Writing tips for mathematical proofs and other mathematical writing

• Use complete sentences.
• Explain what you're doing.
• The intended audience for these problems are people like you: other people taking the same course, with the same background. This should govern the level of detail you choose to include, among other things.
• Avoid abbreviations and some mathematical shorthand; for example, don't use the symbols for logical concepts like "there exists", "for all", "implies", "if and only if", "therefore", "such that" – write the words instead. If you're not sure whether a symbol is okay, look at a math textbook: if it's in there, it's okay, and if not, it's probably not. Here is a list of some of the symbols to avoid:

                     

  You may use these symbols when there are time constraints, or in any informal situation (although I'm not much of a fan of the last five): on an exam, taking notes, etc. (I use them at the board, for instance).
• Note that using symbols for mathematical concepts is in general fine; you need to use words rather than symbols when they deal with logical concepts.
• In general, the proofs and explanations in a typical textbook provide good models for your writing. If you write something that looks completely different, stylistically, from what is in your textbook, you might want to reconsider how you wrote it.
• If you're typing, use italics for letters used as variables or representing mathematical symbols. For example, this is standard: "Let a be an element of the set E", while "Let a be an element of the set E" is not as good. (Using italics also helps to distinguish the word "a" from the variable or element "a".)

If you want to type your homework, a program called "LaTeX" is one standard tool. Here are some links to help you get started:

• The not-so-short introduction to LaTeX
• Getting started with LaTeX
• The LaTeX wikibook

Also, here is a LaTeX file I wrote, and the corresponding PDF file: