BCA Syllabus – Discrete Mathematics

1.3  Discrete Mathematics

First Year          Part III Group A                   First Semester                             Subject Code :   

Unit – 1

Set Theory & Relations - Introduction- sets-Venn-Euler diagrams-Operation on sets-Properties of set operations- verification of basic laws of algebra-principle of duality. Relations – Operation on relations - equivalence relation – Closure and Warshall’s Algorithm- partitions and Equivalence classes.

Unit - 2

Functions & Mathematical induction - Functions and Operators – One - One, Onto functions – special types of functions- invertible functions – composition of functions. Techniques of proofs – mathematical induction

Unit - 3

Recurrence relations and Generating functions - Recurrence – an introduction- polynomial and their relations –Solutions of finite order homogeneous (linear) relations-  Solutions of non-homogeneous  relations- generating functions- Primitive recursive function.

Unit  - 4

Matrix algebra - Introduction- operations-inverse, Rank of matrix – solution of Simultaneous linear equations- Eigen values and Eigen vectors.

Unit - 5

Graph Theory - Basic concepts – Matrix representation of graphs – trees, spanning tree, - shortest path problem.

TEXT BOOK:          

Discrete Mathematics - Dr. M. Venkatraman, Dr. N. Sridharan & N. Chandrasekaran

                                      The National Publishing Company

Chapters  - 1,2,3,4,5,6,7,8,9,10

REFERENCE BOOK:

 Applied discrete structures for computer Science, Alan Doerr & Kenneth levasseur,

Asian Student Edition