Aims: This is the first half of a year long, rigorous, one variable calculus course.

Content: Convergence and divergence for sequences. Completeness of the real numbers. Infinite Series. Continuity for functions on R.

Applications to computational problems and to calculations in probability.

Objectives: Along with the theory listed above, confidence and understanding of careful proof writing.

Books:

Real Analysis by Howie, John M, 2001

Mathematical Analysis and Proof, Stirling, David S. G., 1997

Analysis by its History, Hairer, E. and Wanner, G. 2008