# Senior Seminar Information (Class of 2015)

For the 2014-2015 academic year, the senior seminar topics are Cryptography and The Fundamental Theorem of Algebra.

To ensure the senior seminar experience is an enriching experience it is necessary to keep class sizes relatively small and even. To help the department place students into seminars, each major who plans to take a senior seminar submits a proposal by the last day of classes of the winter semester of the junior year. Some details:

- The proposal is a LaTeX Document, a template, to be filled out carefully by the student. The proposal should be approximately one page. It should describe which senior seminar you prefer to take, and why.
- As a hypothetical example, here is a sample completed proposal in PDF format as Bernhard Riemann would have submitted it.
- Juniors abroad during the winter semester who do not have access to LaTeX may submit a proposal created in Word or whatever software is available. The proposal must follow the format of the sample PDF document.
- By the due date, the completed proposal is to be emailed as a PDF document to Laura Wardwell (lwardwel@bates.edu), Academic Administrative Assistant for Hathorn Hall.
- The PDF file should have a useful, descriptive name. Riemann would’ve named his “BernhardRiemannSeminarProposal.pdf”, for example.
- It is a good idea for juniors to discuss the choice between thesis and seminar with faculty members before writing a proposal.
- The Department meets to consider all thesis and seminar proposals. The Department Chair will notify students of the results of the meeting by the middle of the short-term.
- The course description for the Winter 2014 senior seminars are below.

**Math 495H: Cryptography
**Public Key Cryptography is at the center of most secure transactions we do these days, like using your credit card online or sending and signing secure messages. The security of a cryptosystem relies on finding difficult math problems, like factorization of large numbers and the discrete logarithm problem. After an introduction to the basics, each student studies various methods of encryption like the RSA cryptosystem, the Diffie-Hellman key exchange, Elliptic Curve Cryptography, and various methods of breaking these encryptions. All of these topics draw from previous knowledge in abstract algebra, analysis, geometry, and number theory. Computer algebra systems also are used to illustrate the applications. Prerequisite(s): MATH 301 and 309. Instructor permission is required.

Tentatively scheduled: TR 9:30-10:50

**Math 495L: The Fundamental Theorem of Algebra**

Over the centuries, there have been numerous proofs of the Fundamental Theorem of Algebra (FTA), which asserts that every polynomial of degree *n* must have at most *n* distinct roots over the complex numbers. The great German mathematician Carl F. Gauss (1777-1855) published no fewer than four different proofs of the result. While the name of the theorem foregrounds algebra, none of the known proofs is purely algebraic. Over the centuries, techniques from complex analysis, topology, and field extensions have been employed to give new proofs of the FTA. In this seminar, students explore some of these proofs where the methods are drawn from various subfields in mathematics.

Tentatively scheduled: MW 9:30-10:50