Undergraduate Research Projects

The Department of Mathematics and Computer Sciences offers undergraduate majors an opportunity to work closely with a professor on a project. The project might be publishable research, but it could also just be an interesting project that introduces students to some new mathematics. In any case the project would be worthy of a student presentation at a conference.

The duration of the project might be short or long: a student could work for more than one year on a long-term project, or less than a year on a short-term one.

This is not clerical work. The student will not receive payment or course credit for the project. This will be interesting mathematics that leads to something that a student can write or present. A student could end up with a finished project to hand to a prospective employer or graduate school admissions officer; or just to keep and say, "I did this."

If you are interested in working on a project, please contact the professor listed. You can also discuss project ideas you have with any faculty member, and that faculty member can suggest someone who will work with you.

Potential Projects

Simple Differential Equations and the Growth and Decay of Ice Sheets, Dr. Rick Adkins

In this project we will re-visit and expand upon a project of John Imbrie of the University of Virginia and his daughter Katherine matching periodic earth temperatures reflected in ice cores to when the earth axis tilt wobbled and the planets relative annual position to sun. We will investigate how key aspects of the ice-age record (such as shifts in dominant periodicities) follow from simple ordinary differential equations capturing the essential physics of the growth and decay of ice sheets.

Prerequisite: A student working on this project should have successfully completed MATH 241 Differential Equations.

Magic Polygons, Dr. Shelly Bouchat

If you like number puzzles like Sudoku, you might be interested in "magic squares." A 3x3 magic square is a puzzle that has 3 rows, each of which contains 3 boxes. You must place numbers in each box so that the sum of each row, each column, and each of the two diagonals is the same number. This project will focus on expanding this classic puzzle to consider "magic polygons." More details can be found on Dr. Bouchat's web page.

Prerequisite: Just an interest in mathematics.

Area' and Length' Application Using Green's Theorem and More, Dr. John Chrispell

The idea of this project is to create an app for an Android or Apple device that allows the user to calculate the area of a selected region using a touch interface. For instance, an application user could calculate the approximate size of the state of New York. To calculate New York's area a map interface would be used to collect user specified points around the boundary outlining the state and the application would compute the area using a line integral.

The application would be even more useful on a smaller scale. Computing areas of plots of land or towns by again selecting points around the region. As an added feature computing the length of a path selected on an image would also be a neat mathematical feature to add.

Prerequisite: The mathematics needed would be based on MATH 225 Calculus III with use of Green's Theorem and arclength being the core concepts.

The Gamma Function, Dr. Alfy Dahma

The theory of the gamma function was developed in connection with the problem of generalizing the factorial function of the natural numbers. The gamma function is defined as a definite, improper integral, and the notion of factorials is extended to complex and real arguments. This function crops up in many unexpected places in mathematical analysis, such as finding the volume of an n-dimensional "ball". In this project we develop and explore the basic properties of this function.

Prerequisite: MATH 225 Calculus III preferably, but you can get by with a good understanding of infinite series and integration techniques used in MATH 126 Calculus II.

Problems In Mathematical Analysis, Dr. Alfy Dahma

Are you interested in learning skills and techniques required to do research in mathematical analysis? If so, I have just the project for you. I've compiled a list of interesting problems in many areas of mathematics: calculus, set theory, linear algebra, topology, advanced calculus, general elementary analysis, etc. These problems range in difficulty level, and many of the solutions will require you do some of your own independent research. Solutions to some of these problems would be appropriate for presentation at an IUP colloquium or possibly a conference sponsored by a professional mathematical organization.

Prerequisite: Most problems require experience with writing proofs, but there's no harm trying.

Managing the Grading Process of Open-ended Questions on Nationwide Test, Dr. Yu-Ju Kuo

Have you ever taken a nationwide standardized test, such as an AP exam? Do you wonder how and where they are graded in a limited amount of time? This is a type of logistic problem occurring in business settings. Through this project, students will build a simplified Arena (simulation software) model for the above system, conduct sensitivity analysis for various resources and cost factors, propose reasonable ways to improve the system, and verify the proposed methods.

Prerequisite : No previous knowledge of Arena is required. Students should be comfortable playing with the software and will investigate the model in the directions of their choice.

Least is the Best, Dr. Yu-Ju Kuo

A common concern in industry is optimization: minimizing the cost, maximizing the profit, optimizing resource utilization, and so on. Students learn basic optimization techniques in calculus courses. But to what is it applied? What if the objective function is non-differentiable? What if variables are discrete? In this project, students can choose their preferred "no-so-nice" application and explore heuristic approaches to estimate the optimum and the optimizer.

Prerequisite : A student working on this project should have successfully completed MATH 225 Calculus III, MATH 171 Linear Algebra, and COSC 110.