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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)

Lecture 20 - Euler Graphs, Hamiltonian Circuits

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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