This course is a careful, rigorous treatment of the foundations of calculus. Topics to be covered include: sets and functions, mathematical induction, the algebraic and order properties of the real numbers, convergence of sequences, limits, differentiation, and integration. Throughout the course we will emphasize clear mathematical exposition and methods of proof. In addition to gaining an understanding of the topics listed above, students who complete this course will be able to: read and understand mathematical exposition; think critically as mathematicians and present convincing arguments; express the idea of a theorem or a proof graphically; and read and write formal proofs. This class will help prepare students for further advanced study in mathematics, economics, and physics. It will also be of value to those who wish to explore the logical underpinnings of calculus, gain increased facility with abstract mathematical thought, or sharpen analytic and critical reasoning skills. This course will be taught in a seminar style; students will frequently be asked to prepare proofs and examples for discussion in class and to work collaboratively on problems. Evaluation will be based on weekly problem sets and active class participation. Advanced. No Lab Fee. Prerequisites: Calculus II and permission of instructor. Class size limited to 5.
Text: Kenneth A. Ross. Elementary Analysis: The Theory of Calculus. Springer. 1980.