http://sites.math.rutgers.edu/~zeilberg/math611.html
Official name: `642:611 Topics in Applied Math (Experimental Math)'.
GREAT NEWS RELEASE, Nov. 19, 2004
This course is now part of the Canon! No longer an adhoc
"topics" course. Thanks to our visionary gradchair,
Professor
Chuck Weibel,
[read his
message],
it will, for everafter, be a named
course called "Experimental Mathematics" and even has
an eponymous number 640:640
(creatively named by Prof. Weibel), so it could be nicknamed
"640 squared". Notice the significance of the 640 prefix!
It is a pure, rather than an applied, math, course. Indeed
it is not mathematics for experimenters but rather
experimentation for mathematicians.
Last Update: Dec. 18, 2004.
TEXT: The Maple Book by Frank Garvan
(Chapman and Hall) and handouts.
 Teacher:
Dr. Doron ZEILBERGER ("Dr. Z")

Classroom:
Allison Road Classroom Building
[Busch Campus], Room 116 [Inside computer lab].

Time: Mondays and Thursdays , period 3 (11:30am12:50pm)

Dr. Zeilberger's Office: Hill Center 704 ( Phone: (732) 4451326)

Dr. Zeilberger's Email:
zeilberg at math dot rutgers dot edu

Dr. Zeilberger's Office Hours: MTh 10:3011:00.
Outline
Experimental Mathematics used to be considered an oxymoron, but
the future of mathematics is in this direction. In addition to
learning the philosophy and methodology of this budding field,
students will become computeralgebra wizards, and that should be
very helpful in whatever mathematical specialty they'll decide
to do research in.
We will first learn Maple, and how to program in it. Then
we will learn how to design and conduct mathematical experiments,
that often lead to completely rigorous proofs.
Problem Set 1, due Nov. 29, 2004.
Maple Programs Done in Class
CATA
KOH
GOLAY (bug fixed!)
SADOV
BF (Oct. 18, 2004, the Knock 'm Down game studied by
Arthur Benjamin and Matthew Fluet. )
AL (Oct. 21, 2004, the Amitsur Levitski Theorem)
POLF (Oct. 25, 2004, Polynomial fitting a list)
RUIN (Oct. 25, 2004, Gambler's ruin)
GaussQ (Oct. 25, 2004, Gaussian Quadrature).
LEGENDRE (Oct. 28, 2004, Legendre polynomials from scratch).
LARA (Nov. 1, 2004, guesses rational functions, courtesy of
Lara Pudwell)
ORTHO (Nov. 1, 2004, gueses orhthogonal polynomials)
VATTER (Nov. 4, 2004, Restricted permutations)
PNP (Nov. 8, 2004, Straight Line Programs in order
to prove that P IS NOT NP).
FLT (Nov. 11, 2004, Fermat's Last Theorem).
Eric Rowanld found a polynomial family of solutions
of a^3+b^3c^3=1! (see his
message). Unfortunately, he has been scooped by the
famous number theorist Kurt Mahler, who found it
in 1936 (see Davnetport's book "The Higher Arithmetic"
(Dover, 1983 [originally published by Harper&Brothers, 1960]
p. 164).
GuessM (Nov. 15, 2004, GuessM).
Gchar (Nov. 15, 2004, Gchar).
POLFnew (Nov. 18, 2004, new version of POLF).
GcharNew (Nov. 22, 2004, Expanded version of Gchar).
TomJohnson (Nov. 29, 2004,
Tom Johnson's Perfect Rythmic Tilings) .
Added Nov. 30, 2004: I learned about composer Tom Johnson's
Perfect Rythmic Tilings from JeanPaul Delahaye's fascinating
article in Pour La Science, Novembre 2004. It is
described in
Tom Johnson's lecture.
Lara Pudwell, ran Tom(n,4), for n=1,2..., and found a new
TomJohnson configuration (with n=15), the first ever with k=4.
Stand by for Tom Johnson's musical composition based on
Lara's discovery.
See Lara's
message.
Added Nov. 30, 2004: Sujith Vijay has interesting ideas of
how to prove that
TomJohnson configurations exist for all k and sufficiently
large n.
Read Sujith's
message.
RandWalk (Nov. 29, 2004, Random walks) .
CRAMER (Dec. 2, 2004, Cramers's rule from scratch)
HILL (Dec. 2, 2004, Hill diagrams, a.k.a. trees).
DTrees (Dec. 5, 2004, Tin Bian's program for computing the
number of Rooted (directed) labelled trees).
JacobianConjecture (Dec. 9, 2004,
playing with the still open Jacobian Conjecture and the
recently closed Tame Generator Conjecture).
ASKEY (Dec. 13 2004,
positivity of Taylor coeffs. of rational functions in many variables).
Comitted Projects
 Tian Bin:
Find a proof of FLT (at least for n=3) using the
approach outlined in my paper.
Real Analysis is Degenerate... .

Sam Coskey and Lara Pudwell:
Write a C version for the Tom Johnson Configurations .
DownLoad
Lara and Sam's Cprogram (source code).

Yi Jin:
Discover empirically, and possibly prove, analogs of
the AmitsurLevitski Theorem for symmetric, antisymmetric,
and even quantum matrices.
Download
Yi Jin's Maple Program (source code).
 Chris Mesterharm, Random Walks.
 Mohamud Mohammed: qZeilberger
 Chris Ross:
End Game of Backgammon. Write a program that inputs a
Backgammon position (with the pieces no longer able to
capture), and outputs the expected number of moves to the
end, and the probability of each of the players to win,
using the greedy strategy. Try to find closedform formulas
for general backgammon (with arbitrary number of pieces), and
general die (possibly loaded).
Download
Chris's Ross Project.

Eric Rowalnd:
Do experiments with variation on FLT, n=3.
Posted March 1, 2005. Here are
Eric Rowland's FLT project and
accompanying tables, compiled by Koyama, and corrected by Eric Rowland .

Sujith Vijay: Study the Take 'Em Game of Arthur Benjamn and Matthew Fluet.
Download
Sujith Vijay's Message and Maple Code
Untaken Projects
Write a program that plays, and studies, Renju (generalized TicTacToe)
with a k by k board, and rinarow.
Write a Maple program that automatically generates
a Calculus I exam with `nice numbers' for each and every
kind of problem that showed up in the last five years.
It should also automatically generate the answers.
Write a Maple program that automatically generates
a Calculus II exam with `nice numbers' for each and every
kind of problem that showed up in the last five years.
It should also automatically generate the answers.
Write a package for Coding Theory.
Write a package for Graph Theory, verifying empirically
some famous theorems.
Find out how you and your computer could have discovered
Kathy O'hara's beautiful (KOH), from scratch, at least
for small values of k.