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

SYLLABUS

Semester I - Paper I - Algebra and Trigonometry I

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

Algebra :-

Theory of Equations: Polynomial equations; Imaginary and irrational roots; Symmetric functions of roots in terms of coefficients; Sum of r^th powers of roots; Reciprocal equations; Transformations of equations.

Descartes' rule of signs: Approximate solutions of roots of polynomials by Newton-Raphson method - Homer's method; Cardan's method of solution of a cubic polynomial.

Summation of Series: Binomial, Exponential and Logarithmic series (theorems without proof); summation of finite series using method of differences - simple problems.

Trigonometry :-

Expansions of sin x, cos x, tan x in terms of x; sin nx, cos nx, tannx, sinⁿx , cosⁿx, tanⁿx, hyperbolic and inverse hyperbolic functions - simple problems.

Reference Books :-

1. Algebra : T. K. Manickavachagam Pillal and others (S. Viswanathan publications)

2. Higher Algebra: H. S. Hall and S. R. Knight (HM publications - 1994)

3. Pure Mathematics : Hardy

4. Trigonometry : P. Duraipandian

5. Plane Trigonometry part 2 : S. L. Loney, (Macmillan and Co. London)

6. Algebra, Analytical Geometry (2D) and Trigonometry: Dr. S. Sudha (Emerald Publishers).