# InfoCoBuild

## Discrete Mathematics

Discrete Mathematics. Instructors: Dr. Sugata Gangopadhyay, Dr. Aditi Gangopadhyay, Department of Mathematics, IIT Roorkee. This course covers several important topics of Discrete Mathematics. This includes set theory and logic, relations, partially ordered sets, Boolean algebra and Boolean functions, analysis of algorithms, recurrence relations, finite state machines, discrete probability and graph theory. The applications of these topics are also discussed. (from nptel.ac.in)

 Introduction to the Theory of Sets

 Set Theory Lecture 01 - Introduction to the Theory of Sets Lecture 02 - Set Operation and Laws of Set Operation Lecture 03 - The Principle of Inclusion and Exclusion Lecture 04 - Application of the Principle of Inclusion and Exclusion Logic Lecture 05 - Fundamentals of Logic Lecture 06 - Logical Inferences Lecture 07 - Methods of Proof of an Implication Lecture 08 - First Order Logic 1 Lecture 09 - First Order Logic 2 Lecture 10 - Rules of Influence for Quantified Propositions Mathematical Induction Lecture 11 - Mathematical Induction 1 Lecture 12 - Mathematical Induction 2 Discrete Probability Lecture 13 - Sample Space, Events Lecture 14 - Probability, Conditional Probability Lecture 15 - Independent Events, Bayes Theorem Lecture 16 - Information and Mutual Information Graph Theory Lecture 17 - Basic Definition Lecture 18 - Isomorphism and Sub Graphs Lecture 19 - Walks, Paths and Circuits/ Operations on Graphs Lecture 20 - Euler Graphs, Hamiltonian Circuits Lecture 21 - Shortest Path Problem Lecture 22 - Planar Graphs Relations Lecture 23 - Basic Definition Lecture 24 - Properties of Relations Lecture 25 - Graph of Relations Lecture 26 - Matrix of Relation Lecture 27 - Closure of Relation 1 Lecture 28 - Closure of Relation 2 Lecture 29 - Warshall's Algorithm Partially Ordered Sets Lecture 30 - Partially Ordered Relation Lecture 31 - Partially Ordered Sets Lecture 32 - Lattices Boolean Algebra and Boolean Function Lecture 33 - Boolean Algebra Lecture 34 - Boolean Function 1 Lecture 35 - Boolean Function 2 Discrete Numeric Function Lecture 36 - Discrete Numeric Function Lecture 37 - Generating Function Recurrence Relations Lecture 38 - Introduction to Recurrence Relations Lecture 39 - Second Order Recurrence Relation with Constant Coefficients 1 Lecture 40 - Second Order Recurrence Relation with Constant Coefficients 2 Lecture 41 - Application of Recurrence Relation

 References Discrete Mathematics Instructors: Dr. Sugata Gangopadhyay, Dr. Aditi Gangopadhyay, Department of Mathematics, IIT Roorkee. This course covers several important topics of Discrete Mathematics.