CS39: COURSE TOPICS  (Spring 2013)

Tentative Course Syllabus -- may change based on student feedback!

Week1:  What is symmetry?  Bilateral and rotational symmetries of finite 2D objects.
              2D symmetry in art, architectural facades, and in hub caps.

Week2:  Symmetry by repetition. Linear frieze patterns. Basic symmetry operations

Week3:  Rotational symmetries of finite objects; wrapping friezes around a solid.

Week4:  Symmetries; the Platonic and Archimedean solids.

Week5:  4-dimensional, and higher-dimensional completely regular ("Platonic") solids.

Week6:  Lattices, wallpaper patterns, 2D tilings.

Week7:  Space lattices, 3D tilings

Week9:  Topology: Genus, Euler-Poincare Formula, Euler Characteristic, orientrability, single-sidedness.
              Punching, Zippering, Glueing Operations -- How do they affect Euler Characteristic?
              Complete surface classification [Conway Ch8].

Week10:  Moebius bands, cross caps, Boy's surface . . .

Week11:  Turning a sphere inside out. Regular homotopies of tori and Klein bottles.

Week12:  Tilings of curved spaces: Regular maps

Week13:  Big Bang; the shape of the universe, the Eight-fold Way,
                Symmetries in the standard model of elementary particles.