Instructor:
Ambedkar Dukkipati

TAs: Ashwin Guha and Maria Francis

Venue: L4 (Lecture Hall Complex)

Time: Tuesday and Thursday from 11.30 to 1

- 4 AUG (Tu): Introductory Class: On Logic, Set Theory and Moderen Mathematics
- 9 AUG (Tu): Introduction to Equivalance relations
- 16 AUG (Tu): Equivalance relations and Isomorphism Theorems
- 25 AUG (Tu): Natural Numbers, Axioms, Mathematical Inductions
- 30 AUG (Tu): Definition of Cartisian product from set theory axioms: Axiom of extension and Axiom of specification
- 6 SEP (Tu): Division algorithm for Z; Constructuion of Zn; Definitions of orders, partial and quasi orders.
- 13 SEP (Tu): Well founded and Noetherian relations
- 15 SEP (Th): (Tutorial by Ashwin)
- 20 SEP (Tu): Characterizations of Well foundaed relations and Axiom of Choice
- 21 SEP (Wed): Motivation for Dicksons Lemma, Back to relations, functions and partial functions
- 22 SEP (Th): Compositions of relations and functions, Inverse functions
- 27 SEP (Tu): Left and right inverses and their characterizations, Direct inverses and properties
- 28 SEP (Wed): Towards proving Dickson's Lemma
- 6 OCT (Th): (Tutorial by Ashwin )
- 11 OCT (Tu): Dickson's Lemma
- 12 OCT (Wed): Konig's Lemma
- 13 OCT (Th): (Mid Sem)
- 18 OCT (Tu): Integers: Lecture by Ashwin
- 19 OCT (Wed): Polynomials in one variable by Maria
- 25 OCT (Tu): (Exam paper discussion by Ashwin)
- 1 Nov (Tu) : Semigroups and Monoids
- 3 Nov (Th) : Recurssion theorem
- 8 Nov (Tu) : Basic groups
- 9 Nov (Wed) : Permutations
- 10 Nov (Th): Permutations
- 15 Nov (Tu): group isomorphisms
- 17 Nov (Th): kernels of group homomorphisms, subgroups
- 22 Nov (Tu): Inductive definitions
- 27 Nov (Tu): *******