Analytic number theory is a branch of number theory that uses mathematical analysis to solve number theoretic problems. In this class, we will delve into the field of analytic number theory by looking at several notable problems: divergence of the sum of the reciprocals of primes, the twin prime conjecture, the Collatz conjecture, and Dirichlet's Theorem on arithmetic progressions.

Knowing math is always a useful thing in life, especially when you are trying to solve math problems. But no matter how many practice problems you do, no matter how many books you read, there will always be some times when you have no idea what to do. In this class, we'll develop some strategies for dealing with these sorts of problems, then see how we could have used these strategies to solve at least ten problems (or maybe even 13!) on last year's AIME.

Ice cream is delicious, but unfortunately it takes an awfully long time to make. Fortunately, liquid nitrogen can expedite the process! Liquid nitrogen is a lot like the nitrogen that makes up about 78% of air, except much colder--nitrogen boils at 77 K, or -196 degrees Celsius! We'll start by making some classics like vanilla and chocolate, then move on to more adventurous flavor combinations.

This course will be an overview of plane and solid Euclidean geometry. We will derive theorems about triangles, circles, polygons, and solids from basic geometric facts; and use them to solve problems. Problems will be drawn from both textbooks and middle-school and high school math competitions. Classes will be a mix of lectures and problem-solving sessions.

Analytic number theory is a branch of number theory that uses mathematical analysis to solve number theoretic problems. In this course, we will delve into the field of analytic number theory by looking at several notable problems: divergence of the sum of the reciprocals of primes, the twin prime conjecture, the Collatz conjecture, and Dirichlet's Theorem on arithmetic progressions. (Note: This course is not a rigorous treatment of analytic number theory; it is merely intended to expose you to the field, and we hope that you will continue to explore on your own after the conclusion of the class.)