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Course Detail

Course Name Discrete Mathematics
Course Code 18MAT112
Program B. C. A., B. C. A., B. C. A. (Bachelor of Computer Applications)
Semester Two
Credits Four
Year Taught 2018
Degree Undergraduate (UG)
Integrated Degree
Campus Kochi, Mysuru, Amritapuri

Syllabus

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 Books

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.

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