0
(
ratings
)
1
students
Created by:
Last updated:
Duration:
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
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 NonHomogeneous Recurrence Equations Unlimited
 Lecture 40 – Catalan Numbers Unlimited
 Lecture 41 – Catalan Numbers – Derivation of Closed Form Formula Unlimited
 Lecture 42 – Counting using Principle of InclusionExclusion 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
About the instructor
Instructor Rating
Reviews
Courses
Students