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.

From the over 9000 years that have passed since the inception of the internets, many legacies have come and died. From the infamous days of fark.com, to the hilariously political actions of Project Chanology against the Church of Scientology, internet subculture has molded and formed a new definition for the concept we call "awesome". So, what exactly constitutes awesome? Virality? Interactivity? The pure presence of the lulz? Perhaps. Yet, awesome itself is not restricted to the world of memes, as one may think. For example, through its power of completing teh homeworks of children all over the world, WolframAlpha has also been labeled a vast sea of awesome. Even today, inspired by Awesomeness, the Awesome Foundation grants of $1000 a piece are being given out via the internets to people in real life (is this real life?) to fulfill real life awesomeness (i.e. Google the Boston Hammock). So, how do these people actually detect whether an idea is truly awesome? Well, in this class, through discovery of the many over 9000s of awesome that exist on the internet (I will bring you to some of these awesome objects, but you too, will suggest awesome things for us to analyze), we will analyze exactly what makes them so "awesome". Who knows -- perhaps one day, as a result of this class, you yourself may invent awesomeness on the internet.

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.)