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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