final-guide

# Ill also hold my usual wednesday office hour

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utes and half an hour) to your questions. I’ll also hold my usual Wednesday office hour immediately following class. Here is a list of topics you should concentrate on, roughly in the order we covered them. I’ve tried to indicate what days we covered these topics in class; I may be off by a day in some places since there were some times when I prepared something for one day but didn’t get to it until the following day. Cantor’s power set theorem (3.4; Wed. June 10) The infinite in geometry: proof that the square and the line have the same cardinality, stereographic projection in pictorial terms (3.5; Mon. June 15) The art gallery theorem (4.2; Tue. June 16) Tessellations (Wed. June 17; note that my emphasis here was quite different than that in the text) Polyhedra: duality, counting symmetries, Euler characteristic, angle defects (Thu. June 18; 4.5) Geometry on the surface of spheres and polyhedra (Thu. June 18; 4.6) Hypercubes and hypertetrahedra (Mon. June 22?; 4.7) The Euler characteristic for polyhedra and planar graphs (Mon. June 22; 5.3) The Euler characteristic for surfaces with holes (Tue. June 23; 5.3) Fractals: the Koch snowflake, the Cantor set, the Sierpinski gasket (Wed. June 24 and Thu. June 25; 6.3) Fractal dimension (Wed. June 24 and Thu. June 25; 6.6) The problem of points (Thu. June 25; 7.2) Basics of probability (Thu. June 25 and Mon. June 29; 7.2) Randomness and coincidence (Mon. June 29 or Tue. June 30; 7.3) Probability by counting (Tue. June 30; 7.4) 1

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This list corresponds fairly closely with material that was on the homework; thus making sure you understand how to solve the homework problems will be one of the best ways to study for the exam. Here are some things that I spent a fair amount of time on in class but explicitly will not test. Explicit formulas for stereographic projection, rational points on circles, map projec- tions Proofs of volumes and surface areas of three-dimensional objects The geometry of the universe as a whole Classification of surfaces and the Poincare conjecture Proving that K 3 , 3 and K 5 are not planar Paradoxes in probability 2
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• Summer '09
• Lugo
• Math, Map projection, Mon, Fractal, Euler characteristic

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