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Course10610320545 lectures

Discrete Mathematics

Prof. Sajith Gopalan and Prof. Benny George K · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Mathematical Logic - I

  1. Lec 1: Boolean Functions Video
  2. Lec 2: Propositional Calculus: Introduction Video
  3. Lec 3: First Order Logic: Introduction Video

Mathematical Logic - II

  1. Lec 4: First Order Logic: Introduction (Cont'd) Video
  2. Lec 5: Proof System for Propcal Video
  3. Lec 6: First Order Logic: wffs, interpretations, models Video

Mathematical Logic and Set Theory

  1. Lec 7: Soundness and Completeness of the First Order Proof System Video
  2. Lec 8: Sets, Relations, Functions Video
  3. Lec 9: Functions, Embedding of the theories of naturals numbers and integers in Set Theory Video
  4. Lec 10: Embedding of the theories of integers and rational numbers in Set Theory; Countable Sets Video

Graph Theory

  1. Lec 11: Introduction to graph theory Video
  2. Lec 12: Trees, Cycles , Graph coloring Video
  3. Lec 13: Bipartitie Graphs Video

Graph Theory - II

  1. Lec 14: Bipartitie Graphs; Edge Coloring and Matching Video
  2. Lec 15: Planar Graphs Video
  3. Lec 16: Graph Searching; BFS and DFS Video
  4. Lec 17: Network Flows Video
  5. Lec 18: Counting Spanning Trees in Complete Graphs Video

Set Theory & Number Theory

  1. Lec 19: Embedding of the theory of ral numbers in Set Theory; Paradoxes Video
  2. Lec 20: ZF Axiomatization of Set Theory Video
  3. Lec 21: Partially ordering relations Video
  4. Lec 22: Natural numbers, divisors Video

Set Theory & Number Theory- II

  1. Lec 23: Lattices Video
  2. Lec 24: GCD, Euclid's Algorithm Video
  3. Lec 25: Prime numbers Video
  4. Lec 26: Congruences Video

Combinatorics

  1. Lec 27: Pigeon Hole Principle Video
  2. Lec 28: Stirling Numbers, Bell Numbers Video
  3. Lec 29: Generating Functions Video
  4. Lec 30: Product of Generating Functions Video

Combinatorics- II

  1. Lec 31: Composition of Generating Function Video
  2. Lec 32: Principle of Inclusion Exclusion Video
  3. Lec 33: Rook placement problem Video

Number Theory -II

  1. Lec 34: Solution of Congruences Video
  2. Lec 35: Chinese Remainder Theorem Video
  3. Lec 36: Totient; Congruences; Floor and Ceiling Functions Video

Algebra

  1. Lec 37: Introduction to Groups Video
  2. Lec 38: Modular Arithmetic and Groups Video
  3. Lec 39: Dihedral Groups, Isomorhphisms Video

Algebra-II

  1. Lec 40: Cyclic groups, Direct Products, Subgroups Video
  2. Lec 41: Cosets, Lagrange's theorem Video
  3. Lec 42: Rings and Fields Video
  4. Lec 43: Construction of Finite Fields Video

Live Session

  1. Live Session 04-09-2019 Video
  2. Live Session 30-09-2019 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Computer Science and Engineering
Taught by
Prof. Sajith Gopalan, Prof. Benny George K
Level
Undergraduate
Language
English
Subjects
Computer science, Engineering
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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