Math 613: Effective Methods for Diophantine Problems
Section 201, Spring 2010
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Course Information

Where: MATX 1118
When: MWF 1-2 pm
Course web page: http://www.math.ubc.ca/~bennett/Math613 		Instructor: Prof. M. Bennett
Office: Math 220
Office hours: By appointment.
Email address: bennett@math.ubc.ca
Phone number: 604-822-2251

Text

The course will have no official textbook. There will be occasional handouts.

Evaluation

Grading policy: The course grade will be based upon grades from assignments. Final exam: There will be no final exam.

Course syllabus

We will cover all the material necessary to begin to solve Diophantine problems, primarily through a good understanding of modern transcendental number theory and its applications. In particular, we will prove some or all of the theorems of Hermite- Lindemann, Gelfond-Schneider, Baker and Nesterenko. We will further discuss a variety of open problems such as Schanuel's conjecture and will consider applications to other fields of mathematics. Time permitting, we will delve into other modern effective techniques, including the Hypergeometric method, Chabauty techniques, and the Modular Method used by Wiles to prove Fermat's Last Theorem.

Mike Bennett / bennett@math.ubc.ca