Math 640 (Spring 2025): Suggested EXPERIMENTAL MATHEMATICS Class Projects

https://sites.math.rutgers.edu/~zeilberg/EM25/projs.html

First written: April 6, 2025

This version: April 16, 2025

The class should be partitioned into teams of one, two, three, or four members.

The team leader will be in charge of coordinating the various contributions, and writing up (with the team's help) explaining it

The projects should be ready by: Wed., May 7, 2025, 8:00pm emailed to ShaloshBEkhad@gmail.com. Each project-leader should email TWO attachments: projX.txt and projX.pdf where 1 ≤ X ≤ 6

The student presentation will take place, via WebEx, on May 8, 2025, 9:30-10:50 am (WebEx invitation will be sent by May 6)

See the projects from Spring 2024,
See the projects from Spring 2022,
See the projects from Spring 2021,
projects from Spring 2020,
example from 2019.
another example from 2019 (of a different kind).
an example from 2018 and
another example from 2018.

Suggested projects by Dr. Z.

Project 1:

Expand considerabley the Maple package QC.txt that studies Quantum Computing. In particular have the following:

(i)Write a procedure that implements the "Controled U" operation

(ii) implement as many as possible of the algorithms in chapter 7 of Thomas Wong's book

(iii) implement correctly the quantum circuit that does the Quantum Fourier Transrom with n qubits (I didn't get it to work)

Project Leader: Salman Manzoor

Other team member: Tijil Kiran

Project 2:

Expand considerabley the Maple package AGT.txt that studies Algorithmic Graph Theory

In particular illustrate, and implement the as many as possible of the theorems, proofs and algorithms in Robin Wilson's book . In partucular, finding Hamiltonain paths (if the conditions of Dirac's theorem hold), The perfect matching algorithm, coloring as in Brooke's theorem. Also write an algorithm to compute the chromatic polynomial of any graph, and then use to experiment with RG(n,p) . If you are up to it, implement Chapter 29 in the Nijenhuis-Wilf classic to generate a random rooted unlabelled tree.

Project Leader: Jeffrey Tang

Other team member: Matthew Esaia

Project 3:

Expand the very rudimentary Maple package, AL.txt to discover identities among matrices inspired by the Amitsur-Levitzki theorem also identities inspired by this article

In particular discover such kind of identities for special cases of matrices: symmetric, anti-symmetric, tri-diagonal, upper-triangular, etc.
[This may lead to a publishable paper, if you find anything interesting]

Project Leader: (and only member) Joseph Koutsoutis

Projects suggested by students

Project 4:

"A very fun project I would be interested in is implementing Tarjan's fast algorithm for computing the dominator tree of a diagraph

Project Leader: Nick Belov

Other team members: James Betti, Nuray Kutlu

Project 5:

Gabow's algorithm and related algorithms

Project Leader: Lucy Martinez

Other team members: Pablo Blanco, Aurora Hiveley, Omar Garcia

Project 6:

Computing the Ricci Curvature of Graphs:

See here, here, and here

Project Leader: (and only member) Kaylee Weatherspoon

back to Experimental Mathematics (Spring 2025).