Octonions in Mathematics and Physics
Spring 2002

Tevian Dray & Corinne A. Manogue

Office: Shattuck 208

Phone: 538-3164

Email: tdray@mtholyoke.edu & cmanogue@mtholyoke.edu

Class Meetings: Thursdays from 12:20-1:15 in Clapp 416

(We may occasionally meet across the hall in Clapp 401 or 402.)

Text: Corinne A. Manogue & Tevian Dray, The Octonions (will be distributed as we go along)

Web Site: http://www.mtholyoke.edu/courses/tdray/octonions
Check the web site for announcements and a rough list of what topics will be covered when.

Prerequisites:

Familiarity with complex numbers and linear algebra would be helpful. The ability to multiply matrices is essential.

Grades:

There will be no assigned work, nor is credit being offered, although it may be possible to obtain credit for an independent study project.

Description:

The octonions are a generalization of the familiar real and complex numbers. However, the octonions are neither commutative (ab not equal to ba) nor associatiave (a(bc) not equal to (ab)c). Linear algebra over the octonions is therefore both fun and interesting! Remarkably, this algebra appears to be closely related to deep physics, such as the existence of supersymmetry (string theory).

We will begin by explaining what the octonions are, and then discuss some of their basic mathematical properties. We will then discuss applications to physics. By the end of the semester, we will have at least hinted at the way we use the octonions to attempt to describe the fundamental particles of nature, such as electrons.

You can find some further information about the octonions here (on the website).

tdray@mtholyoke.edu