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

SYLLABUS

Semester III - Paper III - Algebra and Trigonometry II

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

Matrices :-

Symmetric; Skew Symmetric; Hermitian; Skew Hermitian; Orthogonal and Unitary Matrices; Rank of a matrix; Consistency and solutions of Linear Equations; Cayley Hamilton Theorem; Eigen values; Eigen Vectors; Similar matrices; Diagonalization of a matrix.

Group Theory and number theory :-

Equivalence relations; Groups; subgroups - cyclic groups and properties of cyclic groups - simple problems; Lagrange's theorem; Prime number; Composite number; decomposition of a composite number as a product of primes uniquely (without proof); divisors of a positive integer n; congruence modulo n; Euler function (without proof); highest power of a prime number p contained in nl; Fermat's and Wilson's theorems - simple problems.

Summation of series :-

Sums of sines and cosines of n angles which are in AR; Summation of trigonometric series using telescopic method, C + i S method.

Reference Books :-

1. Topics in Algebra: I. N. Herstein (Vikas Publishing Co.)

2. Algebra: S. Arumugam (New Gama publishing house, Palayamkottai)

3. Algebra : T. K. Manickavachagom Pillai and others (S. Viswanathan publishers)

4. Trigonometry: P. Duraipandian (Emerald Publishers)

5. Plane Trigonometry Part 2: S. L. Loney.