UNIVERSITY OF MADRAS
Bachelor in Computer Applications (BCA)
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester I - BCA103 - Mathematics

Lecturer/Lab Hours per Week: 6
Duration: 3 hrs
Max Makrs: 100
Credit: 4

Unit - I: Sets, Relations and functions: Sets - set operations - Cartesian products - -Relation - equivalence relation - partition - partial order relation - Functions Inverse functions - Composition of functions - Properties of functions - Binary operation.

Unit - II

Counting principles- The Pigeonhole principle -. counting - permutations and comb,inations - combinatorial arguments - countable and uncountable sets - lattices. Boolean Algebra: Boo lean functions - Normal forms. Unit : III : Binary operations - Semigroups - product and quotients of semigroups - Gropus - product and quotient groups.

Unit - IV

Linear Algebra: Types of matrices - Matrix operations - canonical forms - Inverse of a matrix - Geometric properties of plane linear transformaticm - Rotation - Reflection - Expansion and compressions - Shears - translation - successive transformation - Inverse transformation - Rank and nullity - Linear systems and matrices - Methods of solution to Linear systems (Cramer’s Rule).

Unit - V

Two dimensional Analytical Geometry: pairs of straight lines - circle - system of circles - parabola- ellipse - hyperbola- polar equations - (standard equations and simple properties)Three dimensional

Books for Study and REFERENCE:

1. Bernard Kolman and Robert C. Busby: Discrete mathematical structures for Computer science 2. ed., Printice Hall, N.J. (1987)
2. Olympia Nicodemi: Discrete Mathematics, CBS Pub. & Distributors, New Delhi, 1989.
3. Vatssa B. S. : Discrete Mathematics, 3 ed. Wishwa Prakasban, New Delhi, 1986.
4. Venkataraman, M. K.: Engineering Mathematics - Vol-I & 2, The National Pub.
Co., Madras (1993 and 1992)
5. Alan Doerr and Kenneth Levasseur: Applied Discrete Structures for computer science, Galgotia publications pvt. Ltd., New Delhi, 1988.
6. P.Duaripandian, S. Udayabaskaran and S. Rajalakshrni, Allied Matheniatics, Muhil Publishers, 2002.
7. M.K. Venkataraman, Advanced Mathematics for Engineers and Scientists, The National Pub. Co.