Last Update: May 10, 2021
The Class should be divided into three to six teams, each with a team leader. Each team can contain from 1 to 2 students (including the team leader).
Students should pick a project by April 5, 2021.
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, 2021, 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 the projects from Spring 2020, See an example from 2019, another example (of a different kind). See also an example from 2018 and another example from 2018.
Use and extend the procedures done in class for statistical analysis of partitions, satisfying various conditions (odd, distinct, etc.) according to natural "random variables" (number of parts, lagrest part, individually and jointly). Conjecture (and possibly prove) explicit expressions for the expectation, variance, and the scaled moments about the mean and conjecture (or prove) the limiting distributions,
Project Leader: AJ Bu
Other team member: Robert Dougherty-Bliss
Added May 11, 2021: This team wishes to wait for the final version before it is posted. So far they did a great job.
Recently the New Times Magazine started this kind of puzzles,
This projects has two parts
Project Leader (and only member): George Spahn
Added May 10, 2021: Here is the neat app .
[Good job!]
Enjoy!
One of the famous open problems in number theory is to prove that the Ramanujan τ function, defined by the generating function
Sum(τ(n)*q^n,n=0..infinity) = q*Prod(1-q^i,i=1..infinity)^24
is never zero (Lehmer's conjecture). Investigate natural generalizations from an experimental point of view, and who knows? prove it.
Project Leader: Yuxuan Yang
Other team members: Zidong Zhang
Added May 10, 2021: here is the article and here is the Maple package. [Good job!]
One way is via "lexicographic greed" due to Aigner in the Boolean lattice case.
Project Leader: Blair Seidler
Other team members: Victoria Chayes
Added May 11, 2021: Here is a a preliminary version. of the project.
Good job, so far.
