Writing tips

• Use complete sentences.
• Explain what you're doing.
• The intended audience for these problems are people like you: people taking an introductory course in real analysis. 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 our 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).
• In general, the proofs and explanations in the textbook provide good models for your writing. If you write something that looks completely different, stylistically, from what is in our 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 the standard tool. Here are some links to help you get started: a brief LaTeX guide, getting to grips with LaTeX, and a list of FAQs.

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