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Discrete Mathematics

Discrete Mathematics. Instructor: Prof. Sourav Chakraborty, Department of Computer Science, Chennai Mathematical Institute. In this course we will cover the basics of discrete mathematics. We will be learning about the different proof techniques and how to use them for solving different kind of problems. We will introduce graphs and see how graphs can be used for modeling of different problems and see how this can help in solving problems. We will learn how to count the number of possibilities that can arise in different situations. (from nptel.ac.in)

Lecture 05 - Elementary Number Theory

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Introduction

Lecture 01 - Course Introduction

Lecture 02 - Sets, Relations and Functions

Lecture 03 - Propositional Logic and Predicate Logic

Lecture 04 - Propositional Logic and Predicate Logic (cont.)

Lecture 05 - Elementary Number Theory

Proof Techniques (Part 1)

Lecture 06 - Formal Proofs: Empirical and Mathematical Proofs

Lecture 07 - Constructive Proofs: Direct Proofs

Lecture 08 - Constructive Proofs: Case Study

Lecture 09 - Constructive Proofs: Case Study (Part 2)

Lecture 09b - Sets, Relations, Function and Logic

Proof Techniques (Part 2)

Lecture 10 - Proof by Contradiction (Part 1)

Lecture 11 - Proof by Contradiction (Part 2)

Lecture 12 - Proof by Contraposition

Lecture 13 - Proof by Counter Example

Proof Techniques (Part 3)

Lecture 14 - Mathematical Induction (Part 1)

Lecture 15 - Mathematical Induction (Part 2)

Lecture 16 - Mathematical Induction (Part 3)

Lecture 17 - Mathematical Induction (Part 4)

Proof Techniques (Part 4)

Lecture 18 - Mathematical Induction (Part 5)

Lecture 19 - Mathematical Induction (Part 6)

Lecture 20 - Mathematical Induction (Part 7)

Lecture 21 - Mathematical Induction (Part 8)

Introduction to Graph Theory

Lecture 22 - Introduction to Graph Theory

Lecture 23 - Handshake Problem

Lecture 24 - Tournament Problem

Lecture 25 - Tournament Problem (cont.)

Graph Theory (Part 2)

Lecture 26 - Ramsey Problem

Lecture 27 - Ramsey Problem (cont.)

Lecture 28 - Properties of Graphs

Modeling of Problems using Linear Programming and Graph Theory

Lecture 29 - Problem 1: Transportation Optimization

Lecture 30 - Problem 2: Bang for Buck in Advertisement

Lecture 31 - Problem 3: Telephone Towers, Problem 4: Scheduling Meetings

Combinatorics

Lecture 32 - Counting for Selection

Lecture 33 - Counting for Distribution

Lecture 34 - Counting for Distribution (cont.)

Lecture 35 - Some Counting Problems

Recurrence Relations

Lecture 36 - Counting using Recurrence Relations

Lecture 37 - Counting using Recurrence Relations (cont.)

Lecture 38 - Solving Recurrence Relations (Part 1)

Lecture 39 - Solving Recurrence Relations (Part 2)

Asymptotic Relations

Lecture 40 - Asymptotic Relations 1

Lecture 41 - Asymptotic Relations 2

Lecture 42 - Asymptotic Relations 3

Lecture 43 - Asymptotic Relations 4

Generating Functions

Lecture 44 - Generating Functions 1

Lecture 45 - Generating Functions 2

Lecture 46 - Generating Functions 3

Lecture 47 - Generating Functions 4

Revision

Lecture 48 - Proof Techniques

Lecture 49 - Modeling: Graph Theory and Linear Programming

Lecture 50 - Combinatorics