# Writing in Math

*Dr. Heather Moreland*

There are two main aspects to writing in the mathematical sciences. The first is to communicate new results and discoveries to fellow scientists through journal articles and presentations. The second is in the presentation of a mathematical computation or proof. This is the type of writing students encounter more frequently during their studies. It is generally not until their senior seminar project that they are first exposed to journal articles. While this is unfortunate, it is also necessary since the students need to accumulate the mathematical knowledge and maturity to be able to synthesize these articles.

New results and discoveries are communicated in several different ways. A refereed journal article is the most classic type of presentation. At most conferences there are sessions where mathematicians present a 15-20 minute summary of their results, consequences, and future work plans. For students, it has become common to present their work in a poster session.

The presentation of a mathematical computation or proof is the most common form of communication. It is often difficult for students to understand that mathematics has grammar and punctuation rules just like English. The appropriate use of symbols and drastically change the meaning of consequences of a mathematical statement. The omission of mathematical context can have catastrophic consequences.

One of the most famous examples was when scientists working on the programming for a NASA space probe did not include the units they were working in (miles versus kilometers). Another group of scientists assumed they were working in one measurement when in actuality they were working in the other. The result was the loss of the space probe as it did not land safely on the planet, but rather hit with such momentum that it was destroyed. I often use this example in my classes to demonstrate how critical it is to effectively communicate what it is you are doing, computing, or showing.

### Writing in the classroom

To assist students in their mathematical communication skills, starting at the 200 level, I incorporate a homework presentation aspect on each assignment. These points are awarded for clarity of exposition, flow of the argument, and readability. While the students often start the semester very resistant to this idea, by the end of the semester they are grateful for the guidance. Several students have commented how this has assisted them in their future courses. This ability to communicate effectively with others will assist the students not only in their academic endeavors, but in their future careers.