Fall, 2016

**Course Description: ** This course is a first introduction to Real Analysis. "Real"
refers to the real numbers. Much of our work will revolve around the real number system. We will start
by carefully considering the axioms that describe it. Students will be asked to consider many functions that
take on real values---that is, each object in our domain will be associated with a real number. For instance,
every point in the plane can be associated with its distance from the origin. Two points in the plane give
rise to a real number: the distance between them. The concept of distance will be a major theme of the course.
"Analysis" is one of the principle branches of mathematics. One often hears
that analysis is the theoretical underpinnings of the calculus, but though this has a kernel of truth, it is an
answer that misleads by oversimplifying. Certainly, analysis had its inception in the attempt to give a careful,
mathematically sound, explanation of the ideas of the calculus. But over the last century, analysis has grown
out of its original packaging and is now much more than simply the theory of the calculus. Analysis is the mathematics
of "closeness"--- the mathematics of limiting processes. The idea of continuity can be phrased
in terms of limits. Both derivatives and integrals are the end results of taking a limit. Compactness
is a property of sets that underlies many of the most important theorems encountered in calculus. These and
related ideas will be the subject of the course. Prerequisites: Math 213 and Math 222 or permission of the
instructor.

If you have any questions, please E-mail me at *schumacherc@kenyon.edu*

or come see me during my

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