Course Catalog

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

Advanced topics in non-linear dynamics

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

Course description not available.

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.

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.

Advanced Linear Algebra

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).  

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.

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

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.

Algebraic Graph Theory

Algebraic Number Theory

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.

Analysis and Geometry

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.

Analytical Methodology

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.

Application of Complex Networks to Landscape Ecology

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.  

Course description not available.

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

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).

Basic Tools in Mathematics

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.

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

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.

Bioinorganic Chemistry

Biomathematics

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.

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

Cancer And Its Therapies

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.

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.

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  

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).

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.

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.

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.

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.

Classical Dynamics

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

Classical Mechanics

(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.

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

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.

Complex Fluids

Complex Networks

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.

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)

Course description not available.

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

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

Course description not available.

Coordination and Bio-Inorganic Chemistry

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). .

Course description not available.

Course description not available.

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

Discrete Mathematics

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

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

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).

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

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

Environment Science

Error Correcting Codes

Evolutionary Game Theory

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.

Course description not available.

Formal Languages and Automata Theory II

Fourier Analysis

Fractal Geometry.

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.

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  

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.

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.

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

Course description not available.

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.

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.

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.

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

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.

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

Graph Theory and Complex Networks

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.

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.

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.

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.

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

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

Internal Project Dissertation

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.

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.

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

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

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

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.

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

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.

Introductory Econometrics

IPR, Patent Laws & Bioethics

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  

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

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.

Course description not available.

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).

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).

Mathematical Methods

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 %

Mathematical Methods II

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

Matrix Analysis

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

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.

Microbial Technology

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).

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).

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.

Next Generation Genomics: Concepts, Methods and Applications

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.

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.

Course description not available.

Numerical Linear Algebra

Operations Research

Optimization

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.

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).

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.

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

Particle and Nuclear Physics

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).

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.

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.

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.

Probability, Statistics, Matrix Theory and Applications

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.  

Programming in Excel VBA

Project Dissertation

Project Dissertation

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.

Quantum Mechanics

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

Reading Course - Biomathematics

Reading Course - Mathematics of Infectious Disease

Reading Course: Probabilistic models and Statistical inference

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.  

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.

Research methodology

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]

Research Project

Review of Classical Electrodynamics

Review of Quantum Mechanics

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.

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.

Soft Matter Physics

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.

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.

Stochastic Processes

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

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.

System/Business Analysis

Time Series And Forecasting

Topics in Complex Analysis

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

Topological Graph Theory

Transition metals in the synthesis of complex organic molecules

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

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.

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.