Mathematics Department - Honors

Honors



The SAS Honors section of Math 103: Topics in Math for the Liberal Arts, is quite different from the non-honors sections.

Imagine an internet without privacy: your e-mails could be read by any motivated eavesdropper, your credit card and bank account information would be public knowledge, and the passwords you enter could never be secret. You could pretend to be anyone, and anyone could pretend to be you. The internet would be brought to its knees without its users trusting that it could keep secrets. But do we actually live in such a world?

This course is about cryptology, the science of hiding information. Historically, sharing secrets over long distances typically meant two parties first had to agree on a password, and then send messages to each other using their secret password. But how can they agree on a password in the first place unless they meet in person, or have a trusted courier?

We will focus mainly on the amazing breakthroughs made in the last 30 years which effectively exploit difficult mathematics problems as a trusted courier. It used to be that these problems frustrated mathematicians; now they are used as locks, challenging problem solvers to pick them. They enable two people who have never met nor communicated with each other to share secrets in public. The problems are typically very simple to state and understand, but practically speaking nobody knows how to solve them fast enough to break these "locks". How do they work? What would it take for someone to break them? What would happen then?

The course will consist of three parts. In the first part we describe some traditional cryptographic ciphers, and the mathematics which breaks them. The second consists of the mathematical "locks and keys" used to keep secrets. In the third part, we explore aspects of mathematics in security, for example in ATM machines, cell phones, remote control car locks, electronic voting machines, DVD encryption, cable TV, ID cards, and more. The mathematics needed is at an elementary level.

Not usable as an elective toward the Math major or minor.


The textbook for this course is The Mathematics of Encryption: An Elementary Introduction by Margaret Cozzens and Stephen J. Miller, 2013, ISBN-13: 978-0821883211


Upcoming Semester: Fall 2016

Instructor: Peter Ullman


Previous semester resources




Regular sections of Math 103 (Topics in Mathematics)



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