins. Determination of Primary structure of Peptides by N-terminal and C–terminal analysis. Synthesis of peptides by N-protection & C-activating groups, Merrifield solid-phase synthesis.
Nucleic acids: Nucleosides and Nucleotides, ATP (energy storage and release), Mechanism of Phosphoryl Transfer Reactions, Composition of nucleic acids. Different types of DNA and RNA, Biosynthesis of DNA, m-RNA and proteins, Determining base sequence of DNA, Lab synthesis of DNA fragments, Polymerase Chain Reaction (PCR).
Textbooks: Principles of Polymerization, George Odian, John Wiley & Sons, Inc., 3rd Ed., 1991. Introduction to Polymer Science and Chemistry: A Problem Solving Approach, Manas Chandra, CRC press, Taylor & Francis, 1st Ed., 2006. Malcolm P. Stevens, Polymer Chemistry: An Introduction, 3rd Edition, Oxford University Press Polymer Characterization: Physical techniques, D. Campbell and J. R. White, Chapman and Hall. London- New York. Organic Chemistry, Paula Yurkanis Bruice, Pearson, 3rd Ed., 2011. Biology, N. A. Campbell, and J. B. Reece, 8th Ed., Pearson Benjamin Cummings, San Francisco. Biochemistry, J. M. Berg, J. L. Tymoczko, and L. Stryer, W. H. Freeman & Co Ltd, 6th Ed., 2002.

PHY557

Prob, Stat, Mat Th.& App

3.00

Graduate

Probability, Statistics, Matrix Theory and Applications

MAT184

Probability

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics, Economics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Any one of Calculus I (MAT 101) or Elementary Calculus (MAT 020) or Mathematical Methods I (MAT 103) or Basic Probability & Statistics (MAT 084)
Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course introduces you to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course is a prerequisite for later courses in Advanced Statistics, Stochastic Processes, and Mathematical Finance, as well as for the Minor in Data Analytics.
Detailed Syllabus: Probability: Classical probability, axiomatic approach, conditional probability, independent events, addition and multiplication theorems with applications, Bayes’ theorem. Random Variables: Probability mass function, probability density function, cumulative density function, expectation, variance, standard deviation, mode, median, moment generating function. Some Distributions and their Applications: Uniform (discrete and continuous), Bernoulli, Binomial, Poisson, Exponential, Normal. Joint Distributions: Joint and marginal distributions, independent random variables, IIDs, conditional distributions, covariance, correlation, moment generating function. Sequences of Random Variables: Markov’s Inequality, Chebyshev’s Inequality, Law of Large Numbers, Central Limit Theorem.
References: A First Course in Probability by Sheldon Ross, 6th edition, Pearson. Introduction to Probability and Statistics for Engineers and Scientists by Sheldon Ross, 2nd edition, Harcourt Academic Press. Theory and Problems of Probability and Statistics by Murray R Spiegel and Ray Meddis, Schaum’s Outlines. John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011. Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance by Kai Lai Chung and Farid Aitsahlia, 4th edition, Springer International Edition, 2004.
Past Instructors: Debashish Bose, Suma Ghosh

MAT284

Probability and Statistics

4.00

Undergraduate

Core course for BSc (Research) Economics. Students of BSc (Research) Mathematics or any B.Tech. program are not allowed to credit this course.
Prerequisites: Calculus I (MAT 101)
Overview: Probability is the means by which we model the inherent randomness of natural phenomena. This course introduces you to a range of techniques for understanding randomness and variability, and for understanding relationships between quantities. The concluding portions on Statistics take up the problem of testing our theoretical models against actual data, as well as applying the models to data in order to make decisions. This course is a prerequisite for later courses in Advanced Statistics, Stochastic Processes and Mathematical Finance.
Detailed Syllabus:
1. Probability: Classical probability, axiomatic approach, conditional probability, independent events, addition and multiplication theorems with applications, Bayes’ theorem.
2. Random Variables: Probability mass function, probability density function, cumulative density function, expectation, variance, standard deviation, mode, median, moment generating function.
3. Some Distributions and their Applications: Uniform (discrete and continuous), Bernoulli, Binomial, Poisson, Exponential, Normal.
4. Sequences of Random Variables: Chebyshev’s Inequality, Law of Large Numbers, Central Limit Theorem, random walks.
5. Joint Distributions: Joint and marginal distributions, covariance, correlation, independent random variables, least squares method, linear regression.
6. Sampling: Sample mean and variance, standard error, sample correlation, chi square distribution, t distribution, F distribution, point estimation, confidence intervals.
7. Hypothesis Testing: Null and alternate hypothesis, Type I and Type II errors, large sample tests, small sample tests, power of a test, goodness of fit, chi square test.
Main References:
• A First Course in Probability by Sheldon Ross, 6th edition, Pearson.
• John E. Freund’s Mathematical Statistics with Applications by I. Miller & M. Miller, 7th edition, Pearson, 2011.
Other References:
• Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance by Kai Lai Chung and Farid Aitsahlia, 4th edition, Springer International Edition, 2004.
• Introduction to the Theory of Statistics by Alexander M. Mood, Franklin A. Graybill and Duane C. Boes, 3rd edition, Tata McGraw-Hill, 2001.

MAT210

Programming

2.00

Undergraduate

Programming

MAT105

Programming in Excel VBA

2.00

Undergraduate

Programming in Excel VBA

MAT799

Project

8.00

Graduate

Project

BIO403

Project Dissertation

12.00

Undergraduate

Project Dissertation

BIO407

Project Dissertation

12.00

Undergraduate

Course description not available.

BIO699

Project Dissertation

16.00

Graduate

Project Dissertation

MAT199

Project I (2nd Part)

3.00

Undergraduate

Project I

CHY601

Quantitative Methods

1.00

Graduate

This course will deal with Data handling and Data Analysis, Elements of Qualitative and Quantitative Logic, including Hypothesis testing, Weight of Evidence, and Domain of Applicability estimation.

PHY409

Quantum Field Theory

3.00

Undergraduate

Review of Klein-Gordon and Dirac equations Solutions of Dirac Equation, Properties of Dirac matrices Free Klein Gordon Field Theory
Self-Interacting Scalar Field Theory
Complex Scalar Field Theory
Dirac Field Theory
Feynman diagrams

PHY503

Quantum Mechanics

3.00

Graduate

Quantum Mechanics

PHY305

Quantum Mechanics I

4.00

Undergraduate

Overview This course (Quantum Mechanics – I) aims to follow up the development in Introduction to Quantum Mechanics (PHY202) with more advanced topics in the fundamental subject of Quantum Mechanics, like representation theory and the Schrödinger, Heisenberg and Interaction (Dirac) pictures, Theory of Angular Momentum, and Time-Independent and Time-Dependent Approximation Methods like Perturbation theory and the Variational Principle. (Some advanced optional topics are marked with * in the syllabus.) It starts with reviewing the basic concepts and surprizes in Quantum Mechanics (QM) with the prototypical example of Photon Polarization in great detail. This course together with the next advanced course (PHY306 : Quantum mechanics – II) is based mainly on the set of celebrated Lecture Notes in QM by Gordon Baym, which formed the subject matter of the Graduate level QM course at the University of Illinois at Urbana-Champaign, and hence would ideally prepare the students at a Graduate QM level, ready to go into research, and ideal for students interested to go into the 4th year extension into B.Sc. Research. It can also be of interest to certain students in Chemistry, Mathematics or some branches of Engineering, provided they have the necessary background.
In addition to the above mentioned precursor course on Basic QM, a background in Basic Electromagnetism and Some Mathematical Methods relating especially to Linear Algebra would be useful, but not an absolute necessity.

PHY306

Quantum Mechanics II

4.00

Undergraduate

1. Advanced Angular Momentum Theory
2. Advanced Topics in Perturbation Theory
3. Identical Particles and Second Quantization
4. Central Potentials and Potential Scattering Theory
5. Interaction of Radiation with Matter
6. Symmetries in Quantum Mechanics

MAT800

Reading course

4.00

Graduate

Reading course

MAT803

Reading Course - Biomathematic

4.00

Graduate

Reading Course - Biomathematics

MAT802

Reading Course - Lie Groups

4.00

Graduate

Reading Course - Lie Groups: Representations and Invariants

MAT806

Reading Course - Math of Inf.

4.00

Graduate

Reading Course - Mathematics of Infectious Disease

MAT801

Reading Course I - Appro

4.00

Graduate

Reading Course - Approximation Problems in Normed Linear Spaces

MAT810

Reading Course: Probabilistic

4.00

Graduate

Reading Course: Probabilistic models and Statistical inference

MAT220

Real Analysis I

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Calculus I (MAT 101)
Overview: This course provides a rigorous base for the geometric facts and relations that we take for granted in one-variable Calculus. The main ingredients include sequences; series; continuous and differentiable functions on R; their various properties and some highly applicable theorems. This is the foundational course for further study of topics in pure or applied Analysis, such as Metric Spaces, Complex Analysis, Numerical Analysis, and Differential Equations.
Detailed Syllabus: Fundamentals: Review of N, Z and Q, order, sup and inf, R as a complete ordered field, Archimedean property and consequences, intervals and decimals. Functions: Images and pre-images, Cartesian product, Cardinality. Sequences: Convergence, bounded, monotone and Cauchy sequences, subsequences, lim sup and lim inf. Series: Infinite Series: Cauchy convergence criterion, Infinite Series of non-negative terms, comparison and limit comparison, integral test, p-series, root and ratio test, power series, alternating series, absolute and conditional convergence, rearrangement. Continuity: Limits of functions, continuous functions, Extreme Value Theorem, Intermediate Value Theorem, monotonic functions, uniform continuity. Differentiation: Differentiable functions on R, local maxima, local minima, Mean Value Theorems, L'Hopital's Rule, Taylor's Theorem.
References: A Basic Course in Real Analysis by Ajit Kumar and S Kumaresan. CRC Press, 2014. Introduction to Real Analysis by R G Bartle & D R Sherbert, John Wiley & Sons, Singapore, 2/e (or later editions), 1994. Elementary Analysis: The Theory of Calculus by Kenneth A Ross. Springer India, 2004. Analysis I by Terence Tao. Hindustan Book Agency. 2nd Edition, 2009. Principles of Mathematical Analysis by Walter Rudin. McGraw-Hill. 3rd Edition, 2006. Mathematical Analysis by Tom Apostol, Narosa, New Delhi, 2/e, 2002. Calculus, Volume 1, by Tom Apostol, Wiley India. 2nd Edition, 2011.
Past Instructors: Pradip Kumar

MAT221

Real Analysis II

4.00

Undergraduate

Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab): 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: Real Analysis I (MAT 220)
Overview: Continuing the work done in MAT 220 of understanding the rigor behind one-variable Differential Calculus, this course dwells on various aspects of Integration as well as functions on higher dimensional spaces. We discuss sequences and series of functions; uniform convergence and consequences; some important approximation theorems for continuous functions; rigorous discussions of some special functions; and finally the world of functions of several variables.
Detailed Syllabus: Integration: Upper and lower Riemann integrals, basic properties of Riemann integral, Riemann integrability of continuous and monotone functions, non-Riemann integrable functions, Fundamental Theorem of Calculus and consequences. Sequences and Series of Functions: Pointwise and uniform convergence, uniform convergence and continuity, series of functions, Weierstrass M-test, uniform convergence and integration, uniform convergence and differentiation, equicontinuous families of functions, Stone-Weierstrass Theorem. Some Special Functions: Power Series, the exponential, logarithmic and trigonometric functions. Topology of Rn: Open and closed sets, continuous functions, completeness, compactness, connectedness. Functions of Several Variables: Derivatives, partial and directional derivatives, Chain Rule, Inverse Function Theorem.
References: Analysis II by Terence Tao. Hindustan Book Agency. 2nd Edition, 2009. Principles of Mathematical Analysis by Walter Rudin. McGraw-Hill. 3rd Edition, 2006. Real Mathematical Analysis by Charles C Pugh. Springer India. 2004. Mathematical Analysis by Tom Apostol, Narosa, New Delhi, 2/e, 2002. Calculus, Volume 2, by Tom Apostol, Wiley India. 2nd Edition, 2011.

MAT320

Real Analysis II

4.00

Undergraduate

Overview: Continuing the work done in MAT 220 of understanding the rigor behind one-variable Calculus, this course dwells on various aspects of functions on more general spaces, namely, metric spaces. A brief introduction to the generalities of metric spaces leads to discussions on functions on metric spaces; sequences and series of functions on metric spaces; uniform convergence and consequences; some important approximation theorems for continuous functions; rigorous discussions of some special functions; and then finally to the world of functions of several variables.
Detailed Syllabus:
1. Integration: Upper and lower Riemann integrals, basic properties of Riemann integral, Riemann integrability of continuous and monotone functions, non-Riemann integrable functions, Fundamental Theorem of Calculus and consequences.
2. Topology of Rn: Open and closed sets, continuous functions, completeness, compactness, connectedness.
3. Sequences and Series of Functions: Pointwise and uniform convergence, uniform convergence and continuity, series of functions, Weierstrass M-test, uniform convergence and integration, uniform convergence and differentiation, equicontinuous families of functions, Stone-Weierstrass Theorem.
4. Some Special Functions: Power Series, the exponential, logarithmic and trigonometric functions.
5. Functions of Several Variables: Derivatives, partial and directional derivatives, Chain Rule, Inverse Function Theorem.

BIO303

Recombinant DNA Technology

3.00

Undergraduate

Isolation of DNA, cDNA synthesis, chemical synthesis of DNA by phosphoramidite method. Introduction of DNA into living cells, Introduction to gene cloning and its uses, tools and techniques: plasmids and other vectors, DNA, RNA, cDNA. Enzymes used in genetic engineering. Restriction endonucleases and restriction mapping, DNA ligase, DNA polymerase-I, reverse transcriptase, Sl nuclease, terminal nucleotide transferase, alkaline phosphatase, polynucleotide kinase, polynucleotide phosphorylase. Production of proteins from cloned genes: gene cloning in medicine (Pharmaceutical agents such as insulin, growth hormones, recombinant vaccines), gene therapy for genetic diseases.
Cloning vectors- salient features, plasmid vectors, phage vectors, cosmids, phagemids (Lambda and M13 phages), viral vectors (SV40, Baculo and CMV), artificial chromosomes BAC, YAC and MAC.
Ligation of DNA to vectors – cohesive end, blunt end, - homopolymer tailing, linkers and adaptors. Gene transfer techniques- transformation, transfection, microinjection, electroporation,
lipofection and biolistics. Reporter gene assay, selection and expression of r-DNA clones. Polymerase Chain Reaction, PCR variations and their applications
DNA sequencing - chemical, enzymatic and NGS methods. Salient features of human genome project. Applications of genetic engineering in agriculture, animal husbandry, medicine and industry.
Recommended Books: Recombinant DNA Technology, Watson, J. D., Pub: W. H. Freeman. Gene cloning and DNA analysis, Brown, T. A., Pub: Wiley Blackwell A John Wiley & Sons, Ltd. Principles of Gene manipulation: an introduction to Genetic Engineering, Primrose, Old R. W., Primrose, S.B., Pub: Blackwell Science Ltd.

MAT744

Representation Theory

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 634 (Differential Geometry) and MAT 640 Graduate Algebra I
Overview: Representations of groups realize the group elements as linear transformations on vector spaces, or even more concretely, as matrices. This enables the use of linear algebra to study algebra, and connects group theory with other areas such as geometry, harmonic analysis and number theory. In this course, we will first study the representation theory of finite groups, and then that of compact groups.
Detailed Syllabus:
Part 1: Representations of Finite Groups
Review of group actions, representations, unitarizability and unitary equivalence of finite dimensional representations of finite groups, complete reducibility, group algebra as a *-algebra, regular representations, matrix coefficients, Schur’s lemmas, tensor products of representations, orthogonality of matrix coefficients, orthogonality of characters, direct sum decompositions, projection formulas, dimension theorem, character tables, Frobenius-Schur theorem on real and quaternionic representations, Fourier analysis on finite groups, subgroups of index 2, induced representations, Frobenius character formula, Frobenius reciprocity, Mackey irreducibility criterion.
Part 2: Representations of Compact Groups
Review of manifolds and Lie groups, the classical compact groups, topological properties of G and G/H, invariant forms and integration, Haar measure, examples of Haar measure for matrix groups, matrix coefficients, characters, Schur orthogonality, review of spectral theory, Schur’s lemma, regular representations, Frobenius reciprocity, Peter-Weyl theorem, representations and harmonic analysis of SU(2), Fourier theory.
References: Representation Theory of Finite Groups by Benjamin Steinberg, Springer. Representations of Finite and Compact Groups by Barry Simon, Graduate Studies in Mathematics, American Mathematical Society. Representation Theory – A First Course by William Fulton and Joe Harris, Springer. A First Course on Representation Theory and Linear Lie Groups by S C Bagchi, S Madan, A Sitaram, and U B Tewari, Universities Press. Compact Lie Groups by Mark R Sepanski, Springer. Short Courses in Mathematics by S Kumaresan, Universities Press.

BIO401

Research methodology

3.00

Undergraduate

Research methodology

BIO700

Research Methodology

3.00

Graduate

Research Methodology

CHY600

Research Methodology

3.00

Graduate

1. Quantitative Methods:
This module will deal with Data handling and Data Analysis, the elements of Quantitative Logic, including Hypothesis testing, Weight of Evidence, and Domain of Applicability estimation.
2. Research Literature and Seminar:
This part of the course will be conducted as a Journal Club. Each week one student will be expected to read and summarize a research paper from the recent literature in an area outside their
immediate domain of research. The student will familiarize himself/herself with the background necessary to understand the research paper, and will be expected to critically analyze the work and to answer questions from other students and from the faculty moderator(s). Also covered: the research process - meaning of research, objectives, motivation, types; method vs. methodology,
scientific and research method, and detailed description of the research process.
3. Grantsmanship:
This module will deal with identification of a research problem, formulation of a testable hypothesis and design of experiments to address the question. Strategies for writing a fundable research
proposal will be discussed, with particular emphasis on the Specific Aims, and succinctly conveying the significance of the problem to both technical and non-technical readership. Students will refine both writing and presentation skills during this module. Experts will be invited from funding agencies like DBT, DST, ICMR and Wellcome Trust/DBT Alliance to provide recent updates and guidelines for grant submission (as part of an yearly mini-symposium).
[Core course required of all Ph.D. students]

MAT898

Research Methodology

4.00

Graduate

Research Methodology

BDA800

Research Project

16.00

Graduate

Research Project

BDA801

Research Project Part II

16.00

Graduate

Research Project Part II

PHY509

Rev. Classical Electrodynamics

1.50

Graduate

Review of Classical Electrodynamics

PHY506

Rev. Classical Mechanics

1.50

Graduate

Review of Classical Mechanics

PHY508

Rev. Quantum Mechanics

1.50

Graduate

Review of Quantum Mechanics

PHY507

Rev. Statistical Mechanics

1.50

Graduate

Review of Statistical Mechanics

PHY558

Semiconductor Physics and Devices

3.00

Graduate

This course outlines the physics, applications and technology of Semiconductors. The course covers energy band structures in semiconductors, dopants and defects, charge transport, electronic and optical properties, excitons and other quasi-particles, semiconductor heterostructures, diodes, LEDs, photovoltaic, LASERS and field-effect transistors (FETs). The concepts of these conventional devices will be extended to the emerging areas of new generation of flexible electronic and optoelectronics devices based on unconventional materials like metal oxides and organic semiconductors.

CHY498

Senior Project

6.00

Undergraduate

Individual faculty mentor(s) assigned to each student.
Undergraduate research allows students to integrate and reinforce chemistry knowledge from their formal course work, develop their scientific and professional skills, and create new scientific knowledge. Original research culminating in a comprehensive written report provides an effective means for integrating undergraduate learning experiences, and allows students to participate directly in the process of science. Students enrolled in this course carry out an individual hands-on project over the full academic year, on a topic chosen from any area of Chemistry, and are assigned to a faculty mentor for their supervision.
Course Evaluation: This course will be evaluated based on: an Oral Presentation and Examination before the Department, at the end of the first semester of research, dealing with the formulation of the research problem and survey of existing literature in the field. The student will be expected to demonstrate sufficient mastery of the background in the subject necessary to carry out research. a comprehensive written Project Report and Oral Presentation / Examination before the Department, at the completion of the project. The Project Report should contain a comprehensive account of the student’s research, and should demonstrate the student’s understanding of the research area, familiarity with the techniques used, and ability to report research data in a clear manner and to draw logical conclusions from the results.
This course carries an S/U grade.

CHY499

Senior Project

6.00

Undergraduate

Individual faculty mentor(s) assigned to each student.
Undergraduate research allows students to integrate and reinforce chemistry knowledge from their formal course work, develop their scientific and professional skills, and create new scientific knowledge. Original research culminating in a comprehensive written report provides an effective means for integrating undergraduate learning experiences, and allows students to participate directly in the process of science. Students enrolled in this course carry out an individual hands-on project over the full academic year, on a topic chosen from any area of Chemistry, and are assigned to a faculty mentor for their supervision.
Course Evaluation: This course will be evaluated based on: an Oral Presentation and Examination before the Department, at the end of the first semester of research, dealing with the formulation of the research problem and survey of existing literature in the field. The student will be expected to demonstrate sufficient mastery of the background in the subject necessary to carry out research. a comprehensive written Project Report and Oral Presentation / Examination before the Department, at the completion of the project. The Project Report should contain a comprehensive account of the student’s research, and should demonstrate the student’s understanding of the research area, familiarity with the techniques used, and ability to report research data in a clear manner and to draw logical conclusions from the results.
This course carries an S/U grade.

MAT792

Signal and Image Processing

4.00

Graduate

Signal and Image Processing

PHY416

Soft Matter Physics

3.00

Undergraduate

Soft Matter Physics

PHY572

Soft Matter Physics

3.00

Graduate

Soft Matter Physics

PHY550

Solid State Physics

3.00

Graduate

This course covers the application of concepts of classical mechanics, electrodynamics, quantum mechanics and statistical physics to study properties and structure of matter (solids and liquids). It also aims to develop an understanding of behavior of applied materials.

PHY505

States of Matter

3.00

Graduate

States of Matter

PHY302

Statistical Physics

4.00

Undergraduate

1. The Fundamentals of Statistical Mechanics
1. Introduction
2. The Microcanonical Ensemble.
3. Entropy and Temperature
4. The Canonical Ensemble
5. The Partition Function , Energy and Fluctuations, Entropy, Free Energy
6. The Chemical Potential
7. Grand Canonical Ensemble, Grand Canonical Potential, Extensive and Intensive Quantities
2. Classical Gases.
1. Ideal Gas, Equipartition of Energy, Boltzmann's Constant, Gibbs's Paradox
2. Maxwell Distribution, Kinetic Theory
3. Diatomic Gas, Interacting Gas, Mayer f Function, Virial Coecient
van der Waals Equation of State, The Cluster Expansion.
3. Quntum Statistical Mechanics
1. The Postulate of Quantum Statistical Mechanics
2. Density Matrix
3. Ensembles in Quantum Statistical Mechanics
4. The Third Law of Thermodynamics
5. Fermi Systems, Bose Systems.
4. Phase Transitions
1. Liquid-Gas Transition, Phase Equilibrium, The Clausius-Clapeyron Equation,The Critical Point
2. The Ising Model, Mean Field Theory, Critical Exponents, Validity of Mean Field Theory.
3. Some Exact Results for the Ising Model, The Ising Model in d= 1 Dimensions 2d Ising Model.
4. Landau Theory, Second Order Phase Transitions, First Order Phase Transitions,
5. Landau-Ginzburg Theory, Correlations, Fluctuations.

MAT684

Statistics I

4.00

Graduate

Core course for M.Sc. Mathematics.
Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 184 (Probability) for undergraduates.
Overview: This course builds on a standard undergraduate probability and statistics course in two ways. First, it makes probability more rigourous by using the concept of measure. Second, it discusses more advanced topics such as multivariate regression, ANOVA and Markov Chains.
Detailed Syllabus: Probability: Axiomatic approach, conditional probability and independent events Random Variables – Discrete and continuous. Expectation, moments, moment generating function Joint distributions, transformations, multivariate normal distribution Convergence theorems: convergence in probability, Weak law of numbers, Borel- Cantelli lemmas, Strong law of large numbers, Central Limit Theorem Random Sampling & Estimators: Point Estimation, maximum likelihood, sampling distributions Hypothesis Testing Linear Regression, Multivariate Regression ANOVA Introduction to Markov Chains
References: Statistical Inference by Casella and Berger. Brooks/Cole, 2007. (India Edition) An Intermediate Course in Probability by Allan Gut. Springer, 1995. Probability: A Graduate Course by Allan Gut. Springer India. Measure, Integral and Probability by Capinski and Kopp. 2nd edition, Springer, 2007.

MAT584

Stochastic Processes

4.00

Graduate

Stochastic Processes

BIO521

Structural Biology

3.00

Graduate

Structural Biology

CHY112

Structure and Bonding

5.00

Undergraduate

Basic Chemistry
Unit-1: Chemical periodicity
Chemical periodicity
Periodic table, group trends and periodic trends in physical properties. Classification of elements on the basis of electronic configuration. Modern IUPAC Periodic table. General characteristic of s, p, d and f block elements. Position of hydrogen and noble gases in the periodic table. Effective nuclear charges, screening effects, Slater’s rules, atomic radii, ionic radii (Pauling’s univalent), covalent radii. Ionization potential, electron affinity and electronegativity (Pauling’s, Mulliken’s and Allred-Rochow’s scales) and factors influencing these properties. Inert pair effect. Group trends and periodic trends in these properties in respect of s-, p- and d-block elements.
Unit 2:Chemical Bonding and structure and acid-base reactions
Ionic bonding: Size effects, radius ratio rules and their limitations. Packing of ions in crystals, lattice energy, Born-lande equation and its applications, Born-Haber cycle and its applications. Solvation energy, polarizing power and polarizability, ionic potential, Fazan’s rules.
Covalent bonding: Lewis structures, formal charge. Valence Bond Theory, directional character of covalent bonds, hybridizations, equivalent and non-equivalent hybrid orbitals, Bent’s rule, VSEPR theory, Bonding, inductive effect, Hyperconjugation effect, mesomeric effect shapes of molecules and ions containing lone pairs and bond pairs (examples from main groups chemistry), Partial ionic Character of covalent bonds, bond moment, dipole moment and electronegativity differences. Concept of resonance, resonance energy, resonance structures
Acid-Base reactions
Acid-Base concept: Arrhenius concept, theory of solvent system (in H2O, NH3, SO2 and HF), Bronsted-Lowry’s concept, relative strength of acids, Pauling rules. Amphoterism. Lux-Flood concept, Lewis concept. Superacids, HSAB principle. Acid-base equilibria in aqueous solution and pH. Acid-base neutralisation curves; indicator, choice of indicators.
Unit 3: An Introduction to Coordination Compounds
Group theory, Bonding in coordination compounds, d-orbitals, t2g-eg splitting, structures of coordination complexes, octahedral and tetrahedral complexes, square planar complexes
Unit 4: Basics of Organic Chemistry
Homolytic and heterolytic bond fission.
Hybridization, Bonding, inductive effect, Hyperconjugation effect, mesomeric effect, acidity and basicity of organic molecules, pKa,. Organic reactions; nucleophilic substitution, elimination, addition and electrophilic aromatic substitution reactions. Basic concept for characterization of organic molecules.
Reaction intermediate: Carbocations, carbanions, free radicals,carbenes, Benzynes - their shape and stability.
Electron displacements Inductive, electromeric, resonance, hyperconjugation.
Electrophiles and nucleophiles. Nucleophilicity and Basicity
Intermolecular forces of attraction: van der Waals forces, ion-dipole, dipole-dipole and hydrogen bonding.
Aromaticity and Tautomerism
Acidity/Basicity: Alkanes/Alkenes, Alcohols/Phenols/Carboxylic acids, Amines
Molecular chirality and Isomerism
Cycloalkanes (C3 to C8): Relative stability, Baeyer strain theory and Sachse Mohr theory.
Stereochemistry
Structural- and Stereo-isomerism.
Molecular representations: Newman, Sawhorse, Wedge & Dash, Fischer projections and their inter conversions.
Conformations and Conformational analysis: Ethane, n-butane, ethane derivatives,
cyclohexane, monosubstituted and disubstituted cyclohexanes and their relative stabilities.
Geometrical isomerism in unsaturated and cyclic systems: cis–trans and, syn-anti isomerism, E/Z notations. Geometrical isomerism in dienes- Isolated and conjugated systems, determination of configurations.
Chirality and optical isomerism: Configurational isomers. Molecules with one or two chiral centres- constitutionally symmetrical and unsymmetrical molecules; Enantiomers and Diastereomers. Optical activity, Disymmetry, Meso compounds, racemic modifications and methods of their resolution; stereochemical nomenclature: erythro/threo, D/L and R/S nomenclature in acyclic systems.
Measurement of optical activity: specific rotation.
Substitution reactions:
Free radical- Halogenation, relative reactivity and selectivity. Allylic and benzylic bromination.
Nucleophilic Subsititution (SN1, SN2, SN1′, SN2′ SNi)
Electrophilic Substitution (SNAr, Addition Elimination vs. Elimination addition)
Organometallic reagents

BIO535

Synthetic Biology

4.00

Graduate

Synthetic Biology

CHY502

Synthetic Organic Chemistry

3.00

Graduate

1) Organic Synthesis and Structure
a. Mechanism,
b. Applicability and limitations of the major reactions in organic synthesis.
c. Stereochemical control in synthesis.
2) New Synthetic Reactions and Catalysts
a. Recent highlights of new synthetic reactions and catalysts for efficient organic synthesis.
b. Mechanistic details as well as future possibilities will be discussed.
3) Tactics of Organic Synthesis
a. A dissection of the most important syntheses of complex natural and unnatural
products.
b. Synthesis, planning and methodology.
c. The logic of synthesis.
d. Biogenesis.

BIO602

Sys. Biology & Molecular Netw.

3.00

Graduate

Systems Biology and Molecular Networks

BDA600

System/Business Analysis

2.00

Graduate

System/Business Analysis

BDA670

Text Analytics

3.00

Graduate

Course description not available.

MAT690

Time Series And Forecasting

3.00

Graduate

Time Series And Forecasting

MAT551

Topics in Algebraic Topology

4.00

Undergraduate

Course Description: The course will cover topics such as differential forms, spectral sequences and characteristic classes. The exact choice of topics will depend on the instructor and students. Students should have prior exposure to the basic concepts of topology and algebraic topology.

MAT726

Topics in Complex Analysis

4.00

Graduate

Topics in Complex Analysis

MAT606

Topics in Mathematics

4.00

Graduate

Topics in Mathematics

CHY344

Topics In Nanotechnology

3.00

Undergraduate

The next few years will see dramatic advances in atomic-scale technology. Molecular machines, nanocircuits, and the like will transform all aspects of modern life - medicine, energy, computing, electronics and defense are all areas that will be radically reshaped by nanotechnology. These technologies all involve the manipulation of structures at the atomic level - what used to be the stuff of fantasy is now reality. The economics impact of these developments has been estimated to be in the trillions of dollars. But, as with all new technologies, ethical and legal challenges will arise in their implementation and further development. This course will examine the science of nanotechnology and place it in the larger social context of how this technology may be, and already is, applied. Underlying physical science principles will be covered in lecture sessions and students will read articles from current news sources and the scientific literature. There will be presentations on scientific literature on topics of student interests, to examine the science and applications of a well-defined aspect of nanotechnology of their choosing. Lecture material will focus on the principles behind modern materials such as semi-conductors (organic, inorganic) and novel nanostructures.
COURSE CONTENT: Introduction Bulk Vs. Nano Quantum confinement effect Surface area to volume ratio Effect on Properties: Material (electrical, magnetic, mechanical etc.) and structural properties Carbon nano-architectures: Fullerene, SWNT, MWNT, Graphite etc., Classification of structure Q-Dots • Bonding parameters Methods of preparation Nanomaterial’s synthesis: Top down and Bottom up approach, Physical and chemical methods Applications (Nano-machines, solar cells, coatings, MEMS, nano-medicine, sensors, miscellaneous) Characterization Techniques and Instruments: Microscopy SEM, TEM, AFM, X-Ray diffraction, UV-vis, Photoluminescence, Raman, FTIR, ESR, XPS, BET, DLS, Zeta potential

PHY417

Topics in Quantum Many Body Th

3.00

Undergraduate

This course (Topics in Quantum Many-Body Theory) aims to introduce the student with ample knowledge of Quantum Mechanics (qualified all of IQM, QM-I and QM-II) to the complexity of the many-body problem, mainly in the field of Condensed Matter Physics, though some of the methods go well beyond the scope of Condensed Matter Physics. Many-body Physics is the study of systems with a very large number of coupled degrees of freedom, typically involving a system of many (often ~ Avogadro’s Number ~ 1023) interacting particles. An exact solution of this would ideally involve the solution of ~ coupled Schrödinger Equations, which is essentially and unsolved problem! So the methods of Many-body Physics involve making useful and valid approximations to extract useful information about the system, without having to do a full exact solution of the many-body problem. This could involve, for example, the reduction of the fully interacting problem to a non-interacting or weakly interacting problem via certain “canonical transformations”. The prototypical example in this case is the resolution of the complex motion of crystal lattices into independent and non-interacting oscillator modes called “Phonons”, in the harmonic approximation. The interactions between these Phonons when anharmonic effects are included is weak, compared to that between the original lattice atoms. Similarly “elementary excitations” of the strongly coupled Heisenberg Spins on a lattice, are non-interacting spin-waves or “magnons”, to a first approximation, and magnon-magnon interactions are relatively weak.
This course will familiarize students with the concepts of “Elementary Excitations” in many-body systems, like “quasi-particles” and “collective excitations” etc. Also the concepts of “Broken Symmetry” and the idea of “Emergent Complexity” will be emphasized, following the prophetic article “More is Different” by P.W. Anderson. It also inspects Spin Systems and related complexities in some detail. Other approximations and methods of calculations like “Mean-field Theories”, “Green’s Functions and the Renormalization method” etc. will be dealt with. “Linear Response Theory” and “Kubo Formulae” that connects theory to experiments will also be covered. We will also try to cover “Many-body Perturbation Theory” and some aspects of “Strong Correlations”.

MAT645

Topological Graph Theory

4.00

Graduate

Topological Graph Theory

MAT622

Topology

4.00

Graduate

Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 231/320 Real Analysis II for undergraduates, MAT 621 for graduate students.
Overview: This course concerns 'General Topology' which can be characterized as the abstract framework in which the notion of continuity can be framed and studied. Thus topology provides the basic language and structure for a large part of pure and applied mathematics.
We will take up the following topics: Open and closed sets, continuous functions, subspaces, product and quotient topologies, connected and path connected spaces, compact and locally compact spaces, Baire category theorem, separability axioms.
Detailed Syllabus: Review: Operations with infinite collections of sets, axiom of choice, Zorn's lemma, real line, metric spaces. Topological Spaces: Definition and examples of topological spaces, Hausdorff property, fine and coarse topologies, subspace topology, closed sets, continuous functions, homeomorphisms, pasting lemma, product topology, quotient topology. Connectedness and Compactness: Connected spaces and subsets, path connectedness, compact spaces and subsets, tube lemma, Tychonoff theorem, local compactness, one-point compactification, Baire category theorem. Separation Axioms: First and second countability, separability, separation axioms (T1 etc.), normal spaces, Urysohn lemma, Tietze extension theorem. Topics for Student Presentations: Order topology, quotients of the square, locally (path) connected spaces, sequential and limit point compactness, topological groups, nets, applications of Baire category theorem.
Main Reference: Topology by James R. Munkres, 2nd Edition. Pearson Education, Indian Reprint, 2001. Basic Topology by M. A. Armstrong. Springer-Verlag, Indian Reprint, 2004. Topology by K. Jänich. Undergraduate Texts in Mathematics, Springer-Verlag, 1984. Introduction to Topology and Modern Analysis by G. F. Simmons. International Student Edition. McGraw-Hill, Singapore, 1963. Topology of Metric Spaces by S. Kumaresan. 2nd edition, Narosa, 2011.

CHY422

Transition metals in...

3.00

Undergraduate

Transition metals in the synthesis of complex organic molecules

MAT000

Tutorial

3.00

Undergraduate

Tutorial

MAT299

Undergraduate Seminar

3.00

Undergraduate

A major elective for BSc (Research) Mathematics 2nd and 3rd year students only.

MAT399

Undergraduate Seminar

4.00

Undergraduate

Core course for BSc (Research) Mathematics.
The Undergraduate Seminar is an introduction to the activity of research in mathematics. One aim is to help students prepare for their Undergraduate Thesis by practicing, on a smaller scale, the skills of literature survey, public presentations, and mathematical writing.

PHY499

Undergraduate Thesis

12.00

Undergraduate

Undergraduate thesis is a research project, spread over two consecutive semesters, in which students will work extensively on a research problem of current interest under the guidance of a faculty member.

MAT499

Undergraduate Thesis II

8.00

Undergraduate

Compulsory final semester course for BSc (Research) Mathematics.
Prerequisites: MAT498 Undergraduate Thesis I.
Overview: The course can take a variety of forms, from a reading course on advanced topics to computational work in an application of mathematics. The work will be presented in a public seminar at the end of the academic year.
Details:
The student must select and gain the consent of a project supervisor (from the faculty of the Department of Mathematics) by the end of the first week of his/her seventh semester. If the student is unable to fix a supervisor, the Department Undergraduate Committee will arrange one. The student will begin work during the seventh semester by registering for MAT498 Undergraduate Thesis I.
The supervisor will help the student in deciding the structure of the project and identifying reading material and other resources.
While the supervisor will help and encourage the student, successful completion of the project is the student’s responsibility. Credit will be given for independence and initiative in identifying resources and topics.
The project will conclude with the submission of a written report (dissertation) and a public presentation of the work done.
The dissertation should be a detailed exposition of the work done, including a literature review as well as specific investigations. It should be typeset using LaTeX/MS Word.

Mat132

Vector Calculus and Geometry

4.00

Undergraduate

Core course for B.Sc. (Research) programs in Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 101 (Calculus I)
Overview: Analytic Geometry: Double and triple integrals: Double integrals over rectangles, double integrals over general regions, double integrals in polar coordinates, center of mass, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables. Vector Integration: Vector fields, line integrals, fundamental theorem, independence of path, Green's theorem, surface integrals, Stokes' theorem, Gauss theorem.
References: Calculus, Volume II, by Tom M Apostol, Wiley. Essential Calculus – Early Transcendentals by James Stewart, Cengage, India Edition. Calculus and Analytic Geometry by G B Thomas and R L Finney, 9th edition, Pearson. Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1st edition, Springer (India), 2011. Calculus by Ken Binmore and Joan Davies, 1st edition, Cambridge, 2010.

PHY205

Waves and Oscillations

4.00

Undergraduate

1. Oscillations of Systems with Many Degrees of Freedom
(a) Review of the Harmonic Oscillator
(b) Systems with More than One Degree of Freedom
(c) Linearity, Normal Modes and the Matrix Equation of Motion
(d) Forced Oscillations and Resonance is Systems with More than One Degree of Freedom
(e) The Infinite System and Translational Invariance
(f) Forced Oscillations and Boundary Conditions
2. Traveling Waves
(a) The Continuum Limit of a Discrete System
(b) Longitudinal Oscillations and Sound
(c) Harmonic Traveling Waves in One Dimension Phase Velocity
(d) Index of Refraction and Dispersion
(e) Impedance and Energy Flux
3. Modulations, Pulses, and Wave Packets
(a) Group Velocity
(b) Pulses
(c) Fourier Analysis of Pulses
(d) Fourier Analysis of Traveling Wave Packet
4. Waves in Two and Three Dimensions
(a) Harmonic Plane Waves and the Propagation Vector
(b) Water Waves
(c) Electromagnetic Waves
(d) Radiation from a Point Charge
5. Polarization
(a) Description of Polarized States
(b) Production of Polarized Transverse Waves
(c) Double Refraction
(d) Bandwidth, Coherence Time, and Polarization
6. Interference and Diffraction
(a) Interference between Two Coherent Point Sources
(b) Interference between Two Independent Sources
(c) How Large Can a “Point” Light Source Be?
(d) Angular Width of a “Beam” of Traveling Waves
(e) Diffraction and Huygen’s Principle
(f) Geometrical Optics