Integrated MSc-PhD Program


KSMB02: Basic Analysis


The Peano axioms, Set theory Fundamentals, Functions, Cardinality of sets, Integers and rationals, The integers, The rationals, Gaps in the rational numbers, The real numbers, Cauchy sequences, The construction of the real numbers, Ordering the reals, The least upper bound property, Real exponentiation, Limits of sequences, real number system, Suprema and Infima of sequences, Limsup, Liminf, and limit points, Rearrangement of series, The root and ratio tests, Infinite sets, Countability, Uncountable sets, The axiom of choice, Ordered sets.

Suggested texts:

          1. Terence Tao, Analysis. I, third ed., Texts and Readings in Mathematics, vol. 37, Hindustan Book Agency, New Delhi (Chapters 1-8)