Writing in Mathematics

Colin S., Writing Center tutor and writing fellow

Please keep in mind that these are only general guidelines; always defer to your professor's specifications for a given assignment. If you have any questions about the content represented here, please contact the Writing Centers so that we can address them for you.

Introduction

Writing in math is refreshing and infuriating: refreshing because it is finally possible to be right, really and truly correct; infuriating because it takes much more rigorous evidence to show that you are correct than that you are probably correct as we often do in everyday conversation, or even most academic discourse. The important thing to understand is that in math there are precise ways to prove precise things.

The question still remains, “What is math writing?” Unfortunately, there’s no straightforward answer since students usually write math to demonstrate understanding, whereas professional mathematicians usually write to demonstrate truth. In both, however, math writing is a mixed language that combines mathematical notation (equations, proofs, graphs, etc.) and written text. In both, there are general standards and expectations for what should be written and how.

Here’s a rule of thumb to help one write clearly and concisely in math:

• Assume that your reader knows almost as much about math as you do but thinks that you are wrong. In other words, assume you are writing for a skeptical peer.

Assuming a peer reader helps to avoid two common problems:

1) assuming that your reader knows everything about math already, or
2) assuming that your reader knows absolutely nothing at all. The first problem can lead to logical gaps or missing work due to the belief that your reader will fill in the missing steps, while the second problem can make your writing cumbersome to read and time-consuming to write.

Preferred Bibliographic Style

Mathematics does not have a single bibliographic style. Ask your professor for his or her preferred bibliographic style especially if you need to consult resources beyond the class textbook.

Common Writing Assignments

Short answer questions: This is the most common type of question that one will see on math homework and examinations because it allows the writer to show his or her work rather than simply responding with an answer. In answering a short answer, it is important to strive for clarity by explaining graphs, equations, written explanation appropriate. Although the procedure for how to solve a math problem is frequently well defined, there are many cases, in application problems for example, where the writer must use the tools learned in class to solve an altogether new problem. In this case especially, it is essential to show which mathematical methods you used, and also why you chose to take the approach you did.

Proofs: Both the most rigorous and the most decisive, the mathematical proof is a method of proving with certainty that something is true (or false). All proofs begin with some sort of axioms or assumptions.

Key Terms

One of the most helpful ways to begin to learn math is by understanding the words that are used to refer to certain types of mathematical processes. The following is a list of common and essential terms to know:

• Expression: An expression in math is like a phrase in English. For example, “2x+10y+18” is an expression because it contains no mathematical “verbs” like “=” (is equal to).”


• Equation: An equation is something that says two expressions are equivalent. For example, “y=2x” is an equation because it states that the variable “x” doubled is “y.” In this case, the equals sign is the mathematical verb that makes this more than just an expression.


• Calculate: This term is often used synonymously with the word “compute,” and is generally used to ask for arithmetic simplification. For example, “calculate (compute) 1776+2010” means, “make these two terms into one.”


• Solve (or “solve for”): This term refers to isolating a specified variable or group of variables on one side of an equation. A familiar example is “solve 2x+4=10 for x.” A slightly more advanced example would be “Solve for G in F=mMG/r^2.” In both of these cases you are trying to get an equation of the form “x (or G)=some expression.”


• Derive: This term is generally used to ask for a demonstration of why something is true by combining or manipulating more fundamental truths.


• Show: This term is usually used to ask for an informal proof that something is true. You are generally free to incorporate whatever methods would be most persuasive in order to demonstrate the desired truth. You can use calculations, logical reasoning, combinations of equations, or written text to show your reasoning.


• Simplify: This term refers to reducing an expression to its most simple form either by reducing the number of terms, consolidating like-terms, or factoring as fully as possible. For example, the answer to “Simplify x+x+2” would be “2(x+1)” because it contains the fewest number of terms and is fully factored.

Helpful Resources

Mauer, S. Common Errors in Writing Mathematics.

http://www.swarthmore.edu/NatSci/smaurer1/WriteGuide/write_errors.pdf - A guide to common errors in mathematical writing from Swarthmore College Professor of Mathematics Stephen B. Maurer available for free downloading in PDF format.

Steenrod, Norman. How to Write Mathematics. American. Mathematical Society.1983.

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