NPTEL : NOC:Discrete Mathematics (IIITB) (Computer Science and Engineering)

Co-ordinators : Prof. Ashish Choudhury


Lecture 1 - Introduction to Mathematical Logic

Lecture 2 - Logical Equivalence

Lecture 3 - SAT Problem

Lecture 4 - Rules of Inference

Lecture 5 - Resolution

Lecture 6 - Tutorial 1 - Part I

Lecture 7 - Tutorial 1 - Part II

Lecture 8 - Predicate Logic

Lecture 9 - Rules of Inferences in Predicate Logic

Lecture 10 - Proof Strategies - I

Lecture 11 - Proof Strategies - II

Lecture 12 - Induction

Lecture 13 - Tutorial 2 - Part I

Lecture 14 - Tutorial 2 - Part II

Lecture 15 - Sets

Lecture 16 - Relations

Lecture 17 - Operations on Relations

Lecture 18 - Transitive Closure of Relations

Lecture 19 - Warshall’s Algorithm for Computing Transitive Closure

Lecture 20 - Tutorial - 3

Lecture 21 - Equivalence Relation

Lecture 22 - Equivalence Relations and Partitions

Lecture 23 - Partial Ordering

Lecture 24 - Functions

Lecture 25 - Tutorial 4 - Part I

Lecture 26 - Tutorial 4 - Part II

Lecture 27 - Countable and Uncountable Sets

Lecture 28 - Examples of Countably Infinite Sets

Lecture 29 - Cantor’s Diagonalization Argument

Lecture 30 - Uncomputable Functions

Lecture 31 - Tutorial - 5

Lecture 32 - Basic Rules of Counting

Lecture 33 - Permutation and Combination

Lecture 34 - Counting Using Recurrence Equations

Lecture 35 - Solving Linear Homogeneous Recurrence Equations - Part I

Lecture 36 - Solving Linear Homogeneous Recurrence Equations - Part II

Lecture 37 - Tutorial 6 - Part I

Lecture 38 - Tutorial 6 - Part II

Lecture 39 - Solving Linear Non-Homogeneous Recurrence Equations

Lecture 40 - Catalan Numbers

Lecture 41 - Catalan Numbers - Derivation of Closed Form Formula

Lecture 42 - Counting Using Principle of Inclusion-Exclusion

Lecture 43 - Tutorial - 7

Lecture 44 - Graph Theory Basics

Lecture 45 - Matching

Lecture 46 - Proof of Hall’s Marriage Theorem

Lecture 47 - Various Operations on Graphs

Lecture 48 - Vertex and Edge Connectivity

Lecture 49 - Tutorial - 8

Lecture 50 - Euler Path and Euler Circuit

Lecture 51 - Hamiltonian Circuit

Lecture 52 - Vertex and Edge Coloring

Lecture 53 - Tutorial 9 - Part I

Lecture 54 - Tutorial 9 - Part II

Lecture 55 - Modular Arithmetic

Lecture 56 - Prime Numbers and GCD

Lecture 57 - Properties of GCD and Bézout’s Theorem

Lecture 58 - Linear Congruence Equations and Chinese Remainder Theorem

Lecture 59 - Uniqueness Proof of the CRT

Lecture 60 - Fermat’s Little Theorem, Primality Testing and Carmichael Numbers

Lecture 61 - Group Theory

Lecture 62 - Cyclic Groups

Lecture 63 - Subgroups

Lecture 64 - Discrete Logarithm and Cryptographic Applications

Lecture 65 - More Applications of Groups

Lecture 66 - Rings, Fields and Polynomials

Lecture 67 - Polynomials Over Fields and Properties

Lecture 68 - Finite Fields and Properties - I

Lecture 69 - Finite Fields and Properties - II

Lecture 70 - Primitive Element of a Finite Field

Lecture 71 - Applications of Finite Fields

Lecture 72 - Goodbye and Farewell