**The Real Number System: **Set theoretic statements, the real and complex number systems, principle of mathematical induction, ordered sets.

**Sequences and Series:** convergent or divergent sequences and series, Some Special Sequences, Subsequence, Tests for convergent or divergent sequences and series.

**Limits, Continuity and Differentiability:** Limit of a function, prove various theorems about limits, sequences and functions. Continuity of real valued functions, prove various theorems about continuous functions with emphasize on the proofs. Derivative of a function, proof of various theorems about dif-

ferentiability of the function. Bolzano-Weierstrass theorem, Mean value theorem.

**Riemann Integration:** Riemann sums, Riemann integral, proof of various results about the Riemann integrals.