MAT202 Real Analysis
This course builds on the foundation of MAT110 and equips the student with the basic ideas and concepts of Real Analysis. It is a one-semester course that covers, in a brief and elementary way, the most important topics in the subject in real analysis rather than a lengthy, detailed, comprehensive treatment, which normally requires an entire academic year. Successful completion of this course should provide students with a foundation for their understanding of calculus, which will enhance teaching of mathematics up through secondary school level.
The Real Number System: Axioms for a Field, the extended real numbers, sequences of real numbers, open and closed sets of real numbers, continuous functions, Borel Sets
Basic Topology: Finite, Countable and Non-Countable Sets, Metric Spaces, Compact Sets, Perfect Sets, Connected Sets
Integration: The Riemann Integral, the Lebesgue Integral.
Lebl, Jiri, Basic Analysis: Introduction to Real Analysis, Jiri Lebl: Univ of Wisconsin – Madison, 2013. (http://www.jirka.org/ra/)
Protter, Murray H., Basic Elements of Real Analysis, Springer-Verlag, 1998.
Royden, H.L., Real Analysis, 3rd Ed. Prentice Hall 1988.
Rudin, W., Principles of Mathematical Analysis, 3rd Ed., McGraw-Hill. 1976.
Trench, William F., Introduction to Real Analysis, William Trench: Trinity University, 2003.
Interactive Real Analysis, http://mathcs.org/analysis/reals/index.html
Larson, Lee, http://www.math.louisville.edu/~lee/RealAnalysis/realanalysis.html
Lebl, Jiri, Basic Analysis: Introduction to Real Analysis, http://www.jirka.org/ra/
O’Connor John, A first Analysis course, http://www-groups.mcs.st-andrews.ac.uk/~john/analysis/index.html