Number Theory - Arithmetic Geometry, Function Fields, and Zeta Functions
Mathematics 605B: spring 2014
Lecture: MWF 10:00-10:50, Engineering E206.
Detailed information on homework
The study of number theory originated in ancient civilizations
such as those of China and India and was developed in great depth in Europe
in the 17th and 18th centuries.
Number theory is known for having problems that are easy to state yet which
can only be solved using complicated structures.
For example, it took 300 years to find a complete proof of Fermat's Last Theorem.
Number theory is a subject that's intertwined with group theory, algebraic
geometry, combinatorics, and complex analysis. It's become popular recently
because of its applications to coding theory and cryptography.
Number theory is a vast subject. In this course, we will focus on Arithmetic Geometry, Function Fields, and Zeta Functions. See syllabus for list of topics.
The project is an opportunity to learn more about a topic in number theory that interests you or will be relevant for your future graduate work. It gives us a chance to hear about important ideas which we will not have time to cover in class. It is also a good opportunity to develop more skill at writing and speaking on mathematics.
Help: Help is always available if you have trouble with homework or lecture material. If your classmates can't answer your question, come ask me! Office hours will be (TBA) or are available by appointment.