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

Course description not available.

Advanced Biostatistics

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

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

Course description not available.

Advanced Instrumentation

Advanced mathematical Methods in Physics

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

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

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

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

Algebraic Graph Theory

Course description not available.

Algebras of Operators

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

Analytic Number Theory

Analytical Methodology

Course description not available.

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

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

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

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

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

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

Course description not available.

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.

Comparative Genomics, Proteomics and Metabolomics

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

Geometry of Curves and Surfaces

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

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

Green Chemistry and Sustainability

Hardy-Hilbert Spaces and Applications 

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.

Course description not available.

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.

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

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

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

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

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

Course description not available.

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

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

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

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

Mathematical Computing

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

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

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

Course description not available.

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.

Metric Spaces

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

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.

Course description not available.

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

Numerical PDE

Optimal control of systems governed by PDEs

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

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

Course description not available.

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).

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

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

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

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

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.

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

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

Reading course

Reading Course - Lie Groups: Representations and Invariants

Reading Course - Approximation Problems in Normed Linear Spaces

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

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

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

Research Methodology

Research Methodology

Research Project Part II

Review of Classical Mechanics

Review of Statistical Mechanics

Course description not available.

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

Course description not available.

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

Topics in Mathematics

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

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

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.