A Primer for Undergraduate Research: From Groups and Tiles to Frames and Vaccines

A Primer for Undergraduate Research is a collection of eleven topics ranging from linear and abstract algebra to partial differential equations and graph theory. Each chapter presents a list of suggested prerequisites (or level of mathematical maturity, in some instances) for the topic and begins with an introduction and basic theorems. The core of the chapter then provides a broad context for, and then a generalization of, a series of suggested problems for a student to work on. Throughout the chapter, theorems and exercises are typically included as stepping stones for understanding before reaching the main research question(s) of the chapter.

Although the breadth of the topics presented in A Primer allows for a great deal of flexibility in audience, each proposed question has a very narrow scope. This is both helpful and limiting: reducing the scope of the problem allows an undergraduate to begin work without struggling to hone the question, but at the same time requires the advisor to have more than a passing understanding of the background material to be of assistance. The background information in each chapter typically includes a series of references for definitions and theorems which can be used to scaffold student (and advisor) knowledge for a stronger project.

Overall, the questions posed by the authors appear to span a variety of mathematical interests and fields and are suitable as single or multi-semester student projects.

Megan Sawyer is an assistant professor of mathematics at Southern New Hampshire University in Manchester, NH.