Course

Logic, Mathematical Reasoning and Counting: Logic, Prepositional
Equivalence, Predicate and Quantifiers, Theorem Proving, Functions, Mathematical
Induction. Recursive Definitions, Recursive Algorithms, Basics of Counting,
Pigeonhole Principle, Permutation and Combinations. (Sections: 1.1 -1.3, 1.5 -1.7,
2.3, 4.1 – 4.4, 5.1 – 5.3 and 5.5)

Relations and Their Properties: Representing Relations, Closure of Relations,
Partial Ordering, Equivalence Relations and partitions. (Sections: 7.1, 7.3 – 7.6)
Advanced Counting Techniques and Relations: Recurrence Relations, Solving
Recurrence Relations, Generating Functions, Solutions of Homogeneous
Recurrence Relations, Divide and Conquer Relations, Inclusion-Exclusion.
(Sections: 6.1 – 6.6)

Graph Theory: Introduction to Graphs, Graph Operations, Graph and Matrices,
Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest Path
Problem, Planar Graph, Graph Colorings and Chromatic Polynomials. (Sections:
8.1 – 8.8)

Text Book

1. Kenneth H. Rosen, “Discrete Mathematics and its Applications”, Tata McGraw-
2. Hill Publishing Company Limited, New Delhi, Sixth Edition, 2007.

References

1. R.P. Grimaldi, “Discrete and Combinatorial Mathematics”, Pearson Education,
   Fifth Edition, 2007.
2. Thomas Koshy, “Discrete Mathematics with Applications”, Academic Press,
   2005.
3. Liu, “Elements of Discrete Mathematics”, Tata McGraw- Hill Publishing
   Company Limited , 2004.