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.
- Algorithmic number theory
- factorization
- primality testing
- Diophantine equations
- Catalan's conjecture
- Modularity and Fermat's last theorem
- Diophantine approximation
- Continued fractions
- Thue, Siegel and Roth theorems
- Analytic number theory
- Riemann zeta function (analytic continuation, Riemann hypothesis)
- geometry of numbers
- Algebraic number theory
- Finite extensions of Q
- Cubic reciprocity
- Finite fields
- Quadratic forms
- Class numbers
- Other topics
- Gauss and Jacobi sums
- Expander graphs and Ramanujan graphs
- Quaternions and the four-square theorem