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

SYLLABUS

Semester V - Paper X - Real Analysis I

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

Sets and functions :-

Sets and elements; operations on sets; functions; real valued functions; equivalence; countability; real numbers; least upper bounds.

Sequences of Real Numbers :-

Definition of a sequence and subsequence; limit of a sequence; convergent sequences; divergent sequences; bounded sequences; monotone sequences; operations on convergent sequences; operations on divergent sequences; limit superior and limit inferior; Cauchy sequences.

Series of Real Numbers :-

Convergence and divergence; series with non-negative numbers; alternating series; conditional convergence and absolute convergence; tests for absolute convergence; series whose terms form a non-increasing sequence; the class 1².

Limits and metric spaces :-

Reference Book :-

1. Treatment as in "Methods of Real Analysis" : Richard. R. Goldberg (Oxford and IBH Pubhshing Co.)

Ch 1 - full.

Ch 2 - Sections 2.1 - 2.10.

Ch 3 - Section 3.1 - 3.4, 3.6, 3.7, 3.10.

Ch 4 - full