# ESP Biography

## XINKE GUO-XUE, MIT Junior studying mathematics

Major: mathematics

College/Employer: MIT

## Brief Biographical Sketch:

I study math and piano.

## Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M7490: quadratic reciprocity in Splash! 2013 (Nov. 23 - 24, 2013)
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.

M7574: Conic sections extravaganza in Splash! 2013 (Nov. 23 - 24, 2013)
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!