FSEM 100E4 | Cryptology


As early as the time of Julius Caesar, people have tried to communicate secretly with others. Today we use passwords and PINs to authenticate who we say we are and to link our actions to our identity. We purchase products online, never thinking twice about entering our credit card number – a direct link to our money – into a web browser. We do this comfortably because of high-powered mathematics. Cryptology is the area of mathematics that studies cryptography, the art of encrypting messages, and crypt-analysis, the science of breaking encrypted messages. This first-year seminar studies these ideas broadly through mathematical explorations accessible to the inquisitive student with only basic algebra skills. Modular arithmetic, greatest common divisors, and large prime numbers play a supporting role in our course, but learning to research, write, and speak effectively, both individually and in a team, are the featured acts. We look at how to encrypt text and images, and we exchange our encrypted messages, challenging our classmates to break our ciphers. Major advances in cryptology throughout history will also be explored, from the early times of Caesar and Vigenère to the more recent discoveries of public key ciphers used in modern electronic commerce. In the end, you will have gained insights into the deep mathematical and statistical ideas that drive the implementation and analysis of modern cryptological techniques, as well as the nuances and pitfalls of creating secure encryption systems.

Photo of Jeb Collins, Assistant Professor of Mathematics

Jeb Collins, Assistant Professor of Mathematics

I have been a professor at Mary Washington for 3 years. I’ve always enjoyed mathematics, mostly for the opportunity to solve problems. I really enjoy looking at a problem and attacking it in different ways to figure out the solution, it is my form of creativity. I also enjoy the computational aspects of mathematics, since I started my undergraduate career as a computer science major. I’m always looking for ways to use my love of programming to solve math problems. These days I do not have to look far, as many problems both in mathematics and any science require computational techniques to obtain a solution. When not working on math I enjoy spending time with my wife and two children and reading. I also like to crochet and do woodworking. I’m just starting out with woodworking, but have made some pens and a cutting board, and I’m having fun figuring it out.

Photo of Jennifer Magee, Senior Lecturer in Mathematics

Jennifer Magee, Senior Lecturer in Mathematics

I discovered my love of math as a sophomore at Washington & Jefferson College, where I went on to major in math with a minor in economics. In hopes of continuing to do more math purely for the sake of doing math, I continued my education, earning a Masters of Arts in pure mathematics at Bowling Green State University. It was during my time as a graduate student teaching assistant that I discovered the joy of teaching. I came to UMW in 2013 and regularly teach many of the 100- and 200-level math courses. My favorite part of teaching at UMW is getting to know my students and showing them that math can be fun. Outside of the classroom, I enjoy playing board games, baking, and practicing yoga.