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.
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