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September 25, 2023

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Description

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)

Course Curriculum

    • Lecture 01 – Introduction to Mathematical Logic Unlimited
    • Lecture 02 – Logical Equivalence Unlimited
    • Lecture 03 – SAT Problem Unlimited
    • Lecture 04 – Rules of Inference Unlimited
    • Lecture 05 – Resolution Unlimited
    • Lecture 06 – Tutorial 1: Part 1 Unlimited
    • Lecture 07 – Tutorial 1: Part 2 Unlimited
    • Lecture 08 – Predicate Logic Unlimited
    • Lecture 09 – Rules of Inferences in Predicate Logic Unlimited
    • Lecture 10 – Proof Strategies I Unlimited
    • Lecture 11 – Proof Strategies II Unlimited
    • Lecture 12 – Induction Unlimited
    • Lecture 13 – Tutorial 2: Part I Unlimited
    • Lecture 14 – Tutorial 2: Part II Unlimited
    • Lecture 15 – Sets Unlimited
    • Lecture 16 – Relations Unlimited
    • Lecture 17 – Operations on Relations Unlimited
    • Lecture 18 – Transitive Closure of Relations Unlimited
    • Lecture 19 – Warshall’s Algorithm for Computing Transitive Closure Unlimited
    • Lecture 20 – Tutorial 3 Unlimited
    • Lecture 21 – Equivalence Relation Unlimited
    • Lecture 22 – Equivalence Relations and Partitions Unlimited
    • Lecture 23 – Partial Ordering Unlimited
    • Lecture 24 – Functions Unlimited
    • Lecture 25 – Tutorial 4: Part I Unlimited
    • Lecture 26 – Tutorial 4: Part II Unlimited
    • Lecture 27 – Countable and Uncountable Sets Unlimited
    • Lecture 28 – Examples of Countably Infinite Sets Unlimited
    • Lecture 29 – Cantor’s Diagonalization Argument Unlimited
    • Lecture 30 – Uncountable Functions Unlimited
    • Lecture 31 – Tutorial 5 Unlimited
    • Lecture 32 – Basic Rules of Counting Unlimited
    • Lecture 33 – Permutation and Combination Unlimited
    • Lecture 34 – Counting using Recurrence Equations Unlimited
    • Lecture 35 – Solving Linear Homogeneous Recurrence Equations, Part I Unlimited
    • Lecture 36 – Solving Linear Homogeneous Recurrence Equations, Part II Unlimited
    • Lecture 37 – Tutorial 6: Part I Unlimited
    • Lecture 38 – Tutorial 6: Part II Unlimited
    • Lecture 39 – Solving Linear Non-Homogeneous Recurrence Equations Unlimited
    • Lecture 40 – Catalan Numbers Unlimited
    • Lecture 41 – Catalan Numbers – Derivation of Closed Form Formula Unlimited
    • Lecture 42 – Counting using Principle of Inclusion-Exclusion Unlimited
    • Lecture 43 – Tutorial 7 Unlimited
    • Lecture 44 – Graph Theory Basics Unlimited
    • Lecture 45 – Matching Unlimited
    • Lecture 46 – Proof of Hall’s Marriage Theorem Unlimited
    • Lecture 47 – Various Operations on Graphs Unlimited
    • Lecture 48 – Vertex and Edge Connectivity Unlimited
    • Lecture 49 – Tutorial 8 Unlimited
    • Lecture 50 – Euler Path and Euler Circuit Unlimited
    • Lecture 51 – Hamiltonian Circuit Unlimited
    • Lecture 52 – Vertex and Edge Coloring Unlimited
    • Lecture 53 – Tutorial 9: Part I Unlimited
    • Lecture 54 – Tutorial 9: Part II Unlimited
    • Lecture 55 – Modular Arithmetic Unlimited
    • Lecture 55 – Modular Arithmetic Unlimited
    • Lecture 56 – Prime Numbers and GCD Unlimited
    • Lecture 57 – Properties of GCD and Bezout’s Theorem Unlimited
    • Lecture 58 – Linear Congruence Equations and Chinese Remainder Theorem Unlimited
    • Lecture 59 – Uniqueness Proof of the CRT Unlimited
    • Lecture 60 – Fermat’s Little Theorem, Primality Testing and Carmichael Numbers Unlimited
    • Lecture 61 – Group Theory Unlimited
    • Lecture 62 – Cyclic Groups Unlimited
    • Lecture 63 – Subgroups Unlimited
    • Lecture 64 – More Applications of Groups Unlimited
    • Lecture 65 – Discrete Logarithm and Cryptographic Applications Unlimited
    • Lecture 66 – Rings, Fields and Polynomials Unlimited
    • Lecture 67 – Polynomials over Fields and Properties Unlimited
    • Lecture 68 – Finite Fields Properties I Unlimited
    • Lecture 69 – Finite Fields Properties II Unlimited
    • Lecture 70 – Primitive Element of a Finite Field Unlimited
    • Lecture 71 – Applications of Finite Fields Unlimited
    • Lecture 72 – Goodbye and Farewell Unlimited

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