Here's are some suggestions for topics for your final project. More topics will show up here over time, and this list will never be comprehensive. When you think you know (even roughly) what you'd like to work on, please come talk to me.

Here are some more detailed ideas about final projects.

Algorithmic number theory
- factorization
- primality testing
Analytic number theory
- prime number theorem
- Riemann hypothesis
- geometry of numbers
Algebraic number theory
- Finite extensions of Q
- Cubic reciprocity
- Finite fields
- Quadratic forms
- Class numbers
Other topics
- Elliptic curves
- Diophantine approximation
- Gauss and Jacobi sums