University of Madras - Syllabus of Bachelor of Science (BSc) Mathematics - Semester III - Allied - Mathematics for Statistics I

UNIVERSITY OF MADRAS

B.Sc. DEGREE COURSE IN MATHEMATICS

SEMESTER SYSTEM WITH CREDITS

(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Allied - Mathematics for Statistics I

Duration of Examination: 3 hrs

Maximum Marks: 100

Credits: 4

Sets, Operations on sets - real valued functions - countability - real numbers bounds, supremum and infimum - sequence of real numbers - limit inferior and limit superior and limits of real sequences - limit theorems - summability of convergence and divergence of series with non-negative terms - alternating series - conditional and absolute convergence - rearrangement of series - test for absolute convergence - summation by parts.

Continuity and derivative - the derivative of a real function - mean value theorems Taylor's theorem - concept of uniform continuity - Riemann integrals, sufficient condition for Reimann integrability, Darboux theorem, fundamental theorem of integral calculus - first mean value theorem - concept of Riemann Stieltijes integral its existence and properties.

Improper and infinite Riemann integrals - Gamma beta integrals - multiple integrals - their evaluations using transformations of variables - simple example of multiple integrals relevant to statistical methods. Laplace Transformation (LT) - definitions, LT of the function t, eat, cos at, sin at eat cos bt. eat sin bt, Transform f' (t), f" (t) - inverse LT relating to the above standard functions.

Books for Study & Reference:

Gold berg, R.R. (1970) Methods of Real Analysis, Oxford and IBH.

Apostol, T.M (1985): Mathematical Analysis, Narosa publications.

Narayanan and Manickavasakam pillai - Ancillary Mathematics Book II.

Bartle, R.G. & Shebert, DR. (1982): Introduction to Real Analysis, Wiley Eastern & Sons.