**Course outline**- Introduction
- Classical Mechanics
- Continous Symmetries – Noether theorem
- Scattering
- Klein-Gordan Field
- Canonical quantization
- Klein-Gordan Propagator
- Dirac Field
- Relativistic covariance
- Dirac equation
- Dirac matrices
- Quantization
- Discrete symmetries C, P, T
- Interacting Field theory
- Relativistic Perturbation theory
- Wick's theorem
- Feynman Rules
- S Matrix
- Digrammatics
- Applications
- Electron-Positron scattering
- g – 2
- Renormalization and Regularization

**Text books**- Quantum Field theory – Mark Srednicki (Cambridge, 2006)
- An introduction to Quantum field theory - M. Peskin and D. V. Schroeder (Persus, 1995)
- Quantum field theory in Condensed matter - Alexei M. Tsvelik (Cambridge, 2003)
- Quantum field theory in a nut shell – A. Zee (University Press)

This course is a basic introduction to general theory of relativity and its applications to isolated macroscopic objects and cosmology.

**Course outline**- Covariance of Physical Laws
- Special Relativity
- The Equivalence Principle
- Space and Spacetime Curvature
- Tensors in Curved Spacetime
- The Geodesic equation
- Curvature and Einstein Field Equations
- Geometry Outside of a Spherical Star
- Tests of General Relativity
- Black Holes
- Gravitational Radiation
- Cosmology

**References**- Gravity- An introduction to Einstein's general relativity – James B. Hartle (Addison-Wesley, 2003)
- Gravitation and Cosmology - S. Weinberg (Wiley, 1972)
- Introduction to General Relativity - J. V. Narlikar (Cambridge)

The aim of this course is to introduce the Mathematics and Physics majors basic concepts and techniques to solve second order (ordinary and partial) differential equations. Here is the flow chart giving the course outline.

*Credit: Pranav Khandelwal for making in xfig*

The aim of this course is to introduce the basic concepts of statistical mechanics to students from all four streams -- Biology, Chemistry, Mathematics and Physics. Hence, the approach is more towards understanding and using techniques to apply to different areas of science than the mathematical rigour. The course does not require knowledge of Hamlitonian/phase-space structure while it requires a preliminary knowledge of quantum mechanics.

So, the course structure will be different compared to the standard text books like Huang, Pathria, Reichl. Most part of the course will focus on systems with discrete energy levels like Harmonic oscillator, spin systems (with and without interactions) in Microcanonical and canonical ensemble picture. After familiarizing with discrete systems, continous systems --- like ideal gas, black-body radiation --- will be discussed. If time permits, the connection between statistical mechanics and path integrals will be introduced.

**Course outline**- Review of thermodynamics
- Basics of statistical Mechanics
- Definition of state of system: Macroscopic and Microscopic
- Connection between Micro-state and Macrostate
- Concept of ensemble
- Systems with constant energy: Microcanonical ensemble
- Maximum probabliity postulate and Boltzmann entropy (Microcanonical ensemble)
- Application of Boltzmann entropy formula to simple systems
- Systems with varying energy: Canonical emsemble
- Boltzmann probability distribution law
- Canonical Ensemble
- Difference between microcanonical and canonical ensemble
- Partition function
- Gibbs entropy and relation to Boltzmann entropy
- Validity of canonical ensemble
- Systems with varying energy and number: Grand-canonical emsemble
- Need for definition of chemical potential
- Mathematical definition of chemical potential
- Grand-canonical Ensemble
- Grand-partition function
- Application of canonical ensemble to discrete systems
- Einstein model of solids
- Paramagnetic systems in external magnetic field
- Interacting spin systems -- 1-D Ising model
- Application of canonical ensemble to continous systems
- Ideal monoatomic and polyatomic gases
- Black-body radiation
- Debye model of solids
- Semi-classical partition function
- Cluster expansion
- Non-ideal gases
- Quantum ideal gases
- Bose-Einstein
- Fermi-Dirac
- Applications

**References**- F. Reif, Statistical Mechanics, Berkeley Vol: 5
- Callen, Thermodynamics and Thermostatistics, Wiley
- Mandl, Statistical Physics, II edition