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Master of Science

Our master's program in mathematics will give you a competitive edge to reach your career goals, whether you plan to teach, work in industry, or pursue a Ph.D.

Research Projects

Previous Graduates

Graduate Teaching Assitantships

Financial Aid

How to Apply

Contact Information

Curriculum (30 Semester Credit Hours)

Core Courses (12 hours)

MATH 5305:  Statistical Models

MATH 5308:  Abstract Algebra

MATH 5350:  Linear Algebra

MATH 5320:  Real Analysis

One-hour Seminar Courses (3 hours)

MATH 5198:  Research Analysis

MATH 5186:  Math Ideas I

MATH 5186:  Math Ideas II

Electives (15 hours)

Mathematics Education

MATH 5371:  Euclidean and Non-Euclildean Geometries

MATH 5373:  Theory of Functions

MATH 5375:  Statistical Reasoning and Probability

MATH 5376:  Topics in Secondary Mathematics

MATH 5377:  In-Depth Mathematical Reasoning

MATH 5378:  Technology-Aided Mathematics

MATH 5379:  Trends and Issues in Research

Data Mining and Statistics

MATH 5362:  Data Warehousing

MATH 5364:  Data Mining I.

MATH 5366:  Data Mining II

MATH 5301:  Nonparametric Statistics

Pure and Applied Mathematics

MATH 5306:  Dynamical Systems

MATH 5309:  Complex Variables

MATH 5330:  Mathematical Modeling

MATH 5340:  Topology

MATH 5360:  Numerical Analysis

MATH 5699:  Internship 

 

Research Projects

Random Billiard Dynamical System Models for Gas-Surface Interactions

Mary Barker

Presented at the 96th Annual Meeting of the Texas Section of the MAA, Nacogdoches, TX, April 2016

Chemical engineering problems require mathematical models for gas-surface interactions that are both rigorous and intuitive. Building on advances in billiard dynamical systems (theory) and GPU-based parallel processing (simulation), Mary Barker is helping develop particle-based models of gas-surface interactions free from continuum approximations.  This allows her to study diffusion and thermodynamical processes in small-scale and rarified systems.

entropyproductionrate

Mary has written a parallel algorithm using NVIDIA’s CUDA architecture to simulate these systems.  She is currently exploring the effects of particle size and density on thermal and density gradients, rate of heat flow, and entropy production rate.  She also plans to use the algorithm to study thermophoresis (preferential drift of a large particle caused by non-uniform temperature environment), which has applications to carbon sequestration and pollution control.

Mary Barker and Scott Cook

Mary Barker with her faculty mentor, Dr. Scott Cook.

Predicting Party Affiliation Using Social Media

Mikaela Jordan, Adam Swayze, and Joseph Brown

Presented at the 96th Annual Meeting of the Texas Section of the MAA, Nacogdoches, TX, April 2016

JordanSwayzeBrown

The past ten years have seen a dramatic increase in both the number of political online media sources and the  appropriation of online media by political campaigns. The widespread use of Twitter, Facebook, and other social media  sites for political purposes offer novel ways to quantify political affiliation and predict a litany of characteristics about  online posters. Incorporating data from social media profiles into traditional political analysis techniques has become a  necessity for accurate polling and predictions for elections.  For instance, the following map shows US counties colored by which 2016 Presidential candidate has the most Facebook likes in each county.

US Political Map

In this project, Mikaela Jordan, Adam Swayze, and Joseph Brown applied text mining algorithms, including natural language processing methods, to build models for predicting party affiliation based on geotagged Twitter data.  Over 20,000 tweets pertaining to the primary elections were obtained by searching for certain key phrases, and a term-frequency matrix was built for predicting party affiliation using support vector machines, neural networks, and random forests.

Political Word Clouds

TF Matrix

Going forward, Mikaela, Adam, and Joseph plan to use social media to predict district-level outcomes in the 2016 national elections, while expanding the scope of their text mining algorithms to include information from online news articles, debate transcripts, and other sources.

Analyzing EEG Entropy for Predictions of Seizures

Jonathan Stewart

Presented at the 96th Annual Meeting of the Texas Section of the MAA, Nacogdoches, TX, April 2016

Jonathan Stewart

The onset of epileptic seizures can be predicted by examining changes in recorded entropy measures of electroencephalography (EEG) readings.  Jonathan Stewart is working on detecting preictal EEG states (those immediately preceding a seizure) by applying data mining algorithms to changes in both the permutation entropy and wavelet entropy measures.  The training data set for this project consists of 96 individual EEG time series, each containing 10 minutes of data sampled at 400 Hz, and half of these EEG sequences were labeled as preictal.

Taking the collection of time series obtained from each participant's EEG readings, the measurements were binned into collections of 256 consecutive points in time each.  The entropy measures were then applied to each collection of points, and a random forest model achieved accuracies over 90% for both the wavelet and permutation entropy measures.  Jonathan's next goal is to move into multichannel analysis using joint entropy measures and two dimensional wavelet transforms.

Finding an Optimal Game Theory Strategy Using Genetic Algorithms

David Ebert

Presented at the 96th Annual Meeting of the Texas Section of the MAA, Nacogdoches, TX, April 2016

Fargo is a multiplayer dice game with a complex decision tree, and since the strategy space is so large, finding an optimal strategy using a direct search is not possible.  David Ebert decided to approach this problem using genetic algorithms, where each strategy is represented by a gene vector, and better strategy vectors are obtained through stochastic natural selection of these genes. During each turn of this game, the active player rolls 10 dice, scoring 100n points for each triple n rolled (except 1000 points for three 1's), plus an additional 100 points for each 1 rolled, and 50 points for each 5 rolled. After removing the scoring dice, a player must choose to either stop rolling and end their turn, or else continue rolling, risking their current points in hope of increasing their score.

Example Fargo Turn

Under certain conditions, a player's turn can repeat, which results in the expected value equation being recursive, and solving this equation yields

Fargo Recursion

The result of 100 genetic algorithm trials returned an optimal expected value of 962.33 with a strategy vector corresponding to aggressive play, as long as at least 4 dice remain.  Continuing research will explore various ways to optimize the endgame, where expected value is no longer the most important factor, as a player strives to beat their opponents to 10,000 points.

Genetic Algorithm

Sentiment Analysis of Geotagged Tweets in Los Angeles County

David Ebert and Parker Rider

David Ebert and Parker Rider are working with engineering professor Dr. Arthur Huang, applying sentiment polarity analysis techniques to geotagged tweets collected from Los Angeles county. After systematically cleaning the tweets and extracting a semi-supervised training set consisting of tweets with positive and negative emoticons, this semi-supervised set was used to evaluate four lexicons to see which one most effectively identified sentiment of tweets.  

wordclouds

Afterwards, a normalized difference sentiment index was used to identify words from within the emoticon training set that are good indicators of whether a tweet is positive or negative. This index was used to make a term-document matrix, over which a random forest classifier was trained. Preliminary results indicate that the random forest approach achieves significantly higher accuracy than the lexicon classifier. Further research will explore ways to improve tweet cleaning and tune the classifier before applying the classifier to geotagged Los Angeles county tweets, using neighborhood sentiment scores to find out what neighborhood characteristics correlate to positive tweets. 

tweetclassification

tweetsentimentdistributions

David Ebert, Arthur Huang, and Parker Rider

David Ebert (left) and Parker Rider (right) with their faculty mentor, Dr. Arthur Huang (center).

Bayesian Ensemble Models of Climate Variability in South Texas

Juliann Booth and Nina Culver

Possibly the most important application of data mining in the 21st century is building and refining models of climate change and then using those models to predict climate behavior in local regions.  Juliann Booth and Nina Culver are using Bayesian model averaging to predict future precipitation in South Texas, an important concern, given the projected decline in water availability in this region by 2050.

South Texas Water Availability

Thirty-five CMIP5 models f1,...,f35 for temperature and precipitation were obtained from the World Climate Research Programme's Working Group on Coupled Modeling.  For each model fk, the probability of observing a temperature/precipitation measurement y is p(y|fk), and the probability that fk is the best model given observed target data yT is p(fk|yT).  Synthesizing these two types of probabilities using Bayes' theorem yields the overall probability of observing a future temperature/precipitation measurement y as follows:

Bayesian Model Averaging

Below is a visualization of temperature predictions for the thirty-five CMIP5 models for the South Texas region being studied.

CMIP5 Models for Temperature

Modeling Nitrate Contamination in Water Wells Based on Proximity to CAFOs

Charles Tintera and Lain Tomlinson

Nitrate contamination of ground water is a serious health concern, which can lead to conditions such as methemoglobinemia (blue baby disease), miscarriages, and non-Hodgkin lymphoma, and the EPA has therefore set a maximum contaminant level (MCL) for nitrate of 10 mg/L.  Proximity of concentrated animal feed operations (CAFOs) to water wells has been linked to nitrate contamination of those wells, and Charles Tintera and Lain Tomlinson are currently applying data mining techniques to model this relationship more accurately.

A novel feature of this project is modeling flowpaths in the aquifer from a given CAFO using the hydraulic gradient obtained from the Global Information System (GIS).  By taking into account the distance from a well to a CAFO's flowpath, the length of that flowpath, and the waste application rate at that CAFO, a CAFO Migration Score (CMS) is calculated to summarize the overall impact of CAFOs on the well under consideration.  The Epanechnikov kernel is applied to model diminished probabilities of contamination that result from increased distances from the flowpath.

CAFO Migration Score

Once CAFO migration scores were computed, a logistic regression model demonstrated a highly statistically significant relationship between CMS and nitrate contamination (P = 7.19 x 10-12).  In the image below, 344 wells have been broken into 10 deciles based on CAFO migration score, so each point in this plot represents approximately 34 wells.  The x-coordinate of each point is the average CMS value for wells in that decile, and the y-coordinate is the observed number of wells in that decile with nitrate concentrations exceeding 3 mg/L.  The plot indicates strong agreement between the observed data and the logistic regression model, as confirmed with a Hosmer-Lemeshow goodness of fit test.

LogisticRegressionModel

Charles and Lain are now working to extend this analysis to include more variables, such as depth to water table, pH, total dissolved solids, percent clay, percent organic matter, and annual rainfall.  They are also applying random forests, support vector machines, k-nearest neighbors, and other classification algorithms to improve the model's classification accuracy.  Because testing for nitrate contamination is expensive, the goal is to provide a tool that will help farmers estimate a well's probability of being contaminated using readily available information about that well.

Effectively Using Data Warehousing to Store Nonprofit Data

Juliann Booth, Lain Tomlinson, and Parash Upreti

Presented at the 12th Annual Pathways Student Research Symposium, Corpus Christi, TX, October 2015

2nd Place Master's Presentation in Mathematics

BoothTomlinsonUpreti

The Wilson County Fair originally began in 1919 in the city of Lebanon, Tennessee, moving to Wilson County in 1979. Since then, the fair has attracted hundreds of thousands of people, including last year, when 557,702 people attended. The current database used to schedule volunteers is inefficient with many duplicates, spelling errors, and lack of cohesiveness across the tables. Juliann Booth, Lain Tomlinson, and Parash Upreti used the concepts of primary keys, foreign keys, recursive relationships and third normal form to create a cohesive, less complex database that will decrease the occurrence of double-bookings.  

Because this is a nonprofit organization working with volunteers only, it is imperative to keep the database as organized yet as simple as possible. After putting the database in third-normal form, an entity relationship diagram was created, resulting in many errors being caught and corrected. Still, Juliann, Lain, and Parash noticed that the database was not properly organized to accomplish the goal of scheduling the volunteers, so a new entity relationship diagram was created in order to optimize volunteer scheduling. The schematic below shows the original ERD, the modified ERD in third-normal form, and the modified ERD used to optimize scheduling.

  
Fair ERD


Future work will focus on implementing improvements to the user interface and evaluating the performance of the improved database during the 2016 Wilson County Fair. 

Detecting Anomalous Crop Insurance Claims using Satellite Images

Rebecca Ator, Charles Gibson, Dan Mysnyk, and Adam Wisseman

Presented at the National Consortium for Data Science, Chapel Hill, NC, May 2014

Research assistants Rebecca Ator, Charles Gibson, Dan Mysnyk, and Adam Wisseman implemented a method for screening crop insurance claims for fraud using satellite images.

Using the difference between the red and infrared bands in a satellite image, it is possible to calculate the normalized difference vegetation index, or NDVI, which serves as a proxy for the amount of green vegetation in a given geographic region, and therefore, the health of crops being grown in that area.  A k-means algorithm was applied to cluster NDVI curves for Nebraska crop insurance claims, resulting in a relatively healthy cluster (Cluster 1) and an unhealthy one (Cluster 2). 

This clustering was then compared to spot checklist (SCL) flags, used by CAE to flag anomalous insurance claims.  A Fisher's exact test comparing the clustering to the SCL flags resulted in a p-value less than 10-5, demonstrating a highly statistically significant association between the NDVI clusters and the SCL flags.

k-means NDVI Clustering

Below, Charles, Adam, Rebecca, and Dan are shown speaking with Kirk Bryant, Deputy Director for Strategic Data Acquisition and Analysis for the USDA Risk Management Agency at the National Consortium for Data Science Data Showcase.

National Consortium for Data Science

Kaggle Solar Energy Prediction Competition

Rebecca Ator, Charles Gibson, Dan Mysnyk, and Adam Wisseman

Presented at the 11th Annual Pathways Student Research Symposium, Kingsville, TX, November 2013

Rebecca, Charles, Dan, and Adam competed in the American Meteorological Society’s Solar Energy Prediction Contest, placing 17th out of 160 teams.  The goal of this competition was to determine which data mining techniques are most effective at predicting incoming solar radiation at solar farms (red points in the below picture) based on weather data provided by the Global Ensemble Forecasting System (blue points).

solar

Accurately predicting solar radiation is important for successful implementation of solar power, since incorrect estimates can result in costly purchases of energy from other power plants.  The data mining research assistants used support vector regression to obtain a model for predicting solar radiation, which they presented at the 2013 Tarleton Student Research Symposium and the Pathways Student Research Symposium at Texas A&M University-Kingsville.

Previous Graduates

Below are LinkedIn profiles for some of our previous graduates.

AdamWisseman

RebeccaAtor

JamesPeiskee

KaileyKeith

BlakeLohnWiley

VirginiaSeale

SoryCisse

RobertHess

CharlesGibson

LukeBarr

PhillipKristufek

JohnKoo



Graduate Teaching Assistantships

Tarleton State University has one of the strongest mathematics education programs in the state, and our graduate teaching assistants are in high demand for teaching positions at the high school and university level after graduating from Tarleton.  

Graduate teaching assistants receive assistance to improve their teaching by working one-on-one with a faculty mentor and attending professional development meetings. GTA's teach one course each fall and spring and receive $11,800 for a 9-month appointment.

Financial Aid

In addition to our graduate teaching assistantships, scholarships are available for first time graduate students at TSU.  More information can be found here:

Financial Aid Information

How to Apply

To apply to the M.S. program in mathematics, please complete the following four steps.

Contact Information

Department Head:
Dr. Bowen Brawner
Mathematics Building, 142
Email: brawner@tarleton.edu

Dr. Jesse Crawford
Coordinator of the Graduate Program in Mathematics
Email: jcrawford@tarleton.edu
Office: MATH 332
Phone: 254-968-9536

Dr. Jesse Crawford

Dr. Eileen Faulkenberry
Graduate Advisor
Email: efaulkenberry@tarleton.edu
Office: MATH 207
Phone: 254-968-1985

Dr. Eileen Faulkenberry

Mailing Address:
Department of Mathematics
box T-0470
Stephenville, TX  76402

Phone:  254-968-9168

Fax:  254-968-9534