Writing in the Reed Math Department
The main expectation for writing in math is simple: clear and correct prose. Thus, the information on this page focuses mainly on small-scale mechanics of writing mathematics. See the Resources for Paper Help page for more general writing concerns. While it is easy to get distracted by the complexities of LaTeX (a document preparation system for high-quality typesetting that is widely used by mathematicians), your prose should clearly explain the mathematical symbols, equations, proofs, and reasoning. The words should set the stage for later parts of a long proof and make as clear as possible why the current steps are
For more information about LaTeX, see the LaTeX Project. For help with the actual LaTeX coding, take a look at The LaTeX Companion by Michel Goosens et al. or First Steps in LaTeX by George Gratzer.
There are only a limited number of ways to describe steps in a proof. "Thus", "therefore", "so", and "then" are common words used to express "from that fact or reason" or "as a result". Some other options include: hence, since, for that reason, for this reason, for which reason, consequently, ergo, and accordingly. Try to rotate between these phrases instead of using the same one over and over.
When describing a mathematical object in prose, write both what it is and its name. For example, "the formula f(x) describes..." is preferable to "f(x) describes...". It is easy to forget what each symbol stands for, so remind your reader often. In addition, it is helpful to write out an equation or formula in words either before or after the actual mathematical symbols. A simplistic example would be: "y = 3x + z, or in other words, the equation describing a plane through the origin where y is a linear combination of x and z".
Finally, keep in mind that the words and the math should say the same thing. Just as it is difficult to understand a long and convoluted equation, it is equally difficult to understand a long and convoluted sentence. Keep it simple, check your spelling and grammar, and make sure that the prose is clear.