David C. Kelly, professor emeritus of mathematics, has taught at New College, Oberlin, and Talladega College.
He holds an AB from Princeton, an SM from MIT, and an AM from Dartmouth. He has, since 1971, directed the well-respected Hampshire College Summer Studies in Mathematics for high ability high school students.
His interests include analysis, probability, the history of mathematics, recreational mathematics, and 17.
The complex numbers, described by Leibniz as amphibia between existence and non-existence, are now an important tool for both pure and applied mathematics. They have a fruitful geometric interpretation, provide an algebraic closure to the reals (in the sense that all polynomials with coefficient in C have roots in C), and allow, with a more coherent theory than for real variables, the development of the calculus. The important exponential function, in particular, extends elegantly to the complex domain. This course will concentrate on the differentiation and integration of complex functions and their mapping properties. We will see application of our theory to geometry, dynamics (including the Mandelbrot set), and physics. A working knowledge of elementary calculus is assumed. There will be a weekly problem session attached to the course and regular written assignments.
It has been argued that puzzling is as intrinsic to human nature as humor, language, music, and mathematics. Zeno's paradoxes of motion and the liar and heap paradoxes ("This sentence is false," "Does one grain of sand change a non-heap into a heap?) have challenged thinkers for centuries; and other paradoxes have forced changes in philosophy, scientific thinking, logic, and mathematics. We'll read, write, and talk about the Riddle of the Sphinx, the Minotaur's Maze, the Rhind papyrus, Pythagorean mysticism, Archimedes' wheel, Fibonacci's rabbits, Durer's magic square, Konigsberg's bridges, Lewis Carroll, Sam Loyd, E.H. Dudeney, Mvbius's band, Maxwell's Demon, Schrodinger's cat, Hempel's raven, the theorems of Kurt Godel and Kenneth Arrow, the Loony Loop, Rubik's cube, the Prisoner's Dilemma and the unexpected hanging, Russell, Berrocal, Christie, Escher, Borges, Catch-22, Sudoku, Gardner, Coffin, Kim, Smullyan, and Shortz. Recreational mathematics will pervade the course, and we'll grapple with irrationality, pigeonholes, infinity, and the 4th dimension. We'll discover, create, classify, share, enjoy, and be frustrated and amazed by lots of visual illusions, mechanical, take-apart, assembly, sequential, jigsaw, word, and logic puzzles. We'll hone our problem-solving skills and consider the pedagogic and social value of puzzles. Armed with examples and experience, we might find some possible answers to "what makes a puzzle 'good'?" and "why do people puzzle?"
Director of Summer Studies in Math Casual
Mail Code NS
893 West Street
Amherst, MA 01002