UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN SOFTWARE ENGINEERING
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - BSE 201 - Computer Oriented Mathematics

Lecture Per Week: 6 hrs
Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

Unit I

Propositions and compound propositions - logical operations - truth tables - tautologies and contradictions - logical equivalence - algebra of propositions - conditional and biconditional statements - arguments - logical implications - quantifiers - negation of quantified statements - basic counting principles - factorial - binomial coefficients - permutations - combinations - pigeonhole principle - ordered and unordered partitions

Unit II

Order and inequalities - mathematical induction - division algorithm - divisibility - Euclidean algorithm - fundamental theorem of Arithmetic - congruence relation - congruence equations - semigroups - groups - subgroups - normal subgroups - homomorphisms - rings - integral domains - fields - polynomials over a field

Unit III

Roots of equations: Graphical methods - bisection methods - false - position method - fixed point interaction - Newton - Raphson method - secant method - multiple roots - system of nonlinear equations - roots of polynomials, conventional methods - Mueller's method - Bairstow's method

Unit IV

Algebraic equations: Gauss elimination - nonlinear system of equations - Gauss Jordan - LU decomposition - matrix inverse - error analysis - tridiagonal systems - cholesky decomposition - Gauss Seidel

Unit V

Differentiation and integration: Trapezzoidal rule - Simpson's rule - Romberg integration - Gauss quadrate - Richardson extrapolation - derivatives and integrals for data with errors

Books for Study

1. Seymour Lipschutz and marc Lipson - Discrete Mathematics Second Edition - Tata McGraw Hill Edition, 1999.

2. Steven C.Chopra and Raymond P.Canale, Numerical methods for Engineers - Third Edition, McGraw Hill International Edition, 1998.