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June 22 5.3 • the euler characteristic for surfaces

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Unformatted text preview: 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 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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June 22 5.3 • The Euler characteristic for surfaces with...

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