2009 April 27 / E-Mail Me

My 2008-2009 comps group is studying geometric algebra (not to be confused with algebraic geometry). This is an enjoyable little neighborhood of mathematics with some important residents:

- normed division algebras (real numbers, complex numbers, quaternions, octonions)
- Clifford algebras (real numbers, complex numbers, quaternions, and others, but
*not*octonions) - Bott periodicity (some geometric phenomena repeat every 2 or 8 dimensions)
- Lie groups (such as O(n), SO(n), Pin(n), Spin(n), and even E8 and G2)
- geometry and mathematical physics

- Rotations describes rotations in terms of matrices, angles, complex numbers, and quaternions.
- The Octonions by John Baez of UC-Riverside is our main text. I recommend all of Baez's Fun Stuff.
- cayleydickson.nb is a
*Mathematica*notebook for computing with Cayley-Dickson numbers. It's quite unpolished. - clifford.nb is a
*Mathematica*notebook for computing with Clifford alebras. It's a work in progress.