Unit 1

Binary operations, group, semi group,monoid, abelian group, subgroup(simple theorems without proof) Boolean algebra-definition-principle of duality-theorems.

Unit 2

Basic Counting Principles, Generating Functions, Euler’s phi-function and its Application to Cryptography.

Unit 3

Relations and their properties – relation matrix, graph of a relation – types of relations -equivalence relation – n-ary relations

Unit 4

Advanced Counting Techniques: Recurrence Relations, Solving Linear Recurrence relations, Divide and Conquer Algorithms and Recurrence relations, Generating Functions, Inclusion Exclusionprinciplesand their Applications.

Unit 5

Introduction to Graph Theory: Graphs, Bipartite Graphs, Eulerian and Hamiltonian Graphs, Graph Connectivity.

Text Book

1. Kenneth H. Rosen, Discrete Mathematics and its Applications, McGraw Hill.

Reference

1. R. P. Grimaldi, “Discrete and Combinatorial Mathematics”, Pearson Education, Fifth Edition, 2007.
2. Thomas Koshy, “Discrete Mathematics with Applications”, Academic Press, 2005.