Summer 1998
R. C. Cowsik Algebra Groups,Group actions, Sylow theorems, Linear Algebra, symmetry, rings. Ref: Artin chapters 1-6 and 10,11 M. S. Raghunathan Analysis Dedekind cuts & consruction of real numbers, Metric Spaces, continuity, differentiation and integration in R^n Ref: Rudin - Principle's of Mathematical Analysis (Chapters 1-9) C. S. Rajan Number Theory Congruences, Fermat's Little theorem, Euler's theorem, Arithmatic functions, Mobius inversion. Ref: Niven Zukermann - Elementary No. TheorySummer 1999
S. Ramanan Elementary topology till Urysohn's Lemma and Tietze Extension Theorem Ref: Munkres - Topology - A first Course R. C. Cowsik Modules and elementary field theory Ref: Artin Chapter 11,12,13 Arvind Nair Representation theory of finite groups Ref: Artin, Serre (Representation theory of finite groups) J. K. Verma Galois Theory Basic Algebra by Jacobson chapter 4 Indranil Biswas Differential Topology: Introduction to Differential Manifolds Ref. Gullemin Pollak C. S. Rajan Inverse and Implicit Function Theorem Ref: RudinSummer 2000
J. K. Verma Commutative Algebra: Ref: Atiyah - Macdonald (Chapters 1-8) R. C. Cowsik Semi simple rings and modules, Wederburn's Theorem, etc. Injective and Projective Modules. Ref: Jacobson vol.2 M. S. Raghunathan Para compactness, partitions of unity Ref: Topology by Munkres Venkatraman Manifolds, Tangent spaces, Pre Images of regular values, Differential Forms, De Rham complex. ref: Lie groups and manifolds S. Ramanan Chain Complexes, Homological Algebra and defined singular Homology group and long exact sequence Ref: Harper A. J. Parameswaran Homotopy inavriance of Homology, Excision Theorem, Meyer- Vietoris Theorem and examples. Ref: Harper S. Ramanan Sheaf Theory, Sheaf Cohomology and De rham's Theorem A. R. Shastri Complex Analysis Ref: Alhfors, Rudin R. R. Simha Measure Theory Ref: Rudin - Real & Complex Analysis - Chapter 1,2,3