Discrete Mathematics (English)

   Friday, March 22, 2024   

Starting a new Lecture Notes Series on Discrete Mathematics

Youtube Lecture Playlist Credits 

Channel Name: NPTEL IIT Guwahati

So Let Us Start to This Journey of Learning 

Discrete Mathematics By Lecture Notes together!

Lecture 1: Discrete Mathematics

Lecture 2: Lec 1: Boolean Functions

Lecture 3: Lec 2: Propositional Calculus: Introduction

Lecture 4: Lec 3: First Order Logic: Introduction

Lecture 5: Lec 4: First Order Logic: Introduction (Cont'd)

Lecture 6: Lec 5: Proof System for Propcal

Lecture 7: Lec 6: First Order Logic: wffs, interpretations, models

Lecture 8: Lec 7: Soundness and Completeness of the First Order Proof System

Lecture 9: Lec 8: Sets, Relations, Functions

Lecture 10: Lec 9: Functions, Embedding of the theories of naturals numbers and integers in Set Theory

Lecture 11: Lec 10: Embedding of the theories of integers and rational numbers in Set Theory; Countable Sets

Lecture 12: Lec 11: Introduction to graph theory

Lecture 13: Lec 12: Trees, Cycles , Graph coloring

Lecture 14: Lec 13: Bipartitie Graphs

Lecture 15: Lec 14: Bipartitie Graphs; Edge Coloring and Matching

Lecture 16: Lec 15: Planar Graphs

Lecture 17: Lec 16: Graph Searching; BFS and DFS

Lecture 18: Lec 17: Network Flows

Lecture 19: Lec 18: Counting Spanning Trees in Complete Graphs

Lecture 20: Lec 19: Embedding of the theory of ral numbers in Set Theory; Paradoxes

Lecture 21: Lec 20: ZF Axiomatization of Set Theory

Lecture 22: Lec 21: Partially ordering relations

Lecture 23: Lec 22: Natural numbers, divisors

Lecture 24: Lec 23: Lattices

Lecture 25: Lec 24: GCD, Euclid's Algorithm

Lecture 26: Lec 25: Prime numbers

Lecture 27: Lec 26: Congruences

Lecture 28: Lec 27: Pigeon Hole Principle

Lecture 29: Lec 28: Stirling Numbers, Bell Numbers

Lecture 30: Lec 29: Generating Functions

Lecture 31: Lec 30: Product of Generating Functions

Lecture 32: Lec 31: Composition of Generating Function

Lecture 33: Lec 32: Principle of Inclusion Exclusion

Lecture 34: Lec 33: Rook placement problem

Lecture 35: Lec 34: Solution of Congruences

Lecture 36: Lec 35: Chinese Remainder Theorem

Lecture 37: Lec 36: Totient; Congruences; Floor and Ceiling Functions

Lecture 38: Lec 37: Introduction to Groups

Lecture 39: Lec 38: Modular Arithmetic and Groups

Lecture 40: Lec 39: Dihedral Groups, Isomorhphisms

Lecture 41: Lec 40: Cyclic groups, Direct Products, Subgroups

Lecture 42: Lec 41: Cosets, Lagrange's theorem

Lecture 43: Lec 42: Rings and Fields

Lecture 44: Lec 43: Construction of Finite Fields