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umdmathstat_dus@d.umn.edu
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Home > Undergraduate Studies > Undergraduate Research

Every year undergraduate mathematics and statistics students at UMD conduct research under the direction of faculty advisors in the Department of Mathematics and Statistics. Undergraduate research projects are supported through a variety of funding sources. One major funding source is the Undergraduate Research Opportunities Program (UROP).

UROP applications are accepted in the Fall and Spring semesters of each academic year. Awards typically include a small stipend and funds for travel expenses, materials and supplies. Applications materials (and more information) can be obtained from the UMD Swenson College of Science and Engineering.

The following abstracts describe undergraduate research projects funded for the 2001-2002 and 2002-2003 academic years:

Adjusting Ranks of Hitters in Baseball

Student Researcher: Kyle Bang
Advisors: Professors J. Gallian
Funding: Undergraduate Research Opportunities Program

Abstract: The careers of Hall of Fame baseball players Ted Williams, Joe Dimaggio, Hank Greenberg, Bob Feller, Warren Spahn and others suffered greatly because of their participation in World War II during their peak years. Likewise, Babe Ruth's lifetime hitting totals are less that they should be because he was a pitcher in his early years. Many baseball fans and statisticians have speculated about what these players would have achieved had their careers not been interrupted. The goal of this research project is to use statistical techniques to estimate how those players would have performed in the missing years and to see what effect that had on their all time place on various career hitting categories. For example, had Ted Williams not missed three years in WWII and two years in the Korean War one can say with 99% certainty that he would have be ranked number 1 in career RBIs (runs batted in) instead of 12th as he now ranks. One part of this project is to carry out this analysis for all players who rank on the top 25 of various categories of statistics. A similar study will be done for Rogers Hornsby, who was disadvantaged by playing his first five years in the dead ball era.

A second goal of this project was to calculate the "domination factor" of the greatest home run hitters in baseball history. One way to measure how much better a player is compared to his contemporaries is to compute a Z score (that is, how many standard deviations his performance is above the mean). For example, three standard deviations above the mean ranks a person in the top 1%. In this project I computed the Z score for various hitting feats. For example, Bath Ruth's 54 home runs in 1921 ranks much higher that Barry Bond's 73 home runs in 2001 because Ruth's total exceeds his competitors far more than Bond's did. Using this method I was able to determine the most dominating players in the history of baseball.

The N-body Problem

Student Researcher: Daniel Gastler
Advisors: Professor B. Peckham and G. Fei
Funding: Undergraduate Research Opportunities Program

Abstract: The behavior of N bodies (planets) under the influence of gravity is one of the oldest problems studied in mathematics. When N is bigger than two, there is no general analytic solution. Consequently, people search for special solutions with symmetry (such as "central configurations") or periodic solutions (such as "correography solutions"), rather than general solutions. In this project, the student is investigating properties of solutions involving four large bodies which stay on a square relative to each other, and four "zero mass" bodies placed on another square. He is looking at varying initial conditions determined by the initial velocity of the large masses and the initial diameter of the "zero mass square." It appears that some initial conditions result in the zero masses escaping, while others do not. The goal is to understand the dependence on initial conditions for escape, and hopefully to find a new periodic orbit from among those that do not escape.

Determining the Role of Technology in Teaching Mathematics

Student Researcher: Heather Kahler
Advisor: Professor C. Latterell
Funding: Undergraduate Research Opportunities Program

Abstract: Are there studies that support the claim that students can learn mathematics through the web? Or even, are there studies that support the claim that students can learn mathematics better through the web than through traditional methods? Actually, the questions remain almost uncharted as very few studies have been done using the web for learning mathematics. To contribute to an answer to these questions, four sections of high school geometry classes taught by the same teacher were evaluated through three mini-studies. Subjects were members of a school set in a medium-sized city in the Midwest. Subjects were of both sexes and enrolled in grades 9-12, with most students from grade 10. The three mini-studies incorporated and evaluated current projects in the classroom that integrated technology and geometry. These studies focused on surface area and volume, the classroom web site, and the Pythagorean Theorem.

Statistical Methods in the Analysis of Microarray Data

Student Researcher: Jesse Kling
Advisor: Professor K. James
Funding: Undergraduate Research Opportunities Program

Estimating Missing Data and Analyzing Variability of FACE Experiment Data

Student Researcher: Mariah Olson
Advisor: Professor K. Lenz
Funding: Undergraduate Research Opportunities Program

Parameterization and Sensitivity Analysis of a Complex Tree Simulation

Student Researcher: Kyle Roskoski
Advisor: Professor K.Lenz 
Funding: Undergraduate Research Opportunities Program

Predicting Success in the NCAA Basketball Tournament (March Madness)

Student Researcher: Kyle Bang
Advisor: Joseph Gallian
Funding: NSF/NSA Duluth Research Experience for Undergraduates Program

Abstract: The goal of this project is to determine which factors are the best predictors of success in the NCAA men's basketball tournament. Correlations between success in the tournament and various statistics such as victories over ranked teams, road winning percentage, 3 points field goal percentage, rebounding margin, turn over margin, and experience of the starters were computed. The results are then used to make predictions about which teams will do well in the 2003 tournament.

Phase-Plane Software for Parameter-Dependent Differential Equations

Student Researcher: Brian Rhiel
Advisor: Professor K. Dib and H. Stech
Funding: Undergraduate Research Opportunities Program

Abstract: A common problem in the analysis of dynamical system models is that of understanding how initial conditions and system parameters affect solution trajectories. For example how, in a predator-prey model, the initial numbers of predators and prey or (per capita) birth rates can influence the long-term predictions of the system. While traditional numerical study would involve performing a sequence of numerical simulations with each run using a specific parameter and initial condition set, this aproach becomes difficult to implement -- especially when there are more than a few system parameters.

The proposal is based on the goal of applying new graphical interface utilities to create a portable program for analyzing parameter-dependent ordinary differential equations. Graphical interface "sliders" raise the possibility of allowing one to examine the immediate influence of parameter changes on a system while it is under simulation. His study involves using Java interface tools to develop a simulator for a wide class of one- and two-dimensional differential equation systems.

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