MATH 499: Mathematics Seminar
Spring 2001, 1 Credit, Tuesday, 8:00-8:50 am, MC 415
Richard J. Maresh, Associate Professor of Mathematics
Office: MC 522Hours: MWF 9-10, T 2-3, R 12-1
Phone: 796-3655Home: 526-4988
Final Exam: Thursday, 10 May 2001, 12:50-2:50 pm
Selected topics of current interest in mathematics are researched and presented. Students and faculty share in the presentations. Prerequisite: consent of instructor and junior or senior status.
Text:Dunham, William. Journey through Genius. (first published by John Wiley & Sons, 1990).
1.This course is something of a “capstone” course for mathematics majors and as such gives students the opportunity to read and present a variety of mathematical topics. The major goals here are to absorb by reading mathematical content and to prepare presentations for the group, in short, to learn to do “mathematical research” and to make mathematical presentations.
2.This course also is the one place in the curriculum where students encounter in a formal way the history of mathematics. Even though this is good for any mathematics major, it is required by the DPI for any math-ed majors, and this course serves the purpose of satisfying that requirement.
The text includes chapters on the following topics. They cover a wide range of history and mathematical content:
1.Hippocrates and the Quadrature of the Lune
2.Euclid’s Proof of the Pythagorean Theorem.
3.Euclid and the Infinitude of Primes
4.Archimedes’ Determination of Circular Area
5.Heron’s Formula for Triangular Area
6.Cardano and the Solution of the Cubic
7.Isaac Newton and the Binomial Theorem
8.The Bernoullis and the Harmonic Series
9.Leonard Euler and His Infinite Sums
10.Euler’s Number Theory
11.Cantor and the Non-denumerability of the Continuum
12.Cantor and the Transfinite Realm
In addition to going through these topics we will try to consider a few other topics.
At the first meeting we will assign chapters to each member of the class and then the weekly activity will be a presentation by a student of the material in the assigned chapter. You should present the material as if you were giving a “lecture”, using appropriate blackboard/overhead skills and being prepared to answer questions anyone might ask.
Grades will be determined by your level of participation and the quality of your presentations; you want to show that you have read the material with understanding and that you can explain it in detail.
Americans with Disability Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs.