There are a number of topics that I want to cover. I want to keep my explanation of the topics as simple as possible. I am aiming for between a pre-calculus to an undergraduate math student. The difficulty in explaining these topics is that there is a lot of compressed information involved. But, most of the topics are used to describe very concrete (concrete in that you can compute answers numerically).
So, here is a short list of topics I am interested in writing about:
- number fields
- p-adic numbers
- Gauss's Disquisitiones Arithmeticae
- elliptic curves
- categories, functors, and natural transformations
- measures
- zeta functions
- zeta functions in terms of p-adic measures
I think this is a good start.