This handbook is directed primarily to
mathematics majors and minors; its purpose
is to provide useful advice and information
so that students can get
the most out of their studies in mathematics.
This handbook should also be a useful resource for
potential majors and minors and for
university personnel who advise students.
The information and policies set forth here
are intended to supplement material contained
in the *Bulletin of Duke University 1996-97:
Undergraduate Instruction*.

This handbook is organized in three main sections.
The first section, **Course Selection**, is intended to assist
students in developing programs of study that meet university
requirements and that serve their educational and professional
objectives.

The second section, **Resources and Opportunities**, describes features
of our program intended to enrich the undergraduate experience
of mathematics students.

The third section, **After Graduation: Educational and Professional
Opportunities**, is intended to give a brief introduction to the
careers and programs of study for which mathematics provides a good
foundation.

A popular modern dictionary (**Merriam Webster's Collegiate
Dictionary*, 10th ed, Merriam-Webster Inc., Springfield, MA, 1993.)
defines mathematics as

mathematics:the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.

However, a strong case can be made that a more complete and
appropriately general definition of mathematics (*Suggested by
phrasing in *A Bridge to Advanced Mathematics* by Dennis
Sentilles. Williams & Wilkins, Baltimore, 1975, p. 147.) is given by

**mathematics: ** the science of abstract structure.

Indeed the inestimable importance of mathematics arises directly from
the identification of mathematics as the study of the essential
structure that remains in a problem or situation after all
nonessential elements have been stripped away. Consequently,
mathematics is a science of extraordinary intrinsic beauty, highly
deserving of study for the sake of that beauty, standing alone. But
owing to its generality and breadth, mathematics is an indispensable
component of rational discourse, sound public policy, scientific
understanding, and technological advancement. On pages 4 and 5, in a
section entitled **The Nature of Mathematics**, some excerpts are
reproduced from an essay that seeks to characterize mathematics and to
describe its emerging role in today's world.

Tue Sep 3 16:48:03 EDT 1996