Lecture 1 - Boolean Functions

Lecture 2 - Propositional Calculus: Introduction

Lecture 3 - First Order Logic: Introduction

Lecture 4 - First Order Logic: Introduction (Continued...)

Lecture 5 - Proof System for Propcal

Lecture 6 - First Order Logic: wffs, interpretations, models

Lecture 7 - Soundness and Completeness of the First Order Proof System

Lecture 8 - Sets, Relations, Functions

Lecture 9 - Functions, Embedding of the theories of naturals numbers and integers in Set Theory

Lecture 10 - Embedding of the theories of integers and rational numbers in Set Theory; Countable Sets

Lecture 11 - Introduction to graph theory

Lecture 12 - Trees, Cycles, Graph coloring

Lecture 13 - Bipartitie Graphs

Lecture 14 - Bipartitie Graphs; Edge Coloring and Matching

Lecture 15 - Planar Graphs

Lecture 16 - Graph Searching; BFS and DFS

Lecture 17 - Network Flows

Lecture 18 - Counting Spanning Trees in Complete Graphs

Lecture 19 - Embedding of the theory of ral numbers in Set Theory; Paradoxes

Lecture 20 - ZF Axiomatization of Set Theory

Lecture 21 - Partially ordering relations

Lecture 22 - Natural numbers, divisors

Lecture 23 - Lattices

Lecture 24 - GCD, Euclid's Algorithm

Lecture 25 - Prime Numbers

Lecture 26 - Congruences

Lecture 27 - Pigeon Hole Principle

Lecture 28 - Stirling Numbers, Bell Numbers

Lecture 29 - Generating Functions

Lecture 30 - Product of Generating Functions

Lecture 31 - Composition of Generating Function

Lecture 32 - Principle of Inclusion Exclusion

Lecture 33 - Rook placement problem

Lecture 34 - Solution of Congruences

Lecture 35 - Chinese Remainder Theorem

Lecture 36 - Totient; Congruences; Floor and Ceiling Functions

Lecture 37 - Introduction to Groups

Lecture 38 - Modular Arithmetic and Groups

Lecture 39 - Dihedral Groups, Isomorhphisms

Lecture 40 - Cyclic groups, Direct Products, Subgroups

Lecture 41 - Cosets, Lagrange's theorem

Lecture 42 - Rings and Fields

Lecture 43 - Construction of Finite Fields