Mathematical Writing Considerations
Student results on writing assignments are often workmanlike on the whole, but let's make some points about mathematical writing that seem not to be universally understood.
- Mathematical notation is part of the text.
- When we read mathematics, the math notation is just a precise shorthand for English words. Equations and expressions must have a context in the writing, must be punctuated just as with the rest of the writing, and should read grammatically. Use math notation whenever it adds precision while keeping the text concise. On the other hand, sometimes it takes so much verbiage to define the variables in question that it is best to use ordinary English text to describe a situation. In choosing to use mathematical formalism we always have to balance what we gain in precision with what we lose in notational complexity.
- Tables and Figures are not part of the text.
- Tables and Figures in mathematical writing are always extras. They sometimes even appear in an appendix. In any case, they should be placed in a floating element with a caption, and labeled. All references to them should be through the label. Thus, we do not usually write: "... as in the figure below." Instead we say "... as in Figure 1." That way, Figure 1 can appear anywhere, even on the next page.
- Do not use computer notation in mathematics.
- When you do decide to be precise by using mathematical
notation, do not try to mix computer notation or
ordinary expressions with the
mathematics. In particular, do not use an asterisk to
represent multiplication, and go ahead and define variables
to represent quantities of interest. For example, the following
expression would be undesirable:
"Day in SVG coordinates = 40+x*0.85."
Instead, one would write something to the effect of:
"Let denote the SVG coordinate associated with a given day of the study; then " Alternatively, if you do not want to go to the trouble of defining a variable, you could write: "The SVG coordinate associated with a day of the study is given by ."
- Do not confuse equations with expressions.
- Be precise in the way you refer to your mathematical notation. Do not call something an equation if it does not contain an equals sign. We frequently use expressions, inequalities, formulae, and many other forms of mathematical notation. If you must refer to those, use an appropriate choice of description.
- Always apply a title and take credit for your work.
- If you are going to spend hours writing an assignment, be sure to give your work some title so that the reader knows what she is about to undertake, and make sure your name appears as the author.
- Include acknowledgements
- If someone helped you in your work, recognize that person in an acknowledgement at the end of your paper.
- Include a list of references. Note that URL references include the date viewed.
- Whenever you learn something from a book or a web site, you must cite that reference. This accomplishes two things: it shows clearly that you are not trying to take credit for the work of others; and it shows how much awareness you have of the literature on the subject.