Math 170 Ideas in Mathematics Amphitheater A1, MWF 11-12 Professor Leila Schneps Office Hours: M 9-11

The goal of this course is to give non-math-oriented students a feel of what doing mathematics is really like, of what it feels like to be a working mathematician, of how mathematical ideas can be exciting, inspiring, striking, unexpected, startling, intriguing, or amazing.

The course will cover some actual elementary mathematics, with the purpose of showing how truly deep so-called "easy" mathematics can be. There will be no tedious computations here, but simple yet historically ground-breaking proofs.

The course will also cover some cultural aspects of mathematics, such as exciting moments of mathematical history, interesting biographical material, and of course a healthy dose of anecdote. These will be presented through a number of works of fiction, biography and autobiography, and some movies, plays or documentaries.

Homework will consist of math problems, but also essays, papers, and a personal presentation. According to their style and preferences, students will have a choice of topics ranging from personal feelings about mathematics to historical aspects to study of an actual mathematical theme.


Some of the mathematical epochs and themes we will cover:
      Ancient Greek mathematics: the earliest notions of axioms and rigorous proof.
      From Greek Antiquity to Italian Renaissance (1500-1600): conic sections, cubics, and the development of algebra.
      The European expansion (1600-1800): struggles with the infinitesimal.
      Some of the major concerns of 19th and 20th century mathematics: sets, the real numbers, logic and paradoxes,
                  encryption and coding, discrimination and racism in mathematics. discrimination and racism in mathematics.


Several films with or about math or mathematicians (I hope we will see some of these in class):
     A Beautiful Mind,   a biographical film with a surprising twist, about a real mathematician, John Nash, who slowly became schizophrenic
     A Brief History of Time,  a film by, with and about Stephen Hawking
     Breaking the Code,   a biographical film about the mathematician Alan Turing, whose life was fraught with unusual difficulties
     Fermat's Last Tango,  a musical (available on DVD from the Clay Institute)
     Fermat's Last Theorem,  a BBC documentary by Simon Singh
     Good Will Hunting,   a 1997 movie about an unsuspected troubled-youngster math genius
     Infinity,  a film by, with and about Richard Feynman enjoying himself, as usual
     It's My Turn,  a 1980 movie in which Jill Clayburgh plays a mathematics professor
     Proof,  a play about mathematics by David Auburn, with Gwyneth Paltrow in the movie version
     Stand and Deliver,  a 1987 film about an inner city calculus teacher who succeeds
     Straw Dogs,  a 1971 movie in which Dustin Hoffman plays a physicist with a flirtatious wife.


An amazing catalog of mathematical fiction:
           Alex Kasman's Math Fiction Site


A truly hilarious list of spoof proof techniques, alas sometimes all too realistic
           Invalid Proofs

A list of books available for borrowing:
     Fermat's Last Theorem,  Simon Singh
                 A lively account of the story of Fermat's last theorem, from its first statement in the 18th century to its proof in 1995.
     Flathead, a romance of many dimensions,  Edwin Abbott
                 A short nineteenth-century novella about living in less dimensions -- and social mores.
     Flowers Stained with Moonlight,  Catherine Shaw
                 A murder mystery oriented around Fermat's last theorem.
     The Library Paradox,  Catherine Shaw
                 A murder mystery in which logic plays a role.
     The Mind-Body Problem,  Rebecca Goldstein
                 A novel about love, math and love of math
     The Nothing that Is,  Robert Kaplan
                 A popular book retracing the origin and history of the concept of zero
     Reality Conditions,  Alex Kasman
                 A book of humorous short fantasy pieces about different sorts of mathematics, some real, some invented.
     Strange Attractors,  Rebecca Goldstein
                 Short stories with plenty of scientists.
     Surely You're Joking, Mr. Feynman,  Richard Feynman
                 Hilarious but true autobiographical sketches of Richard Feynman's own life.
     The Three-Body Problem,  Catherine Shaw
                 A murder mystery in which the three-body problem plays a double role.
     Uncle Petros and Goldbach's Conjecture,  Apostolos Doxiadis
                 A novel in which a mathematician aims too high.