FC 119 - First-Year Seminar: What Is Mathematics? ... Really

Spring Semester, 1995-96

Do you think that mathematics is balancing your checkbook? Or perhaps factoring horrendous polynomials in high-school algebra courses? Do you find yourself freely admitting to anyone who will listen that you don't like mathematics and never were good at it? Then this may be the seminar for you.

Despite having been exposed to mathematics for 12 years of elementary and secondary school, it's likely you have not met the subject mathematicians truly know as mathematics. The goals of this seminar are to introduce students to mathematics, to build an understanding of the processes of mathematics, and to convey some understanding of basic topics in mathematics. The emphasis is on talking and writing about mathematics rather than doing mathematics.

In this seminar, we address such questions as what mathematicians do, how they do it, what mathematicians are and are not, why mathematics works, aesthetics in mathematics, patterns and order in mathematics, algorithmic and dialectic mathematics, and abstraction and generalization. With an idea of what mathematics is about, we then tackle some mathematical issues. As in art and music courses, we study several significant works of mathematics, their mathematician creators, and the periods during which the works were created. By looking at the mathematicians and their lives in addition to their works, we see that mathematics is not a dead subject which was wrapped up centuries ago. On the contrary, it is alive, healthy, and, like other disciplines, subject to the whims of human nature.

Following are a few particulars about this course. Unlike a regular mathematics course, there is no set body of material which needs to be covered. We are thus free to explore ideas as they arise and according to our interests.

CLASS INFORMATION:

• Meeting time: MWF 11:00-11:50
• Meeting room: Glatfelter 102

OFFICE AND OFFICE HOURS:

• Office: Glatfelter 215A
• Office hours: MWF 8:00-9:50 and by appointment

TELEPHONE NUMBER AND E-MAIL:

• Telephone: 337-6630
• E-mail: jfink@gettysburg.edu
• WWW page: http://www.gettysburg.edu/~jfink/jpf.html
• Class e-mail alias: fc-119-a

BOOKS AND READINGS:

We will draw from several sources. Our basic readings include:

• The Mathematical Experience by Philip J. Davis and Reuben Hersh
• Poetry of the Universe, A Mathematical Exploration of the Cosmos by Robert Osserman
• Journey through Genius, The Great Theorems of Mathematics by William Dunham
• Readings in Mathematics, a collection of assorted readings assembled and edited by James P. Fink

GRADING POLICY:

• Your grade will be determined by your scores on the following:
  • class participation, including assigned readings and class attendance and discussion (20%),
  • homework (20%),
  • papers (40%),
  • final exam paper (20%).
  ***Late work will not be accepted.***

ASSIGNED READINGS, HOMEWORK, AND PAPERS:

• Class attendance and discussion are an essential part of this seminar. Thus, the assigned readings must be done before class, and you should be prepared to discuss the readings in class.
• Homework must be written neatly in standard English with complete sentences using 8-1/2 x 11 paper (no ragged edges!). Express yourself clearly and concisely. Careful attention must be given to syntax, punctuation, and correct usage of notation. Do not write to me. Assume instead that you are writing to other students in the class. Grading of homework will be based on content and writing quality.
• There will be several papers of 3-5 pages each. In addition to the expectations for homework, papers must be typewritten (or "word-processed"). To each paper, attach a cover page with the title, your name, the course number and name, and the date of submission.