Natural Science 0167 - Puzzles and Paradoxes

Puzzles can be used to discover mathematics, and to illuminate, motivate, and teach it. Paradoxes perplex and sometimes force foundational philosophical changes. In those contexts we'll consider Zeno's paradoxes of motion, the Tower of Hanoi (its "legend" is fraud); SET, Sudoku, the Bridges of Konigsburg, the Banach-Tarski paradox, Arrow's Theorem, Godel's Theorem, and puzzles created by Zeno, Archimedes, Fibonacci, Lewis Carroll, Sam Loyd, E. Rubik, Martin Gardner, Raymond Smullyan, Stewart Coffin, and John H. Conway. We'll encounter mathematical ideas from probability, combinatorics, geometry, topology, logic, number theory, game theory, and card tricks. Facility with algebra, basic geometry, and logical arguments is required, and students will be expected to expand their mathematical comfort zone, to hone problem solving skills, to make several presentations to the group, and to play with puzzles at the professor's house near campus a few times.

Physical and Biological Sciences Independent Work Quantitative Skills Students are generally expected to spend 8-10 hours per week on prepartion and work outside of class time.