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Notes from the 2002 - 2003 Academic Year: Unit 1: Introduction and Foundations "What is mathematics all about? - The lion, the llama, and the lettuce" by Renzo Cavalieri (September 18, 2002) "What is mathematics all about? - Pick's Theorem" (continued) by Renzo Cavalieri (September 25, 2002) "How to count and climb ladders - proofs and induction" by Nick Korevaar Handouts both courtesy of the Berkeley Math Circle pages at http://mathcircle.berkeley.edu (September 25, 2002) "How to count and climb ladders - trax, trains, and trolleys" by Nick Korevaar (October 2, 2002) Unit 2: Discrete Dynamical Systems "Incidence is No Coincidence" by Nick Korevaar (October 16, 2002) "Directed Graphs" by Hugo Rossi (October 16, 2002) "Diffusion Model" by Hugo Rossi (October 23, 2002) "Weighted Graphs" by Hugo Rossi (October 23, 2002) "Extinction and Population Dynamics" by Nancy Sundell-Turner and Fred Adler (October 30, 2002) "Extinction and Population Dynamics - Part 2" with logistic and tent images by Nancy Sundell-Turner and Fred Adler (November 6, 2002) Unit 3 "Rubik's Cube" by David Hartenstine as well as notes from Tom Davis at Berkeley (November 21, 2002) "Rubik's Cube" (continued) by David Hartenstine (December 4, 2002) Unit 4: Math Contests - For MAA and State Math Contest-Type Problems (For this unit, we used many wonderful problems from old American Mathematics Competitions. The URL for this organization is http://www.unl.edu/amc and, if you visit that site, you will find a wealth of information and resources for high school math contests.) "Geometry" with solutions by Matthew Rudd (January 15, 2003) "Counting and Probability" by Bob Guy (January 22, 2003) "Algebra and Number Theory" by Renzo Cavalieri: introductory problems, their solutions, contest problems, and their solutions (January 29, 2003) Unit 5: Topology "Knots" by Mladen Bestvina (February 12, 2003) "Knots" (continued) by Mladen Bestvina (February 19, 2003) "Graph Theory" by Bobby Hanson (February 26 and March 5, 2003) Unit 6: Geometry "Fractals - Part 1" by Jesse Ratzkin (March 26, 2003) "Fractals - Parts 2 and 3" by Jesse Ratzkin (April 2 and April 9, 2003) Handout by Jesse Ratzkin (April 9, 2003) "The Magic of Numbers" by Florian Enescu (April 16 and April 23, 2003) (Note: To open and print these .pdf files, Adobe Acrobat Reader software is required. Click here to download a free copy of this software.) Notes Main Page