Suppose you want to find if a number is a square modulo p. That is, does $$x^2=a \pmod p$$ have a solution? It turns out there is something called quadratic reciprocity that helps to characterize when this equation has a solution. This class will quickly teach you the facts needed to understand quadratic reciprocity and present an easy-to-remember elementary proof of it.

Ever wondered why cutting a cone (the one that extends infinitely outwards in two direction) with a plane gives you parabola, hyperbola, or ellipse when another standard definition of these 3 conics deal with loci of points? Come to this class to find out why these two definitions are equivalent and possibly learn more fun/interesting facts about conics!