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Texas A&M University

Graduate Student Organization Seminar

Date: November 20, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: C.J. Bott


Title: Why An Algebraist's Favorite Subject Should be Calculus

Abstract: A traditional undergraduate abstract algebra course focuses on groups (which have 1 binary operation) and rings (which have 2 binary operations), but the fact is that there are many more algebraic structures (with 1,2, or more than 2 binary operations) that are ubiquitous in mathematics. In this talk, I will introduce the simplest forms of my two favorite examples of algebraic structures: smooth functions and smooth vector fields in \mathbb{R}^n! While many may be familiar with these sets from calculus, they have an astounding number of binary operations with immediate and interesting geometric consequences. It is my hope that mathematicians of all backgrounds will enjoy seeing these connections in math that are not usually taught in a formal course.