Suggested Projects for Math 640: EXPERIMENTAL MATHEMATICS, Spring 2011

First posted: March 27, 2011

Last Update: May 11, 2011

First draft due May 10, 2011, 11:59:59pm .

Feel free to propose your own project! As long as it uses Maple (or even Mathematica) in a non-trivial way it is fine. It does not have to do anything with Boolean Circuits, or flipping pancakes.

NOTE: Any project can be done by n people, with 1 ≤ n ≤ 2 .

Untaken Projects

• Develop and implement algorithms for proving SAT using PIE, largely expanding PIE.txt
• Generalize Pancake-flipping, by changing the rules, and develop algorithms for sorting, using these rules.
• Look up formal languages and grammars, and develop a Maple package, following your favorite book.
• Write Maple implementations of all the statmenets in the classic Alon-Bopanna article
• Implement, and if possible, improve, the 5n lower bound in the article by Kazuo Iwama and Hiroki Morizumi.
• Write Maple implemenations of the beautiful work of Philippe FLAJOLET(1948-2011) on continued fractions

Taken Projects

• Investigate anti-chains in the Boolean Lattice. [Suggested and claimed by Jacob Baron, see his project description]
• Completely automate, and generalize, the Gates-Papadimitriou pancake-fliping algorithm. (Claimed by Matthew Russel and Tim Naumovitz)
• David Wilson's class project to create a general framework for testing theorems empirically in Arithmetic Combinatorics - Roth's Theorem, Szemeredi's Thoerem, Van der Waerden's Theorem, Folkman's Theorem and so on. (first posted March 28, 2011, in progress).
• Write Maple implementations of all the statmenets in the classic Alon-Bopanna article (claimed by Emily Sergel).
  Added May 11, 2011: Here is Emily Sergel's project.
• Investigate about elliptic curves. Nagell-Lutz's theorem. [Suggested and claimed by Taylor Burmeister].
• Develop a package to work with Coxeter Groups [Suggested and claimed by Matthew Samuel].
• Turning Boolean satisifiability problems into logic puzzles, and exploring the structure of what Raymond Smullyan calls "meta-puzzles", where one of the pieces of information is about the solvability of the puzzle. [Suggested and claimed by Susan Durst].
• Investigate goemetric perfect matchings [suggested and claimed by Justin Gilmer]
• Investigate slicing planes [suggested and claimed by Simao Hernande]