'Discrete Mathematics' is a course offered in the second semester of B. C. A. (Bachelor of Computer Applications) program at Amrita Vishwa Vidyapeetham.
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.
TEXTBOOK
- Kenneth H. Rosen, Discrete Mathematics and its Applications, McGraw Hill.
REFERENCES
- R. P. Grimaldi, “Discrete and Combinatorial Mathematics”, Pearson Education, Fifth Edition, 2007.
- Thomas Koshy, “Discrete Mathematics with Applications”, Academic Press, 2005.
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