CS39: COURSE TOPICS (Spring 2019)
Tentative Course Syllabus -- will change based on students'
progress and 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. The Platonic solids.
Week4: President's Day.
Week5: Symmetries of finite
objects. Genus of handle-bodies. 2-manifolds;
orientability, borders and punctures.
Week6: Moebius bands and Klein bottles. Orientability, single-sidedness.
Week7: Cross caps,
Boy's surface . . . Genus, Euler-Poincare Formula, Euler
Characteristic,
Week8: {Space lattices, 3D tilings. }
Week9: Spring Break.
Week10: {4-dimensional, and
higher-dimensional completely regular ("Platonic") solids.}
Week11: {Lattices, wallpaper
patterns, 2D tilings.}
Week12: {Turning a sphere inside out. Regular
homotopies of tori and Klein bottles.}
Week13: {Tilings of curved spaces: Regular maps}
Week14: Project presentations.
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