MATH 401 Senior Colloquium

An exploration of advanced topics in mathematics, chosen by the instructor. Assessment varies by seminar, but could include written assignments, oral presentations, or exams. Seniors typically take one seminar each semester. Completion of two seminars partially fulfills the comprehensive requirement for graduation with a degree in mathematics. May be repeated once for credit.

Cryptology

Cryptology is the study of sending secret messages over insecure communication channels. Cryptographic capabilities are important to politics and foreign affairs, and underlie the functioning of a great deal of the modern economy. In this course we will study the mathematical theories and techniques that make cryptography function, and also those that break it. We will learn how these mathematical tools influence the use of cryptographic systems, and practice explaining these implications to people without developed mathematical backgrounds.

Applications of Linear Algebra

We will use the book Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, by Jiřì Matoušek.  We will concentrate mostly on the mathematical applications (as opposed to the algorithmic applications).  In the first two class meetings we will learn about (generalized) vector spaces, as preparation for the remainder of the course.