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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)

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.