Discrete Structures

Lectures

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): *******

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