Course Description -- Math 300 -- Fall 2009

Instructor: Louis H. Kauffman

Office: 533 SEO

Phone: (312) 996-3066

E-mail: kauffman@uic.edu

Web page: http://www.math.uic.edu/~kauffman

Office Hours: 2:15PM to 3:00PM on MWF.

This is a course devoted to writing mathematics, and writing about mathematics. You will write three essays, with plenty of time to complete them. We will later make the decisions about when the essays are finally due. You will be asked to hand in drafts of each essay and there will be ample feedback and discussion before the work is completed. In this way, each essay will give you an opportunity to improve your writing skills.

While this is a one-class-hour per week course, there will be a lot of work to accomplish. This course is an important opportunity for you to improve your ability to write and to communicate. Skill in writing and communication is invaluable for all jobs and all professions.

See UMG. This is the website for the Undergraduate Mathematics Journal. It a good source of interesting articles, and the NEXT time we teach this course SOME people will submit papers to this journal! See Old Hats for a good example of a paper published in the Journal.

See Euler's Mathematics This is an excerpt from a recent book introducing proofs and mathematical ideas.

See Euler's Formula. This is a 2-page description of Euler's formula V - E + F = 2 for connected plane graphs. Euler's formula is interesting in its own right and it is a powerful tool for solving many combinatorial problems.

First Assignment: (Due in the second week of the course.)

1. Find an example of one or two pages of writing that you feel to be really excellent. Make a photo-copy of this sample and bring it to class. Please be prepared to read from your writing sample! This writing sample need not be about mathematics. It can be from any part of your reading experience.

2. Choose a simple piece of mathematics that you know well.

Find someone with whom you can discuss this topic or to whom you can teach the topic. Discuss or teach as the case may be. Then write a one page explanation of the topic, in your own words.

(Examples: a proof of the Pythagorean Theorem, why the sum of the angles of triangle is pi, how to solve a quadratic equation, what is a set and what is an infinite set, Euclid's proof that there are infinitely many prime numbers, the concept of probability, what is calculus, what is projective geometry ...)

Again, it will be best if you choose your own topic. The point is simplicity, not complexity. Choose a simple direct message in relation to the topic. Write a concise and readable single page.

3. Think about topics that you would like to explore for the first essay. We will brainstorm about that essay in the second class.

Choose a topic for the first essay and prepare a first draft to be discussed on September 9 if you are in the Wednesday class. If you are in the Monday class, then you are asked to work on the first essay and hand it in on September 14 for the first time.

Continue working on the first essay. Prepare a second draft to hand in on September 14 or September 16 (and keep a copy for yourself).

Prepare an essay on a new topic. This is the third essay in the course.

Find a paper that you enjoy reading (e.g. from the American Mathematical Monthly or the Mathematical Intelligencer. Prepare a one page abstract of the paper in your own words. To see examples of abstracts, look at Mathematical Reviews (MathSciNet.). To see this go [www.ams.org] and click on MathSciNet in the middle-left hand column.

See Article. and Summary of Article. This is an example of an article and a summary of that article as it appeared in Mathematical Reviews.