I. Ph.D. Course Work in Physical Sciences  II. Ph.D. Course Work in Chemical Sciences  III. Ph.D. Course Work in Mathematics 
Courses in Physical Sciences  Courses in Chemical Sciences  Courses in Mathematics 
Note: The PrePh.D. students may take any of the courses listed under M.Sc. Semester IV, as recommended by the Ph.D. Student Advisor.  Core Courses:
Optional Courses:
Note: Students can take the necessary Physics courses from the courses in Physical Sciences according to their interests and needs.
 Core Courses:
Optional Courses:
Note: In addition, students may take the courses on Computational Physics: PS427 (3 credit). The core courses are essential for students with M.Sc. degree in mathematics to expand their knowledge of basic mathematics for doing research. Apart from the three core courses (3 credits each), students may either choose one Research Course (3 credits) and the above mentioned course PS 427 (3 credits) or take two Research Courses (3 credits each).

Details of Courses 
I. Courses in Physical Sciences 
Selected courses are offered each semester from the following list:
Suggested Texts:
PS 603: Topics in Classical and Quantum Mechanics This course is intended as a refresher course for incoming Ph.D. students. It reviews material that has been taught in M.Sc. courses, but with greater emphasis on problemsolving. The actual content and format of the course will depend upon the instructor and the composition of the class. The topics to be covered will be selected from the list presented below. Course Outline: Classical Mechanics
Quantum Mechanics
PS 621: Advanced Statistical Physics This course is also intended as a refresher course for incoming Ph.D. students and reviews material that may have been taught in M.Sc. courses. The topics to be covered will be selected from the list presented below:
This course introduces students to the modeling and characterization of stochastic phenomena. Theoretical concepts are illustrated via many physical examples. Course Outline:
PS 651: Dynamical Systems and Chaos This course is intended for students planning to pursue research in the areas of nonlinearity, classical and quantum chaos and related subjects. Depending on the interests of the students/instructor, the topics to be covered will be chosen from the list below: Course Outline: Dynamical Systems
Classical Chaos
Quantum Chaos
Suggested Texts:
PS 662: Experimental Methods in Physics This course introduces the student to various important experimental techniques in physics. Course Outline:
PS 664: Special Topics in Condensed Matter Physics The topics to be covered will be chosen from the list below.
Course Outline:
Suggested Texts:
PS 721: Nonequilibrium Statistical Mechanics Course Outline:
PS 722: Phase Transitions and Critical Phenomena Course Outline:
PS 723: An Introduction to String Theory Prerequisite: Lagrangian mechanics, Special theory of relativity, Electromagnetism, Quantum Mechanics. Course outline:
Suggested Texts:
Course Outline:
PS 762: Introduction to Computational Neuroscience A major effort is currently under way to understand the operation of the central nervous system, and more specifically, of neuronal networks in the brain. This is of great importance at not only the theoretical level, but also for the possibility of understanding the causes and cures for diseases such as Alzheimer’s and Parkinson’s. The approach presently being taken includes both experimental studies and theoretical and computational modeling to jointly address questions that arise in this area of research. There is an increasing need for scientists trained at the interface of these disciplines who possess a strong analytic background together with a solid understanding of biological phenomena. The present course will teach students the basic set of mathematical and computational techniques required for them to pursue higher level research in the field of neuroscience. It would also prepare them, in part, to be able to move on to various industry jobs that require quantitative and analytic skills. For example, several pharmaceutical companies are actively seeking employees with the background to model and simulate processes on the computer prior to production and testing. The set of lectures will cover necessary techniques to be able to understand various biological questions, to address them mathematically and computationally and then to translate results into a language that is accessible to experimentalists. It is envisioned that students who pass this class will be able to immediately utilize their course work in either an experimental lab or on the way towards a PhD. Further the mathematical content of the course is sufficiently general that it will also allow students to work in modeling of biological problems outside of neuroscience, in fields such as genomics, protein signaling networks and even ecology. This PrePh.D. course will be accessible to final year students of the M.Sc.(Physics) program as well as those of the M.Sc.(Life Sciences) and that it could be an optional course in the M Tech. (Systems Biology) programme as well. Prerequisites: Calculus of many variables, a basic understanding of differential equations, ability to use computer software such as MATLAB and the ability to code in Fortran, C, C++ etc. Course Outline [Approximate number of lectures per topic] Introduction to neuroscience with description of some specific neuronal systems. [2] Mathematical background – Introduction to dynamical Systems, review of basics of differential equations, introduction to phase plane analysis, dimensional reduction techniques including timescale separation ideas. [5] Computational techniques – Introduction to relevant computer software such as XPP and Matlab. Classes during this time to be held in a computer lab in a tutorial manner with demonstrations of software usage. [5] Models of single neurons – Derivation of the HodgkinHuxely equations and various reductions such as the FitzHughNagumo and MorrisLecar models. Analysis of these and other basic models such as the Integrate and Fire model. [6] Models of synaptic interactions – Description of synapses and neurotransmitter release. Mathematical models for excitatory and inhibitory synapses. Models for shortterm synaptic plasticity. [6] Small network dynamics – Focus on understanding and characterizing the dynamics of small networks of excitatory, inhibitory or mixedtype neurons. Detailed analysis of conditions leading to complete synchronization, phase locking or chaotic behavior in such networks. [8] Case studies –The dynamics of several specific biological examples will be explored including problems from the following areas: place cells in the hippocampus, sleep rhythms and oscillations of the thalamus, irregular activity in the basal ganglia, working memory models of the cortex and phase lag models of central pattern generators. [8] Textbooks: The following are list of suggested textbooks, although the course will initially be taught from a set of lecture notes. 1. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, by Peter Dayan and Larry F. Abbott. The MIT Press, 2001. ISBN 0262041995 2. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0262090438 3. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, by Bard Ermentrout, SIAM 2002 ISBN 0898715067 
II. Courses in Chemical Sciences 
1. PS 611C Concepts in Chemistry (3 credits) 
Course outline: General Introduction
Physical Chemistry
Organic Chemistry
Inorganic Chemistry
Suggested Texts:
2. PS 612C Analytical Methods in Chemistry (3 credits) Analytical chemistry is one of the important divisions of chemistry that aids researchers in experimental (classical and applied) chemistry to characterize chemical compounds. This course has been designed to introduce students to the methods and concepts of analytical chemistry and would give an overview of the instruments involved for characterization.
Course outline: Molecular Spectroscopy
Electroanalytical Chemistry
Separation Methods
Surface Characterization by Spectroscopy and Microscopy
Thermal Methods
Statistical Analysis Evaluating Data
Suggested Texts:
3. PS 613C Computational Chemistry and its Applications (3 credits) This course is intended for the incoming PhD students to provide the basic knowledge about computational chemistry methods and its use in connection to the experimental research. The aim of this course is to provide students with basic background on computational methods and molecular modeling, including some handson experiences to get started in modeling the physicochemical properties of molecules. The basic theoretical background will be provided in this course, and the emphasis will be given on handon application of the computational methods to model molecular properties. The topics to be covered will be selected from the list presented below depending on the availability of resources and time. Course Outline: Overview of Basic Quantum Chemistry:
Molecular Mechanics:
Simulation Methods:
Overview of Molecular Orbital (MO) Theory:
Semiempirical Implementation of MO Theory:
Ab Initio HartreeFock Theory:
Overview of Density Functional Theory (DFT):
Brief Overview of Condensedphase Calculations:
Suggested Texts:
4. PS 614C Advanced Spectroscopy and its Applications(3 credits) Course Outline:
Overview Radiative Transitions – Absorption and Emission of Light Nonradiative Transitions Various Photophysical Processes
Laser Fundamentals Some Spectroscopic Techniques Applications
5. PS 615C Supramolecular Chemistry(3 credits) This course is designed to introduce students to the interdisciplinary science of supramolecular chemistry. Thermodynamic and kinetic parameters involved in designing supramolecular systems would be taught in detailed in this course. The course would also give insight into the role of supramolecular chemistry of life and designing artificial mimics pertaining to nature. Course Outline: Principles of molecular recognition
Supramolecular Chemistry of Life
Cation Binding Hosts
Anion Binding Hosts
Binding of neutral molecules
Supramolecular reactivity and catalysis
Transport processes and carrier design
Self Processes
Suggested Texts:
6. PS 616C Molecular Materials(3 credits) This course is designed to introduce students to the basic concepts of chemical interactions and the principles and theories involved in the design of newage applicative materials e.g., molecular sensors and switches, organic light emitting diodes, electrochromic materials etc. This course will also emphasize on how the change in molecular design and molecular interactions can tune or modulate the properties of these materials. Principles underlying the organic/inorganic synthesis and purification of materials through wellknown namedreactions will also be covered in a lucid manner.
[Introductory classes would be planned for physics students] Course Outline: Nature of Chemical Interactions:
How can we design giant structures using weak interactions? Selfassembling systems:
Soft Materials Micelles, Vesicles:
Liquid crystals
Organogels, Hydrogels
Glasses
Molecular devices Molecular sensors and switches:
Organic Light Emitting Diodes (OLED’s):
Electrochromic materials:
Nonlnear Optical (NLO) materials:
How to synthesize molecules?
Suggested Texts:
