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Discrete Mathematics (Web)
Syllabus
Co-ordinated by :
IIT Kanpur
Available from :
2013-05-02
Lec :
1
Modules / Lectures
Contents
Contents
Properties of Integers and Basic Counting
Basic Set Theory
Well Ordering Principle and the Principle of Mathematical Induction
Strong Form of the Principle of Mathematical Induction
Division Algorithm and the Fundamental Theorem of Arithmetic
Relations, Partitions and Equivalence Relation
Functions
Distinguishable Balls
Binomial Theorem
Onto Functions and the Stirling Numbers of Second Kind
Indistinguishable Balls and Distinguishable Boxes
Indistinguishable Balls in Indistinguishable Boxes
Lattice Paths and Catalan Numbers
Catalan Numbers Continued
Generalizations
Advanced Counting and Generating Functions
Pigeonhole Principle
Pigeonhole Principle Continued
Principle of Inclusion and Exclusion
Formal Power Series
Formal Power Series Continued
Application to Recurrence Relation
Application to Recurrence Relation Continued
Application to Recurrence Relation Continued
Applications to Generating Functions Continued
Groups and Polya Theory
Groups
Example of Groups
SubGroups
Lagrange’s Theorem
Applications of Lagrange’s Theorem
Group Action
Group Action Continued
The Cycle Index Polynomial
Polya Inventory Theorem
Topics in Classical Graph Theory
Basic Graph Theory
Graph Operations
Matrices related with Graphs
Matrix Tree Theorem
Eulerian graphs
Planar Graphs
Euler’s Theorem for Planar Graphs
Stereographic Projection
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