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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 54 - Tutorial 9: Part II


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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