CS39: COURSE TOPICS (Spring 2013)
Tentative Course Syllabus -- may change based on student
Week1: What is symmetry? Bilateral and rotational
symmetries of finite 2D objects.
symmetry in art, architectural facades, and in hub caps.
Week2: Symmetry by repetition. Linear frieze patterns. Basic
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.
Zippering, Glueing Operations -- How do they affect Euler
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
in the standard model of elementary particles.