Sequences of Real Numbers: Sequences and their limits, limit theorems, monotone sequences, subsequences and the Bolzano-Weierstrass theorem, Cauchy sequences, properly divergent sequences. Series of Real Numbers: Convergence, tests of convergence, power series, Taylor series, Abel's theorem. Topology of R^n: Open sets, closed sets, cluster points, boundedness, Bolzano ? Weierstrass theorem, compactness, Heine-Borel theorem. Connectedness.