1. Simple introduction to basic Topology: Topological Spaces , Topological Invariants,
Topological Equivalence. (10 Lectures)
2. Homotopy: Homotopy Type, Paths, the Fundamental Group, Homotopy groups. Uses of
3. Differentiable Manifolds: Definition of Manifold, Calculus on Manifolds, Differential
forms, Connections, Curvature, integration on Differential Forms, Electrodynamics in
terms of differential forms.(10 Lectures)
Part 2:Group Theory and Representations[20 lectures)
a) Review of Group Theory and Representations, Representations of finite groups.
Application to crystallography.(8 lectures)
b) Lie Groups and Lie Algebras and their representations.(6 lectures)
c) Familiar Lie groups and Lie Algebras in Physics. (6 Lectures)
Books:
1. Main Text: Lectures on Advanced Mathematical Methods in Physics, Sunil Mukhi and N.
Mukunda, World Scientific (2010).
2. Topology by E.M. Patterson, University Mathematical Texts .
3. Differential Geometry for Physicists and Mathematicians, Jose P. Vargas World Scientific
(2014).
4. Mathematics for Physics, Michael Stone and Paul Goldbart, Cambridge University Press
(2009)
5. Falicov,L.M. Group Theory and Its Physical Applications (Lectures in Physics)( Univ of
Chicago Press,1966)
6. Lichtenberg, D.B, Unitary Symmetry and Elementary particles (Academic Press,1978)
PY555O39 Experimental methods
Important classes of materials: Metals; Alloys; Metallic composites; Polymers; Ceramics,
Glasses and crystals; Preparation of materials: glasses, crystals, thin films.
Phase diagrams, the Phase Rule; soluble, partially soluble and insoluble systems, Solid
solutions and compounds; single and multiphase materials; Ordering phenomena in
substitutional alloys; super lattices
Characterization : Metallography, microstructural characterization using Optical microscopy;
Diffraction techniques; Production of X-rays, crystal Structure determination using X-rays,
Neutrons and Electrons; Thermal analysis using DSC,DTA,TGA; Phase transitions;
Electron Microscopy: SEM, TEM, STM; Compositional characterization using EDAX, WDS
Properties of Materials:
Electrical and galvanomagnetic properties, Ionic conductivity, Production of magnetic fields
and Magnetic properties of materials; basics of Multiferroics - temperature dependence of
electrical and magnetic properties; DC and AC methods; Use of Lock-in-amplifier to improve