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Course11110705841 lectures

Discrete Mathematics

Dr. Sugata Gangopadhyay and Dr. Aditi Gangopadhyay · IIT Roorkee

Start with lecture 1 At NPTEL

Lectures

Set Theory

  1. Introduction to the theory of sets Video
  2. Set operation and laws of set operation Video
  3. The principle of inclusion and exclusion Video
  4. Application of the principle of inclusion and exclusion Video

Logic

  1. Fundamentals of logic Video
  2. Logical Inferences Video
  3. Methods of proof of an implication Video
  4. First order logic(1) Video
  5. First order logic(2) Video
  6. Rules of influence for quantified propositions Video

Mathematical Induction

  1. Mathematical Induction(1) Video
  2. Mathematical Induction(2) Video

Discrete Probability

  1. Sample space, events Video
  2. Probability, conditional probability Video
  3. Independent events, Bayes theorem Video
  4. Information and mutual information Video

Graph Theory

  1. Basic definition Video
  2. Isomorphism and sub graphs Video
  3. Walks, paths and circuits operations on graphs Video
  4. Euler graphs, Hamiltonian circuits Video
  5. Shortest path problem Video
  6. Planar graphs Video

Relations

  1. Basic definition. Video
  2. Properties of relations Video
  3. Graph of relations Video
  4. Matrix of relation Video
  5. Closure of relaton(1) Video
  6. Closure of relaton(2) Video
  7. Warshall's algorithm Video

Partially ordered sets

  1. Partially ordered relation Video
  2. Partially ordered sets Video
  3. Lattices Video

Boolean algebra and boolean function

  1. Boolean algebra Video
  2. Boolean function(1) Video
  3. Boolean function(2) Video

Discrete numeric function

  1. Discrete numeric function Video
  2. Generating function Video

Recurrence relations

  1. Introduction to recurrence relations Video
  2. Second order recurrence relation with constant coefficients(1) Video
  3. Second order recurrence relation with constant coefficients(2) Video
  4. Application of recurrence relation Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Taught by
Dr. Sugata Gangopadhyay, Dr. Aditi Gangopadhyay
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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