NOC:Discrete Mathematics (Prof. Sajith Gopalan)


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