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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)

Introduction


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

References
Discrete Mathematics
Instructor: Prof. Sourav Chakraborty, Department of Computer Science, Chennai Mathematical Institute. In this course we will cover the basics of discrete mathematics.