Writing for Mathematics, MATH 300, Spring 2010

Instructor: Daniel Groves, 538 SEO e.mail

Course webpage: http://www.math.uic.edu/~groves/teaching/2009-10/300W/

Course hours:

Wednesday, 2:00-2:50 PM, Room 321, Taft Hall.

Office hours:

Monday 1:00-1:50pm, Wednesday 1:00-1:50pm, SEO 538.

Grading Scheme:
30% of your grade will be based on class participation. The remaining 70% will be based on the portfolio of all of your work during the semester.

TeX:
In this course, there will be a number of written assignments. These will be written in TeX, or some variant thereof. (My favourite variant is LaTeX, which I find much easier to use than ordinary TeX. There are other variants that you might like more.)
It is each student's responsibility to work out how to use TeX on a computer of their choosing.

Writing Center:
The English Department runs a writing center, where you can get help with all aspects of writing:
http://www.uic.edu/depts/engl/writing/
(You can make appointments, which is probably a good idea).

Course description:
There are two writing aspects to this course. The first involves writing mathematics, and the second writing about mathematics, or topics of a mathematical flavour. For writing mathematics, there will be many short (approximately a page) assignments, which will mostly involve explaining a piece of relatively easy mathematics (usually in the form of a proof). There will also be two longer essays, on topics of your choice (obviously with a mathematical flavour to them).
Another aspect of the course is spending some time thinking about fundamental issues of mathematics. (For example, at some point I'll ask you to write an essay entitled `What is Mathematics?')

Essays:
There will be two long (6-8 pages) essays due throughout the semester, on a mathematically-related topic of your choice. For each of these, a draft will be due a couple of weeks before the final version.

The first long essay is due on March 17, at the beginning of class (the essay is still to be e.mailed to me). This essay should be 6-8 pages long, on a mathematically related subject of your choice (check your topic with me before you write the essay). Of course, this essay should be written in (La)TeX.
The First Draft of the first long essay is due on Wednesday, March 3.

Writing Assignments:

  • Due Wednesday, January 20, 11am (NOTE: This is NOT at the beginning of lectures, but three hours earlier).

    Give a one page proof that the square root of 2 is not a rational number. Your target audience is friend who is an undergraduate at UIC, but not a Math Major.
    This assignment must be written in TeX (or LaTeX, or amxTeX, or Lyx, or whatever variant of TeX you want to use). You should e.mail me the source code (a .tex file or something similar) and the compiled code, which can be in PDF, PS or DVI format. If you want to use a different format for the compiled version, check with me in advance. Also, please tell me in the e.mail which flavour of TeX you are using. I will not necessarily expect your source code to compile on my computer, but I will look at it and check that it might reasonably produce the compiled version you've sent me.


  • Due Wednesday, January 27, 11am

    Give a one page proof that there are infinitely many prime numbers. You should be as explicit as possible about defining your terms, the things that you assume and the steps of reasoning that you make. The style should be as formal as possible, so pretend that you are writing for a textbook which is an introduction to pure mathematics.

  • Due Wednesday, February 3, 11am.

    Give a one page introduction tothe concept of the derivative from calculus. Your target audience is a gifted High School student who excels at mathematics, but knows nothing about calculus, or limits.
    You might like to include some pictures. I recommend learning how to do pictures in LaTeX, since it will be a skill coming in handy over the course of the semester. Let me know if you'd like help with this -- you'll need a way of making a picture in a .pdf, .jpg or similar format. (One way of doing this is finding pictureson the internet.)

  • Due Wednesday, February 10, 11am.

    Let b denote a fixed positive integer. Prove the following statement by induction: For every nonnegative integer n there are nonnegative integers q and r so that

    n = qb+r,

    where ris less than b.

  • No class or homework due on February 17.

  • Due Wednesday, February 24, 11am.

    Write a newspaper article (approximately one page long) on symmetry.

  • Due, Wednesday, March 3, 2pm: Draft of the first long essay.

  • Due, Wednesday, March 10, 11am:

    Write a one page essay answering the question `What is mathematics?'

  • Due, Wednesday, March 17, 2pm: First long essay due.

  • Due, Wednesday, April 7, 11am.

    Write an essay of approximately 3 pages on the RSA Public Key Cryptography system. You can write about whatever aspect you like, but you should definitely include a description ofhow the algorithm works. Your target audience is someone who knows some mathematics but not the algorithm. (You can decide whether your reader knows about modular arithmetic, or not. You can also decide whether your reader understands the reason for a public key crypto-system, or anything at all about cryptography.)

  • Due, Wednesday, April 14, 11am.

    Choose a paradox. Examples are Zeno's Paradox, the Liar Paradox, Russell's Paradox, and there are many others. In an essay of about a page, explain what a paradox is, why your choice is a paradox, and give at least one description of an attempt to resolve the paradox.

  • Due, Wednesday April 21, 2pm The first draft of the second long essay.

  • NOTE: There will be no class on Wednesday, April 28.

  • Due, April 30, Anytime. The second long essay.

    The rules for the second long essay are the same as for the first, with the extra rule that you should choose a different topic than your first essay.