Math 640 (Spring 2020): Suggested EXPERIMENTAL MATHEMATICS Class Projects

Last Update: March 29, 2019.

The Class should be divided into three teams, each with a team leader. The team leader will be in charge of coordinating the various contributions, and writing the first draft of a paper that will be definitely posted here. The first, preliminary, "skeleton" versions should be ready by May 10, 2020, but it is hoped that they will be expanded into publishable papers (at least in arxiv.org, and possibly in a a "real" journal. Each paper should be accopmpanied by at least one Maple package. See example from 2019, another example (of a different kind). See also an example from 2018 and another example from 2018.

First Suggested Project: Generalized Gambler's Ruin

Project Leader: Yukun Yao

Other members: tbd

Extend studies of Gambler's ruin, with all its aspects: Simulation, Pure numeric, numeric-symbol, and closed-form (if possible) to other families of directed graphs, not just the line. For example:

• An M by N rectangle (with various conventions of winning and losing) including a torodial rectangle. M should be numeric (i.e. M=2,M=3, M=4) but N symbolic. Then it would be interesting to conjecture, and possibly prove trends as M increases.

• Ring graphs