Checklist for the writing assignments

The following is a list of things that may go wrong in a writing assignment, particularly a mathematical writing assignment. Please have the following comments in your mind when you are typing your homework.

Stylistic issues:

• Format: Double-spaced, one-sided, on 11-inch paper and stapled. Your name and the class/section numbers should be in the upper-right corner of the first page. The pages should be numbered.
• The symbol for the natural numbers should either be the “outline” version, or a bold capital N. If you'd like to use the outline version, try using an outline effect on any (reasonable) sans-serif font. In Microsoft Word, the actual symbol can be found in the symbol table for the “lucida sans unicode” font. Once you've typed it, using cut-and-paste can save on digging through menus.
• Always start a new sentence with a word rather than a symbol or formula.
• Dealing with equations:
  
  • Always italicize variables -- it makes them much easier to read.
  • To whatever extent it is possible, try to typeset your equations nicely, using an equation editor or the like. It's much easier to read a formula with exponents, subscripts, fraction bars and square root symbols than to read one that's loaded with carats, slashes and tons of parentheses so that it can fit in one line of text.
  • It's nice if you can avoid splitting equations across lines of text.
  • If you put an equation on a separate line, it should be centered, and the punctuation rules are the same as if it occured in the regular text. For example you should put a period at the end of an equation if it ends a sentence. Also, if you want to number an equation so that you can refer back to it later, the equation has to go on its own separate line, and the number should go at the margin.
• Try to fit the theorem/corollary and their proofs in good mathematical form, i.e.

  Theorem:...

  Proof:...

  Corollary:...

  Proof:...

  You'll probably want some text before and after, and perhaps some in between, just to ease the transitions. Also along these lines, it's nice to have some sort of “end of proof” signal, such as a “QED” or a black box.

• This is not necessary but just a suggestion. Most mathematics papers are written in the first person plural. In other words, when you need a pronoun, “we” is usually the one you want.

Organizational issues:

• It's generally a good idea to warn the reader of the approach you will be taking, so that statements don't come out of thin air. For example, if you will be using induction, say that before you dive right in to the proof.
• On the other hand, you don't need to (and shouldn't) explain things which should be obvious -- it tends to get in the way and interrupt the flow of ideas. Deciding what's “obvious”, though, is something you have to decide for yourself. However, it's generally easier to write too much and then to cut some out, than to add more later.
• You always should try to minimize the number of questions the reader is going to have. One good application of this principle is in long calculations. If you have ten equations in a row where you've started with a particular equation and then solved for a certain variable, it's often better to pick out the main steps and just include those. For the rest, a verbal description of the steps you haven't shown is often better than showing every step. For example, suppose you are asked to do a word problem which involves some integration. You need to explain how the integral is set up and which method you will use to find the value of the integral. However, during the integration you do not need to show all the simplification step by step, instead just say something like “By substitution u = 2x+3, the integral turns into (insert the integral here) and this simplifies to (insert the simplification here) whose value is 15ln(2x+3) + c.”
• A well organized paper is often much easier to digest than a less organized paper, even if they both say the same things. Breaking the paper up into easily identifiable sections aids the reader in understanding it, and often thinking about how to organize the paper helps you to write more effectively.