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.