Princeton Splash
Welcome to Princeton Splash, a student-run organization at Princeton University

ESP Biography


Major: maths

College/Employer: Princeton

Year of Graduation: 2016

Picture of Frederic Koehler

Brief Biographical Sketch:

Not Available.

Past Classes

  (Look at the class archive for more.)

Permutations in Splash Spring 16
The teacher will teach something interesting about permutations, which are "shufflings" of a set, e.g. a pack of cards. They are pretty important in math, computer science, life, everything. If time permits, some things about the Robinson-Schensted correspondence will be taught. (Don't worry what this is.)

Shadows, Halos, and the Hyperreal in Splash Spring 14
In the late 17th Century, Isaac Newton and Gottfried Liebniz independently developed a revolutionary new mathematics, calculus, based upon a radical new concept: infinitesimals, the infinitely small. Though intuitively elegant, infinitesimals were derided by philosophers for being nonrigorous and possibly nonsensical; mathematicians, unable to rigorously define the concept, chose instead to rebuild calculus without it. It was not until the 1960s that a mathematician, Abraham Robinson, found a rigorous way to define the infinitesimals as part of a "hyperreal line", and thus gave birth to a mathematics of the infinitely small (and the infinitely big). Since then, Robinson's "non-standard" approach has found use both in introductory calculus courses and in the research of world-class mathematicians (e.g. Terrence Tao, Fields medalist). Because the proof of their mathematical "existence" is slightly technical, I would instead like to briefly discuss their usage. In particular I would like students to leave with a basic intuitive understanding of the notions of shadows and halos and their relation to some basic calculus.