Undergraduate Seminar (395-0-51)

Instructors

Jared Wunsch
8474915580
Lunt 212

Meeting Info

Lunt Hall 104: Mon, Wed, Fri 11:00AM - 11:50AM

Overview of class

Title: "The Geometry of Differential Forms"

Here are some simple equations: ∫Xdω=∫∂Xω.dω= 0, d ? ω=j.

They don't look like much, but the first one contains all of the content of Green's theorem, the Divergence Theorem, and Stokes's theorem from multivariable calculus, together with their vast generalization to higher dimensions as described by Élie Cartan in 1945. The pair of equations below it is a modern formulation of Maxwell's equations of electromagnetism, which led Maxwell to realize in 1861 that light is an electromagnetic wave. These powerful equations are very short! This is because the notation of differential forms provides a compact way both to reformulate and to properly understand the geometry of integration and vector calculus in any number of dimensions. It is crucial to understanding modern geometry and high-energy physics. Studying equations with differential forms also leads to powerful tools in the field of topology: you can use them to tell the difference between different higher-dimensional analogues of surfaces ("manifolds").

Prerequisites: Math 320-2 (with 320-3 co-requisite) or 321-2 Math 291-1,2,3 or 334-0 or 330 or 331 sequence

Class Materials (Required)

978-9813272774
Differential Forms 1st Edition
Guillermin, Paine
World Scientific

Class Materials (Suggested)

No materials suggested. See required materials

Enrollment Requirements

Enrollment Requirements: Registration in this course is reserved for students who are majoring or minoring in Mathematics. Registration in this course is reserved for students who are majoring or minoring in Mathematics.