What Is Mathematics?
Residential College Interdivisional Course 216
(Formerly known as:
Math for Poets,
Understanding Mathematics, and
Gödel, Escher, Bach)
Named "Cool Site of the Month" April 1996
by Thomas Jefferson Junior High School,
Salt Lake City, Utah, U.S.A.
  RCIDIV 216-001   Fall '03   T-Th 2:00-3:30 pm   224 Tyler EQ
  Course Syllabus   ... and a few words on Math Appreciation

  Web pages for our recently-published texts:
Class Resources

  • Johann Sebastian Bach (1685-1750)
  • Bach canons and fugues online
  • A Bach home page
  • Bach's listing in the Classical Music Pages.
  • The Bach FAQ
  • Basic Repertoire
  • Bach-Institut, Göttingen
  • The Endlessly Rising Canon, with Shepard scales (audio samples)

  • Maurits Cornelis Escher (1898-1972)
  • Yahoo on Escher
  • An Escher home page
  • And another
  • World of Escher

  • Kurt Gödel (1906-1978), an international panoply
  • From New Zealand, Gödel's Theorem and Information, a paper by Gregory Chaitin
  • From Austria, The Kurt Gödel Society
  • From the UK, The Goedel Programming Language
    and a Kurt Gödel Home Page
  • From Latvia, Around Goedel's Theorem, a (hyper)textbook for students in mathematical logic
  • From Australia, "Can Humans Escape Goedel?", a review of Shadows of the Mind, by Roger Penrose

  • Douglas Hofstadter The Onlie Begetter
  • Indiana CogSci, where he plies his trade
  • another of his books

  • Euclid
  • Euclid's Proposition 47 (an animation)
  • Euclid of Alexandria Home Page
  • Euclid's Prime Number Theorem (there is no largest prime number)
  • a sample page from Euclid's Elements
  • Introduction to Euclid's Elements

  • Lewis Carroll (Charles Lutwidge Dodgson, 1832-1898)
  • LEWIS CARROLL SOCIETY OF NORTH AMERICA (LCSNA) Home Page at (www.lewiscaroll.org)
  • Charles Dodgson, Photographer
  • Metastuff -- Lewis Carroll and Other's Works
  • Martin Gardner's classic The Annotated Alice from Amazon Books.

  • About Stephen Wolfram & aNKoS
  • From Wolfram Science: Book summary, interview, autobiography.
  • Kurzweil on Wolfram
  • An official Math Review
  • An editorial and review from Computer.org.
  • Other reviews

  • About Cellular Automata
  • Game of Life Home Page
  • Google on Game of Life
  • Applets for Game of Life
  • Cellular Automata Music
  • Evolving Cellular Automata
  • Cellular Automata FAQ
  • A Tutorial on Cellular Automata
  • Another Cellular Automata page
  • The Math Forum on Cellular Automata

  • Chaos, Complexity, and Fractal Geometry
  • The Chaos Society
  • Chaos without the math
  • Interactive Course
  • Google on Chaos and Fractals
  • Chaos Theory and Fractal Geometry

  • Fractals
  • Clifford Pickover Visual information. Very visual. Very information.
  • Fractal Microscope
  • Mathematical Art, Graphics, Chaos and Fractals
  • Mandelbrot and Julia Set Explorer Interactive zoom
  • Spanky Fractal Database

  • Eliza & Co. (See below for downloadable Elizas)
  • Eliza, dba: Dr. Werner Wilhelm Webowitz
  • Another Eliza, with a different script
  • Simon Laven's AI-NLP page
    with a full panoply of chatterboxes, some interactive and some downloadable software
  • Julia, Eliza's g'g'g'great-granddaughter
    A case of a human failing the Turing Test
  • And an annotation on the Eliza Effect in AI jargon.

  • Primes
  • Prime numbers in Number Theory
  • Prime number FAQ
  • Prime Numbers and Factoring
  • The Largest Primes
  • Join in The Great Internet Mersenne Prime Search
  • Prime Romance, from this collection

  • Games and Related Matters
  • The Live Artificial Life Page
  • Alife Online (that's A-Life, i.e, Artificial Life -- hey, it's a living)
  • Some games by John Horton Conway

  • Miscellaneous
  • The Erdös Number Project. Erdös Numbers are not your ordinary kind of number.
  • Favorite Mathematical Constants
  • A Postcard from Italy
  • Women and Minorities in Science and Engineering for the math-abused
  • "Metaphors We Compute By", by Yours Truly
  • The UM Math Department
  • Numeric Sequences
  • Alan Turing Home Page

  • Humor   Really, this is humorous. It says so right here...

  • Sight gags and other mercifully short math humor
    Q: What's purple and commutes?
    A: An Abelian grape.
  • Stories and other longer pieces
    "An engineer, a physicist and a mathematician ..."
  • Verse: "Hiawatha Designs an Experiment"
    "In a corner of the forest
     Sits alone my Hiawatha
     Permanently cogitating
     On the normal law of errors."
  • Even Verse: Cecil Adams' version of Schrödinger's Cat, from "The Straight Dope"
        "Schrödinger, Erwin! Professor of physics!
         Wrote daring equations! Confounded his critics!"
  • A British entry, Quotes from lecturers at Cambridge University
    .. including the Sybil Fawlty Prize for Stating the Bleeding Obvious:
        "You don't want to prove theorems that are false."
  • Deviating from mathematics briefly, here is a collection of
      sentences harvested from American students' essays on science exams.
    "Three kinds of blood vessels are arteries, vanes and caterpillers."
    "The pistol of a flower is its only protection against insects."
    "When you smell an odorless gas, it is probably carbon monoxide."
  • Economist Jokes

  • Software
  • Eliza: the first successful AI program, in several versions: (See above for on-line Elizas)
    • Eliza "The classic psychologist-in-a-box artificial intelligence simulation. Will speak if MacinTalk is installed." (For Macintosh only)
    • Eliza for DOS; works from a separate script, so you can modify it.
      (Turn Eliza into a feminist therapist, a paranoid schizophrenic, or even Hannibal Lector)
    • Other Elizas for DOS, from Simon Laven
  • FractInt, by a wide margin the best Fractal generator for DOS.
  • Calculus Calculator, a free graphing virtual math package (DOS only).
    Very impressive, especially at this price.
  • Math directories from the UM Archives: Macintosh, MS-DOS
  • Mathematics and the Liberal Arts, with tons of downloadable math software for students, teachers, and other curious people.

  • Some class projects
  • Conversation Simulators: Modification and Comparison, starring Eliza as Space Ghost and MegaHAL as Socrates, a GEB project by Alex Krusz, 2002.
  • 100,000,000,000,000 sonnets by Raymond Queneau, a GEB project by Andrew Lurie, 2002.

    • General Mathematics Links

  • New this month on the Mathematics Archives
  • University Resource Collections

  • Cornell Math/Science
  • CalTech Math Resources
  • Oklahoma State Math Resources
  • Penn State Math Resources
  • University of Tennessee Math Archives

  • Math History

  • History of Mathematics  Very complete.
  • Legislating Pi by Mark Brader
    Truth is much, much stranger than fiction.
  • A Brief History of Algebra and Computing, by Jonathan Bowen

  • Miscellaneous

  • The American Mathematical Society's MathSciNet
  • The Mathematical Association of America  Not the same organization as the AMS
  • well, maybe a poem
  • The Geometry Center
  • Applied Math
  • WWW Virtual Library: Math
  • CSC Math - Finland
  • Data Powers of Ten
  • Stewart Dickson  A mathematical artist.

    • Last change 11/6/05 John Lawler     The Eclectic Company