I start with the most basic concepts of Lie group and Lie algebra theory. is the ideal illustrative example: readily pictured, yet complicated enough to be interesting. The main goal is the double covering result. I do not take the most direct path to this goal, attempting to make it appear ``naturally''. Once we do have it, the urge to explore some of the related topology is irresistible.

Next comes physics. Usually introductory quantum mechanics starts off with
things like wave/particle duality, the Heisenberg uncertainty principle,
and so forth. Technically these are associated with the Hilbert space of
complex-valued functions on -- not the simplest Hilbert
space to start with. If one ignores these issues and concentrates solely
on spin, the relevant Hilbert space is . (Feynman's *Lectures on Physics*, volume III, was the first textbook to take this
approach in its first few chapters.) makes its entrance as a
symmetry group on . I conclude with a few hand-waves on some
loose ends.

© 2001 Michael Weiss