by Dillon Snyder, Mathematics

Entering college, many undergraduates have experienced some form of writing during their secondary education. Students pursuing a mathematics degree have also certainly engaged with mathematics before college. However, a required aspect of being a mathematics major is the fusion of writing with mathematics. This usually first occurs in a course which introduces proofs and higher math as a whole. As a result, students are presented with the challenge of learning math and learning how to write math at the same time.

By this point in their mathematical careers, most students have only interacted with computational math problems. They can write and solve equations and they understand how to use a variety of functions and operations. Higher mathematics deal with more abstract and generalized situations. The introductory course on higher math marks a change in not only the type of content students learn, but also the way students are expected to think about mathematics.

While students have to manage learning a completely new perspective on mathematics, they must also develop their writing skills through mathematical proofs. A crucial aspect of mathematics is communication, being able to effectively show concepts and reasonings to an external audience. For most students, these proofs will be their first time having to formally communicate their thoughts. The general premise of a mathematical proof is simple: logically show that a statement is true. However, there often is not a singular, clear way to do so. There are many different types of statements to prove, and many different types of proof methods that can be used. In this introductory course, students are expected to learn how to use most of these methods while proving rudimentary statements related to the mathematical content in the course.

By the time students take an introduction to proofs course, they should have taken a first-year writing course. This should help students when writing in mathematics, but there is resistance towards transferring writing skills to mathematics. Since most have not written full sentences when completing math problems in the past, few want to change what they are comfortable with. Rigor and clarity are both quite important in proof writing, especially early on in a person’s mathematical career. The first proofs students write will likely not have full sentences and might contain little to no words. Over time, the expectation is that students become more familiar with both proofs and more abstract mathematics, leading to more detailed and written out proofs.

writing is absolutely necessary for anyone pursuing higher mathematics

Mathematics and writing are often considered two distinct things, nearly opposites from a school perspective. Despite this, writing is absolutely necessary for anyone pursuing higher mathematics. The course on the introduction to proofs and higher mathematics aims to be the starting point for this connection between math and writing. While students learn the foundations that construct the advanced concepts they will see going forward, they must also discover how to utilize these concepts and incorporate them into formal writing. From this course, students truly see what college-level mathematics looks like and the crucial role writing plays for mathematicians.