Extracurricular Mathematics

This summer, I am working on two math projects outside of school.  I am doing this because there is so much to learn in mathematics, and because it is fun!

The first project is a book: $\underline{\textrm{Primes of the Form}\,x^2 + ny^2}$.  One of my professors at CSU Channel Islands recommended it as a “lovely” book.  I am reading through it and solving the problems at the end of each chapter.  An exciting thing I learned: the group of reduced positive definite quadratic forms with a given discriminant, D, is isomorphic to a subgroup of the ideal class group of the quadratic number field with the same discriminant, D.  This was a surprising result because it was not immediately clear to me how quadratic forms, the subject of chapter two of Primes…, were connected to quadratic number fields, a topic we learned in Algebraic Number Theory spring semester.

I am also developing ideas for a paper to be published in The College Mathematics Journal.  The theme is the mathematics of planet Earth.  I need to choose a topic soon; I am leaning towards an environmental topic like ecology or wind energy because I deal with those in my day job.  Actually, I’ve developed some methods at work for modeling wind energy production.  I hope to incorporate these in my paper.

The above two projects will keep me busy and out of trouble during the summer.  Hopefully, I’ll learn some more new things.  Feel free to share below what projects you have taken on this summer.