REU: Products on spaces

This is the web page for the REU class "Products on spaces" which I am teaching this summer.

Schedule: For week 5 and 6 (July 16-27) we meet Tuesday and Thursday 4:30-6:00. For week 7 and 8 (July 30-August 10) we meet Monday, Wednesday and Friday 5:00-6:00. All classes will be in Eckhart 206.

I plan to put lecture notes here after each class, so check back regularly! One reference for much of what I'll be talking about can be found here: John Baez: octonions.

We will prove that the only normed division algebras over the real numbers are R, C, H and O. Along the way we will take a closer look at the quaternions H and the octonions O, and the connection with Clifford algebras. We will study projective spaces, in particular the octonionic projective plane OP^2, and we will see how some of the exceptional Lie groups can be constructed from the octonions.

Notes for lecture 1 as dvi and pdf.
Notes for lecture 2 as dvi and pdf.
Notes for lecture 3 as dvi and pdf.
Notes for lecture 4 as dvi and pdf.
Notes for lecture 5 as dvi and pdf.
Notes for lecture 6 as dvi and pdf.
Notes for lecture 7 as dvi and pdf.
Notes for lecture 8 as dvi and pdf.
Notes for lecture 9 as dvi and pdf.