http://www.math.rutgers.edu/~zeilberg/EM14/projects/SuggestedProjects.html
First posted: March 23, 2014
Last Update: April 15, 2014
First draft due Tue., May 6, 2014, 10:00pm .
It should be in the same publicsecret directory (em14) where
your homework resides. As with the homework, if
you prefer not to have it posted, please say so.
Feel free to propose your own project!
As long as it uses Maple (or even Mathematica, or SAGE) in a nontrivial way it is fine.
I prefer that it would involve Numerical Analysis, but you are welcome to do it
on anything mathematical. You must pick a project (and write a short description in the usual directory) by April 13, 2014, 10:00pm.
NOTE: Any project can be done by n people, with 1 ≤ n ≤ 3 .
The optimal size of a team is 2. Most of the projects are openended, and would
hopefully lead eventually to a published paper, and who knows? perhaps
to a whole thesis.
Untaken Projects
[Please ask me for details, if you are interested]

Use Experimental Mathematics to develop the theory of Orthogonal Polynomials
ab initio (i.e. from scratch), in the style of Lectures 8 and 9,
possibly using WZ theory

Develop a theory of multivariable orthogonal polynomials along similar lines.

Look up the vast literature on RungeKutta methods (some of which uses combinatorics),
and see whether you can improve it, and find new RungeKutta methods.

Use Experimental mathematics to find explicit expressions for solutions of finitedifference equations in
`nice domains'

Experiment with higher order versions of finitedifference operators of differential operators to reduce
both the local truncation errors and the global error.

Systematically investigate the metaFibonacci recurrences discussed in Douglas Hofstadter's
fascinating Experimental Mathematics seminar lecture: part 1, part 2,
Taken Projects

Systematically investigate the conjectures discussed in Douglas Hofstadter's
fascinating Colloquium lecture: part 1, part 2,
[Taken by Katie McKeon and Anthony Zaleski, see their
proposal]

Find codes with neat properties.
[suggested and claimed by Ross Berkowitz (with help from Tom Szinigir).
See Ross Berkowitz's proposal
]

Implement, and possibly extend to PDEs the interesting Interpolation method
suggested in
Tom Sznigir's message
[Claimed by Frank Wagner]

Investigate the gambler's ruin problem in two (and possibly even three!) dimensions,
along similar lines to this gem.
[Taken by Jeff Ames and Kafung Mok,
see their
proposal

Investigate subtraction games (continuing from last year, soon to be a seminal paper) [Taken by Nathan Fox]

See which sets of lines drawn in the plane with over and
under crossings can come from a projection of lines in three space to the
plane.
[Suggested and taken by Cole Franks and Andrew Lohr]

Implement the neat hypermatrix algebra described in
Edinah Gnang's beautiful paper
[Taken by Ha Luu and Somwya Srinivasan, see their
proposal]

Investigate enhanced Enumeration schemes for pattern avoiding permutations
[Taken by Nathaniel Shar]

Independently of this class' official requirement,Anthony Zaleski hopes
to investigate nonlocal isoperimetric poblem
[see his
proposal]
Experimental Math, Spring 2014 main page