## Course Detail

 Course Name Discrete Mathematics Course Code 15MAT201 Program B. Tech. in Computer Science and Engineering Semester Three Year Taught 2019

### Syllabus

##### Unit 1

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)

##### Unit 2

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)

##### Unit 3

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 Books

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

### Resources

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

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