Course Catalog

Students in this course will apply principles from general and organic chemistry, as well as general biology, to understand the molecular processes that characterize life. The goal of this class will be to give students a solid background with which they can appreciate the chemistry of life. Beginning with fundamental principles, the course will then delve into a detailed look at metabolism - the specific means by which organisms use chemical energy to drive cell functions and how they convert simple molecules to complex biological molecules. Students will have the opportunity for independent work, and will apply the principles of biochemistry to a research project that they will design, execute, and present.

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

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

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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.

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

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

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

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Applied Chemistry

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

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

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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

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

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

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

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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.

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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.

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

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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.

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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.

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

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This is an introductory course in condensed matter physics. It covers Crystals, lattices and symmetry group of lattices, lattice vibrations, electrons in solid, conductors, insulators, & semi-conductors.

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

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

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

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

The principles of chemical kinetics, as well as equilibrium and non-equilibrium statistical .mechanics will be covered in this advanced course. The associated computer lab will introduce the student to classical and ab initio quantum molecular dynamics and Monte Carlo simulations of liquids and proteins. The techniques learned in this course will applied to substantive research projects that the students will design, execute, and present. Students will be encouraged to seek avenues for publication of their most significant results BOOKS: Readings will be assigned from multiple sources.

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).

This digital electronic course is a continuation to PHY206 course. This covers the Boolean algebra, logic gates, advanced electronic circuits including, operational amplifiers, adder, A/D and D/A convertors, flip flops, timers, counters. The underlying concepts will be further strengthened by introducing 8085/8086 microprocessor and its programming.

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

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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.

PHY 103 and 104 courses together with their labs forms the foundation, by the end of 1st semester, the student would have mastered the basic concepts underlying the Newtonian physics, Special theory of Relativity, and electromagnetism.

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

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

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

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

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

Course description not available.

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

Vascular Dysfunction: The primary structure, characteristics and function of Endothelial cells. Involvement of endothelial cells in inflammation and pathogenesis following pathogen attack and blood brain 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: Culture of human pathogens, Co-culture and Growth assays, Live cell Immunoflourescence.   References: Recent publications on Host pathogen Interaction and reviews will be provided.

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

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

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

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

Course description not available.

This course aims to expose students to Physics concepts essential to understand Physical aspects of various biological systems and processes.

This course in computational physics is centered around the idea of how to solve the partial differential equations encountered in PHY 104 on a personal computer.

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

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

Both PHY 203 & PHY 204 courses provide a modern introduction to mathematics for physics, using the two unifying ideas of linear vector spaces and differential forms.

This is a continuation of PHY 101 meant for engineers and non-physics majors. The course will introduce students to Electricity and Magnetism, Maxwell’s equations, light as an electromagnetic wave, and wave optics.

This course introduces the fundamental of quantum mechanics. These principles are illustrated by applying them to various interesting contemporary problems, using minimal of mathematical framework.

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

Course description not available.

IPR, Patent Laws & Bioethics

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

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

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

In this course we will learn about cellular macromolecules namely nucleic acids, proteins, carbohydrates and lipids. The chemistry and biochemistry associated with these macromolecules will be discussed. The goal is to learn about important natural molecules, not only from a structural but from a chemical point of view as well. We will talk about the chemistry associated with these molecules, their importance and how we can interfere with it.Classes will be through a combination of group discussions, reading assignments, projects, presentations and lectures. Students are expected to do library research, write papers, and present discussion in class. Review articles and papers used in this course will be provided. COURSE CONTENT:  Introduction Nucleic Acid (DNA and RNA) Background Function and importance Structure Biosynthesis/replication Chemical synthesis Sequencing Maxam Gilbert Sanger dideoxy Bisulfite sequencing Mass spectrometry NGS DNA chemistry DNA damage Spontaneous depurination deamination Alkylation Oxidative DNA damage DNA-DNA crosslinks DNA-Protein crosslinks DNA methylation and demethylation Mutagenesis Repair Epigenetics RNA editing Ribozymes Diseases and carcinogenesis Proteins What are proteins Functions Amino acids Structure (primary, secondary, tertiary, quaternary) Sequencing Chemical and proteomics Peptide synthesis Enzymatic reactions Diseases Lipids Functions and importance Fatty acids Phospholipids Steroids Diseases Carbohydrates Introduction Function and importance in chemistry and biology Glycoconjugates Structural features Biosynthesis Chemical synthesis Industrial preparation Prerequisites: CHY221, CHY112, Biochemistry.

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.

Course description not available.

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.

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.

Course description not available.

Blackbody radiation, Einstein A and B coefficients, absorption and emission of radiation, lineshape functions, natural Lifetime broadening, pressure broadening, Doppler broadening. Rotational Spectroscopy: Rotation and rigid bodies, moment of inertia tensor and principal axis, diatomic and linear molecule: selection rule, centrifugal distortion, rotational line intensities for diatomic and linear molecule, symmetric tops. Vibrational Spectroscopy: Diatomic molecules, wave function for harmonic and anharmonic oscillator, , selection rule, spectrum for harmonic and anharmonic oscillator, Fundamental, overtone, diatomic vibrating rotator and vibration-rotation spectrum: P, Q, R branches, vibrations of polyatomic molecules, Normal mode coordinates and their symmetry, Determining Infrared active vibrations from character table. Light scattering and the Raman effect, classical model of Raman effect, Polarizability tensor, Stokes scattering and Anti stokes scattering, Depolarization ration in Raman, Rotational Raman spectrum for diatomic and linear molecules and symmetric tops, Rule of Mutual exclusion, vibrational Raman spectrum, Raman activity of vibrations from character table. Electronic Spectroscopy: Electronic wave function, hydrogen atom spectrum, orbital angular momentum, electron spin angular momentum, total electronic angular momentum, fine structure of hydrogen atom spectrum, many electron atoms, term symbols, Zeeman effect, electronic spectra of diatomic molecules, vibrational progressions, Frank-Condon principle, Rotational Fine structure, Fortrat diagram, electronic angular momentum for diatomic molecules, spectrum of molecular hydrogen, photoelectron spectroscopy; Fluorescence spectroscopy. NMR: relaxation, 2-D NMR, Bloch equation, factors influencing the coupling constant, germinal coupling, vicinal coupling, heteronuclear coupling, deuterium exchange, simplification of complex spectra in NMR: spin decoupling and Lanthanide shift reagents, Nuclear Overhauser effect (NOE), resonance of other nuclei. 13C NMR: Chemical shift, 13C coupling constants, two-dimensional NMR spectroscopy, NOESY, DEPT, INEPT terminology. Recommended Books: Fundamentals of Molecular Spectroscopy by Banwell, C. N. Modern Infrared spectroscopy analytical chemistry by open learning, by Molecular Fluorescence: Principles and applications by Valeur, Bernard, Berberan-Santos, Mario, N. (available in library). NMR spectroscopy Basic Principles, Concepts and applications in chemistry Organic spectroscopy by William Kemp. Spectroscopy of organic compounds by Kalsi, P. S. 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.

Course description not available.

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

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

Course description not available.

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

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

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

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

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

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

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

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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.

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This course in quantum mechanics builds on PHY 304. It covers scattering theory, systems with identical particles, second quantization, Bose and Fermi Statistics, introduction to atomic and nuclear physics.

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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

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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.

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

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

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

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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.

This course introduces the fundamental concept of statistical physics and thermodynamics from a modern point of view. It covers the fundamental principles of statistical physics and thermodynamics, Classical and Quantum gases, and Phase transitions.

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Structure and Bonding

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.

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The Nature of Materials

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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.

Formalisms, Electron Counting, Bonding (How Things Work) Organometallic Reaction Mechanisms Synthetic Applications of Complexes Containing Metal-Carbon Sigma-Bonds Synthetic Applications of Transition Metal Carbonyl Complexes Synthetic Applications of Transition Metal Carbene Complexes Synthetic Applications of Transition Metal Alkene, Diene, and Dienyl Complexes Synthetic Applications of Transition Metal Alkyne Complexes Note: Each topic will end with a discussion section, where student participation is important and will have direct implication on their grade

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.

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