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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.