COURSE SUMMARY
Course Title:
Discrete Mathematics
Course Code:
18MAT309
Year Taught:
2019
Semester:
4
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Discrete Mathematics' is a course offered in Fifth Semester of B. Sc. - B. Ed. in Physics, Mathematics, Computer Science program at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

#### Scope and Objectives

On completion of the course, the student teacher will;

To enable students to understand the basics of logic, permutations and combinations and use effectively algebraic techniques to analyse basic discrete structures and algorithms.

#### Syllabus

Unit I:

Logic, Mathematical Reasoning and Counting: Logic, Prepositional Equivalence, Predicate and Quantifiers, Theorem Proving.

Unit II:

Basics of Counting, Pigeonhole Principle, Permutation and Combinations.

Unit III:

Relations and Their Properties: Representing Relations, Closure of Relations, Partial Ordering, Equivalence Relations and partitions

Unit IV:

Advanced Counting Techniques and Relations: Recurrence Relations, Solving Recurrence Relations, Solutions of Homogeneous Recurrence Relations.

Unit V:

Graph Theory: Introduction to Graphs, Graph Operations, Graph and Matrices, Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest Path Problem.

#### Textbook

1. Kenneth H. Rosen, “Discrete Mathematics and its Applications”, Tata McGraw- 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.