# InfoCoBuild

## 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)

 Introduction

 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

 References 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.