Splash Biography

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.)

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.