**Class Name: **“First-Year Seminar: Mathematics Beyond Calculus”

**Taught By:** Professor of Mathematics Lynne Butler

*Here’s what Butler had to say about the class:*

This half-course aims to broaden your perspective on what it means to do math. You will encounter math beyond calculus and linear algebra. You will formulate problems, develop strategies for solving them, and explore the mathematical literature. You will improve your ability to think rigorously and communicate mathematical information.

We’ll pursue these goals while applying number theory to public key cryptography. You use public key cryptography when you enter your credit card number on a web page whose URL begins with https, like when you buy a book from Amazon. Any communication over the internet can be intercepted during transmission, but information entered on secure page—that’s what the “s” in https means—is enciphered before it is transmitted. In RSA cryptography, information is enciphered using a public key “n” that is a product of two primes. Amazon publishes n, the public key, so that your browser can encipher your credit card number. When n is hard to factor, your information is secure even if the communication is intercepted!

During seminar meetings we answer key questions about RSA. How does Amazon, knowing the two primes whose product is n, decipher your credit card number? How large does n have to be so that it can’t be factored easily? The first question is precise and easy to answer, the second is not. Doing math begins with formulating questions. Ideas used to answer those questions are explored by working out examples. Answers based on those explorations are verified by rigorous proofs.

I’ve taught public key cryptography as an upper-level elective, but I’m excited to learn alongside first-year students. I would rather assist beginning students to explore what they want to learn rather than teach them what I know and think is important. There are some natural questions to ask, of course, but it will be really fun to explore questions students ask that I haven’t anticipated.

*See what other courses the Mathematics and Statistics Department is offering this semester.*

*Photo: (cc) Vergilius Eremite*

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*Cool Classes is a series that highlights interesting, unusual, and unique courses that enrich the Haverford experience. *