Syllabuzz: MTH 371 – The Mathematics of Secrets

Assistant Professor of Mathematics Chad Awtrey hopes to show the direct applicability of math and help students taking the course build skills transferrable to a number of careers.

By Katie DeGraff

Many of us are tethered to our computers and phones—we email, shop, bank and share family photos electronically. We enter credit card information, transfer money from saving to checking accounts and email baby photos to grandparents in different time zones. We do it readily and often without a second thought, but how exactly does our private information stay that way? It’s simple. Math.

Whether we realize it or not, math is the backbone of online communication. As information leaves its point of origin, it is encrypted to protect us from prying eyes and identity theft. Upon arrival, the information is then decrypted and the transaction is complete. The complexity of the encryption ensures that information remains private while also providing the benefit of speedy results.

To capture math’s utility, Assistant Professor of Mathematics Chad Awtrey set out to create a cryptography class. He wanted to build a course suited for a general audience that would build skills transferrable to a number of careers. He also wanted to demonstrate that math has direct applicability—it’s far from just theoretical knowledge. “Lots of universities have cryptography classes,” he says, “but I wanted to create a course that was decidedly Elon, one that was engaged, that was active and was focused on critical thinking through writing.”

Rather than a traditional lecture format, Awtrey’s course is broken into modules. Students meet in computer labs and work through basic algorithms to understand the “how” and the “why” of their functionality. Each module begins with background readings and computational exercises related to cryptography, which lead to research questions that require the students to generate data and formulate answers to the proposed questions. Rather than simply reporting their conclusions, students then write arguments to document the validity of their answers.

The writing piece of the puzzle is critical, Awtrey says. No matter what students’ ultimate professional goal, they benefit from using writing to present and defend their answers to each research question. In the process, they not only learn the basics of number theory but also about several problems that have research implications. “Many people think all of mathematics is already known,” Awtrey says. “In reality, there are many unsolved problems out there, some even have substantial monetary awards attached to them. Mathematics offers many exciting research opportunities, especially for Elon students.” 

About the professor

Chad Awtrey’s main research interests lie in algebraic number theory, p-adic fields and computational Galois theory. An Elon faculty member since 2010, Awtrey actively engages students in undergraduate research and received the 2014 Early Career Mentoring Award from the Division of Mathematics and Computer Science within the Council on Undergraduate Research. He serves as councilor for both the council and Pi Mu Epsilon, the national mathematics honor society.

Recommended reading

  • The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography by Simon Singh