Writing skills
Kay Kirkpatrick

Why work on your writing?

"I am sorry I have had to write you such a long letter, but I did not have time to write you a short one." --Blaise Pascal

I think that success in any career depends in part on how well you communicate your ideas and persuade other people. Below are some writing exercises leading up to a final paper, and clarity, concision, and coherence all count. This is an opportunity to improve your writing skills, in order to make your ideas more clear and persuasive--and to succeed.

Recommended reading:
Halmos: How to Write Mathematics
Gopen and Swan: The Science of Scientific Writing
Williams: Style: The Basics of Clarity and Grace (any edition), Longman.
Other resources: UIUC Writers Workshop, Purdue Online Writing Lab
HW1: Read John Lee's advice on writing proofs and do a few problems with this advice in mind.

HW2: Pick one of your recent problem set solutions, and explain the context and the key ideas of the problem--in words, with minimal notation and jargon.

HW2: Paul Halmos was a famously good mathematical writer. Read sections 0-5 of his How to Write Mathematics essay and do one of three problems according to your number assigned in class. (If you forget or didn't get your number, generate one for yourself uniformly at random from the set {1, 2, 3}.) You may look at the other two problems, but don't work them out.
P.S. If you do a lot of mathematical writing, you might want to invest in How to Write Mathematics, a book of essays that includes Halmos's.
P.P.S. It's a good time to start learning how to write in LaTeX or some equivalent. You could ask a classmate for previous homework code. And Detexify is a helpful tool.

HW3: Exchanged HW2 with a classmate who did a different problem. Write a peer review of your classmate's homework after consulting advice here or here, for instance. On Oct. 11, you will turn in both the original problem and the peer review (stapled or clipped together).

HW4 (Proposal): Start by copying down the full citation(s) including title and abstract of the proposed research article(s) that your final paper will be about. Then write 500-1000 words persuading me that you are the right person to study this article, that the topic is important, and that it is interesting to me. Include a motivating question that your final paper will answer, or a thesis statement. You may include references to secondary papers at the end, and they don't count towards the word limit.

HW5: Finish reading Halmos's How to Write Mathematics essay (sections 6 and 7 are optional, so just sections 8-20). Then pick about 10-20 lines of text and equations from a probability textbook (e.g., Karatzas and Shreve or Durrett) that you think is not very clear. Copy the passage and then improve it using the principles you've learned: add explanations and clarifications, rearrange the exposition if you think another approach is better, or simplify it to an interesting special case and explain the extension to the general case. As an alternative, you may do the same exercise on a Wikipedia article in probability, taking screenshots (for instance) before and after. In both cases, you should append a couple of sentences about why your revision is better.

HW6: Read Gopen and Swan's piece The Science of Scientific Writing. Then look over your proposal with this advice in mind, because you may want to revise and adapt parts of your proposal for the final paper.

HW7: Find an electronic or paper copy (library or borrow one of mine) of Joseph Williams' Basics of Clarity and Grace (any edition) and read as much as you can. You may also want to start outlining or drafting your final paper.

HW8: A draft of your final paper. You're welcome to adapt parts of your proposal; the key word is "adapt," because the purpose of the final paper is to inform, whereas the purpose of the proposal was to persuade.

HW9: Revising exercise: cutting words. Option 1): take an old email of yours to someone important that was too long (more than 2-3 paragraphs of 2-3 lines each), and trim it down without losing key information. You may fictionalize names, etc., for confidentiality. Include word counts before and after: the after count should be no more than 85% of the before count. Option 2): take the draft of your final paper and trim it down to the 3-6 page limit or to 85% of the previous length. In both cases, you should be able to use what you learned from Williams, Gopen, and Swan, to eliminate unnecessary words and phrases and to make your writing more compact and more elegant.

Final paper.