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.