# ESP Biography

## CHRISTOPHER XU, ESP Teacher

Major: Mathematics

College/Employer: MIT

Year of Graduation: 2021

Not Available.

## Past Classes

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

M13263: Nonstandard analysis and the hyperreal numbers in Splash 2019 (Nov. 23 - 24, 2019)
Do priggish mathematicians shame you for writing down "handwavy" expressions like $$dy=f'(x)\, dx$$ ? Say no more. With the hyperreal numbers, you can use infinitesimals to do your calculus just like Newton and Leibniz in the days of yore. Warning: there will be numbers $$\circledcirc>0$$ smaller than any positive real and $$\omega$$ bigger than any positive integer.

Z13009: Highways of the United States in Spark 2019 (Mar. 16 - 17, 2019)
Everything you ever wanted to know about highways (with an emphasis on the United States).

M12591: Quirky Quarternions: An intro to non-commutative algebra in Splash 2018 (Nov. 17 - 18, 2018)
$$ab = ba$$: You may have learned about this seemingly universal truth in grade school. However, in this class, we'll throw the commutative law of multiplication out of the window, and go back to the drawing boards to define an algebra of numbers with three imaginary units. We will begin the class with a short introduction of complex numbers, their geometric representation as points on the complex plane, and the geometric meaning of their multiplication. We will then introduce the fundamental multiplication law for quaternions, $$i^2 = j^2 = k^2 = ijk = -1$$, and show how everything about quaternions falls into place following this formula. You will also learn a few party-twister tricks that work thanks to quaternion algebra.