## Tutorial: Real Analysis

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.