My name is Jeff Beyerl and I am an assistant professor in the department of mathematics at the University of Central Arkansas. My dissertation was in number theory at Clemson University, May 2012.
Number theory is my forte, although I have broad interests and have found topics ranging from abstract number theory to scheduling to be enjoyable. I have published in number theory and graph theory, and have attended conferences from arithmetic geometry to climate change.
On this website you can find more details about my professional career and some of my hobbies. Other information of interest may be on my sub-pages:
Graph Theory: interval graphs, popular matchings, graph algorithms, graph properties
Mathematical Foundations: generation of closures
Applied: cryptography, operations research, traffic flow and infrastructure design, electric grid stability and energy generation, financial mathematics, rail networks, video game balance
Formal Research and Publications:
The preimage of an eigenform under the Rankin-Cohen bracket operator
(local, MathSciNet, ArXiv) In progress
Factorization of eigenforms
(local, MathSciNet, ArXiv) To Appear, Proceedings of the AMS
Nearly holomorphic eigenforms
(local, MathSciNet, ArXiv) Products of nearly holomorphic eigenforms, Jeffrey Beyerl, Kevin James, Catherine Trentacoste and Hui Xue, The Ramanujan Journal, Volume 27, Number 3, pages 377-386
Pullbacks of Siegel Modular Forms
(local, MathSciNet, ArXiv) Pullbacks of Siegel Eisenstein series and weighted averages of critical L-values, Nadine Amersi, Jeffrey Beyerl, Jim Brown, Allison Proffer and Larry Rolen, The Ramanujan Journal, Volume 27, Number 2, pages 151-162
Quadratic forms over function fields
(local) Masters Thesis
Properties of Drinfeld modules
Generation on the Bingo Closure
(local, MathSciNet, ArXiv)
Depth in Bingo Closure. Jeffrey J. Beyerl, Robert E. Jamison, J. Bowman Light, In Proceedings of the Fortieth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, volume 198, pages 151-156, 2009
A characterization of improper interval graphs
(local, MathSciNet, ArXiv)
Interval Graphs with Containment Restrictions. Jeffrey J. Beyerl, Robert E. Jamison, In Proceedings of the Thirty-Ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, volume 191, pages 117-128, 2008
An approach to the scheduling problem using a popular matching
Balancing action-adventure video games with asymmetrical choices
A differential equation approach to modeling the growth rate of hair
UCA MATH 2335 (2013, 2014)
Transition to advanced mathematics: essentially introduction to proofs and the foundation of mathematics.
UCA MATH 3320 (2013, 2014)
Linear Algebra: emphasis on matrices, not proof based.
UCA MATH 3330 (2014)
Discrete Structures II: a wide range of advanced topics in discrete mathematics aimed at complementing studies in computer science.
Furman MTH 140 (2013)
Integrated Precalculus/Calculus I. The first half of calculus 1: functions, graphs, limits, continuity and derivatives
Furman MTH 110 (2012, 2013)
Finite Mathematics. Terminal mathematics course for nonmajors. Topics include graph theory, network flows, linear programing, set theory, combinatorics, probability, statistics, matrix algebra, Markov chains and financial mathematics.
Duke Talent Identification Program (2012, 2013)
Cryptography, Codebreaking, And The Mathematics Of Spying. Topics covered ancient cryptography through modern day cryptosystems. Mathematics included modular arithmetic, matrix arithmetic, finite fields, and elliptic curves.
Clemson HON 400 (2011)
Honors Contract. Advise a student in advanced study and research to apply statistical techniques to answer a real world question.
Clemson MthSc 309 (2010, 2011, 2012)
Statistical Method I for Business Students. Particularly those who will continue to the sequel. Topics include descriptive statistics, probability, expectations, binomial, normal, sampling distributions, one and two sample estimation and testing, simple linear regression, and analysis of categorical data.
Clemson MthSc 203 (2010)
Statistical Methods I. Data-based course in statistical methodology: probability and counting methods, collecting and summarizing data, the normal distribution, one and two sample inference on means and proportions, simple linear regression, analysis of categorical data.
Clemson MthSc 101 (2008, 2009)
Essential mathematics. Common exams for all sections. Topics were an introduction to logic and set theory, algebra, probability, statistics, graphical representation of data, financial mathematics and voting theory.
Video Game Balance
In general I formalized the notion of "Balance" in video games with asymmetrical choices. In particular I used a convex program to try to optimallybalance offensive skills in the game Diablo III. Currently in progress.
Designed a discrete model for a biological epidemic in the mathematical sciences building at Clemson University. Implemented in Java
Wrote a symbolic calculator and text-parser to (1) parse mathematics expressed in the format given in Unicode Technical Note 28, (2) perform the symbolic operations including fractions, polynomials, and matrix arithmetic, and (3) translate the answer into the original format. Implemented in Java, with a graphical user interface.
Performed an expository analysis of the Department of Transportation crash data for vehicular crashes in 2007. Implemented in SAS using a single database.
Constructed a regression for predicting high school graduation rates based on the demographics of the school. Based on 2006 data, implemented in SAS.
Unofficial (hobby) projects
Job Search Database
During my faculty job search in 2012-2013 I sent out a lot of applications. So I created a database (albeit in Access) to keep track of all the deadlines, documents, contact history, and such.
Blueprints for a house
I have a long term plan to design the house that I will live the majority of my life in, through retirement and old age. Over the course of 2011 I taught myself AutoCAD to develop and record a preliminary design for the house.
Food Price tracker
In 2006 and 2007 I wrote a GUI interface using Java to input the foods that I buy and how much they cost. It then maintains a series of html pages that provide an illustration of how the price of the food I bought varies through the year, and between years. (I no longer use it, however)
As a person interested in the financial markets, I keep a portfolio of my own personal finances and thoroughly analyze all of my investments. The graphs below show my performance overlayed with the S&P 500 as a benchmark.