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Discrete Mathematics

Discrete Mathematics. Instructor: Prof. Ashish Choudhury, Department of Computer Science, IIIT Bangalore. Discrete mathematics is the study of mathematical structures that are discrete in the sense that they assume only distinct, separate values, rather than in a range of values. It deals with the mathematical objects that are widely used in almost all fields of computer science, such as programming languages, data structures and algorithms, cryptography, operating systems, compilers, computer networks, artificial intelligence, image processing, computer vision, natural language processing, etc. The subject enables the students to formulate problems precisely, solve the problems, apply formal proof techniques and explain their reasoning clearly. (from nptel.ac.in)

Lecture 52 - Vertex and Edge Coloring

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Propositional Logic

Lecture 01 - Introduction to Mathematical Logic

Lecture 02 - Logical Equivalence

Lecture 03 - SAT Problem

Lecture 04 - Rules of Inference

Lecture 05 - Resolution

Lecture 06 - Tutorial 1: Part 1

Lecture 07 - Tutorial 1: Part 2

Predicate Logic, Proof Strategies and Induction

Lecture 08 - Predicate Logic

Lecture 09 - 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

Sets and Relations

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

Equivalence Relations, Partitions, Partial Orderings and Functions

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

Theory of Countability

Lecture 27 - Countable and Uncountable Sets

Lecture 28 - Examples of Countably Infinite Sets

Lecture 29 - Cantor's Diagonalization Argument

Lecture 30 - Uncountable Functions

Lecture 31 - Tutorial 5

Combinatorics Part I

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

Combinatorics 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

Graph Theory Part I

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

Graph Theory Part II

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

Number Theory

Lecture 55 - Modular Arithmetic

Lecture 56 - Prime Numbers and GCD

Lecture 57 - Properties of GCD and Bezout'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

Abstract Algebra: Part I

Lecture 61 - Group Theory

Lecture 62 - Cyclic Groups

Lecture 63 - Subgroups

Lecture 64 - More Applications of Groups

Lecture 65 - Discrete Logarithm and Cryptographic Applications

Abstract Algebra: Part II

Lecture 66 - Rings, Fields and Polynomials

Lecture 67 - Polynomials over Fields and Properties

Lecture 68 - Finite Fields Properties I

Lecture 69 - Finite Fields Properties II

Lecture 70 - Primitive Element of a Finite Field

Lecture 71 - Applications of Finite Fields

Lecture 72 - Goodbye and Farewell