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Recent Undergraduate Research Projects in Mathematics at Southern University

This document outlines various undergraduate research projects undertaken by students at Southern University, New Orleans, from 2010 to 2014. Highlighted projects include the exploration of the "Lights Out Puzzle" using SAGE, involving conditions for solvability, reliability and risk analysis collaborations with Dr. Omojola, fractal generation with MATLAB, the ongoing study of the Collatz problem, and a project on fingerprint analysis in collaboration with Dr. Tan. These initiatives were supported by grants from the National Science Foundation and Louisiana Space Consortium.

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Recent Undergraduate Research Projects in Mathematics at Southern University

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  1. Recent undergraduate research projects Zheng Chen Southern university at New Orleans March 2014 2014

  2. Projects (2010-2014) Lights Out Puzzle using SAGE (done) Reliability and risk analysis (cooperated with Dr. Omojola) (done) Fractals using Matlab (done) A holomorphic function “Collatz” problem (in progress) Fingerprints (cooperated with Dr. Tan, in progress)

  3. Project 1: Lights Out Puzzle using SAGE • Using Sage to find the conditions of solvability of Lights Out Puzzle • This research was conducted with funding by a grant from the National Science Foundation (HRD-0928797). • Mr. Gino Loverde, a math major, presented at the Emerging Researchers National (ERN) Conference and won 1st place in Feb. 2012

  4. Introduction to Lights Out Puzzle • Given an initial configuration of all lights on a board, turn off all of them Rules: each light has a button or switch, click one button, the light and its close neighbors will change. Each configuration can be viewed as a matrix with entries in Z(mod(2))

  5. Project 2: Reliability and risk analysis • Cooperated with Dr. Omojola • Supported by Louisiana Space Consortium (LaSPACE), Jan.10, 2011 • Ms. Brandy, a math major, joined this project and provided a poster in a local conference in Dillard University. • Three methods to calculate the reliability of a complicated system

  6. Project 3: Fractals using Matlab • Julia sets of iterations of a particular function quadratic polynomial of form like ; • target is to dealing with rational function of one complex variable of the form • Mr. Gino, a advisee of mine, worked on it in the course Math 400 (Math Seminar) in 2013.

  7. Project 4: A holomorphic function closely related to “Collatz” problem • Ms. Legendre, a math major, is working with me on it • The Collatz conjecture is an unsolved mathematical problem. • Collatz problem (or conjecture, or 3n+1 problem): after a finite iteration of the following function, any positive integer n will reach the number 1

  8. Two functions

  9. Image of unit circle under Collatz function under( 1st and 2nd iteration)

  10. Project 5 Fingerprints (in progress) • In this project, we will study and investigate how to extract terminations and bifurcations points from a fingerprint image by MATLAB operations.

  11. Cooperators • Dr. Tan, SUNO: on fingerprints, in progress, to be funded by Board of Regents in Louisiana, 2014. • Dr. Omojola, SUNO: on liability and risk analysis 2012.

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