Analysis is the branch of mathematics concerned with issues that have their roots in calculus. The purpose of this course is to take the student on a leisurely and scenic stroll through parts of the world of analysis as to allow for a better understanding of some of the ideas of calculus. The student will meet certain methods and ways of thinking which will be useful for significant mathematical ingsight. The Mathematical Analysis course provides a glimpse of a few of the beauties, curiosities, and even pathologies that, for some, make mathematics more an addiction than an occupation.

Here is a sampling of the questions that will be answered during the course:

+Why are the real numbers so much more important in calculus than the rational numbers?

+How far does the analogy between the hyperbolic functions and the trigonometric functions extend?

+Are there more rational numbers than there are integers? (NO!)

+Are there more real numbers than there are rationals? (YES!)

+In the sequence of integers, how often do the prime numbers occur?

+I understand why the square root of two is irrational, but why are e and pi irrational?

+What does the Heisenberg Uncertainty Principle have to do with integration by parts?

+Students will be assessed on the basis of their in-class participation, on homework assignments and, possibly, on a project.