Matrix Lie Groups
In the Spring 2016 semester I hope to offer the fundmentals of Lie Groups as a 1hr course which typically meets on M from 3:30-5:00pm.
Course Planner can write in homework numbers as course unfolds.
In the interest of helping the self-study of future students we'll record our meetings at:
You Tube Playlist I try to post each Lecture here soon after it is given
We follow Stillwell's Naive Lie Groups text fairly closely. The page numbers below refer to Stillwell's text. Lie Groups can be defined in a more abstract fashion which requires maturity in manifold theory and topology. However, Stillwell's approach is more elementary and the proofs require little more than the usual calculus and linear algebra. Furthermore, the examples in this course have rich geometric and historical significance which sometimes get lost in the mature graduate version of this course.
- M:1-18, Geometry of complex numbers and quaternions (p.1-22)
- M:1-25, Groups (p.23-47)
- M:2-1, Generalized rotation groups (p.48-73)
- M:2-8, Generalized rotation groups (p.48-73)
- M:2-15, The exponential map (p.74-92)
- M:2-22, The exponential map (p.74-92)
- M:3-21, Structure of Lie algebras (p.144-138)
- W:3-30, Structure of Lie algebras (p.114-138)
- M:4-4, The matrix logarithm (p.139-159)
- M:4-11, The matrix logarithm (p.139-159)
- M:4-18, Topology (p.160-185)
- M:4-25, Simply connected Lie groups (p. 186-203)
- M:5-2, Simply connected Lie groups (p. 186-203)
Homework will be given from Stillwell and other relevant sources. I intend to collect and grade the homework weekly (600pts). A two midterms (200pts) and final exam (200pts) will also be given.
The background picture is based on a picture I saw at this website
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Last Modified: 1-13-2016