This is an introductory course in real analysis. Starting with a rigorous look at the laws of logic and how these laws are used in structuring mathematical arguments, this course develops the topological structure of real numbers. Topics include limits, sequences, series and continuity. The main goal of the course is to teach students how to read and write mathematical proofs.
- Understand the axiomatic development of number sets.
- Understand the logical construct of a mathematical proof.
- Understand and utilize the basic topology of the real numbers.
- Understand the rigorous development of the calculus, including the theory of limits and differentiation, and the Mean Value Theorem