Beyerl logo

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:

Research and Publication list (Research Statement) (Publication List)
Research Interests:
  • Number Theory: modular forms, Eigenforms, L-functions, Rankin-Cohen bracket operator, perfect numbers, quadratic forms, Drinfeld modules
  • Algebraic Structures: generation of groups
  • 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:
  • Improper Interval Graphs
    (local, MathSciNet, ArXiv) In progress

  • Video Game Balance
    (local, MathSciNet, ArXiv) Accepted

  • The preimage of an eigenform under the Rankin-Cohen bracket operator
    (local, MathSciNet, ArXiv) In progress

  • Factorization of eigenforms
    (local, MathSciNet, ArXiv) Divisibility of an eigenform by aneigenform, Jeffrey Beyerl, Kevin James, and Hui Xue. Proceedings of the American Mathematical Society, Volume 142, Number 1, pages 29-38.

  • 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
Informal Research and independent studies:
  • An approach to the scheduling problem using a popular matching
  • A differential equation approach to modelling the growth rate of hair
  • I'm currently (2014) learning python and database management
Computer Presentations
Slides Title Location Date Notes
(0.9MB) Achieving balance in the ARPG genre of video games with asymmetrical choices Florida Atlantic University: Forty-fifth Southeastern International Conference on Combinatorics, Graph Theory, and Computing March 2014 ERP
(0.2MB) When is the Rankin-Cohen Bracket Operator an Eigenform? Clemson: PANTS XXI Dec 2013 NR
(1.7MB) Wikiversiy in Teaching Rock Hill: MAA southeastern conference, session on general math education. March 2013 EREd
(0.8MB) Optimizing balance in video games with asymmetrical choices San Diego: Joint Mathematics Meetings, MAA Session on Mathematics and the Arts: Practice, Pedagogy, and Discovery, II. Jan 2013 ERO
(0.2MB) Divisibility of Eigenforms, and computing a function of the $j$-invariant Boston: Joint Mathematics Meetings, AMS Session on Number Theory, Field Theory, and Polynomials, II Jan 2012 NRP
(1.2MB) Divisibility of an Eigenform by Another Eigenform Wake Forest: AMS special session on Modular Forms, Elliptic Curves, and Related Topics Sep 2011 NRP
(0.0MB) Factorizations of Eigenforms and Maeda's Conjecture Armstrong Atlantic State University: SERMON 2011 Apr 2011 NRP
(0.2MB) The Product of Nearly Holomorphic Eigenforms is Rarely an Eigenform University of South Carolina: PANTS XIV Dec 2010 NRP
(2.9MB) A Selection of Interesting Sets Clemson: Graduate Student Seminar Jan 2010 E
(0.3MB) Counting Latin Squares Clemson: Graduate Student Seminar Aug 2009 E
(0.8MB) Binary Quadratic Forms over $\F[T]$ and PIDs Clemson: Masters Defense Apr 2009 NER
(0.5MB) Generation in the Bingo Closure Florida Atlantic University: Fortieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing Mar 2009 DRP
(0.3MB) Interval Graphs Where No Interval Contains Two Others Florida Atlantic University: Thirty-Ninth Southeastern International Conference on Combinatorics, Graph Theory, and Computing Mar 2008 GRP
R Research Talk
E Expository Talk
Ed Education Talk
N Number Theory
D Discrete Math
G Graph Theory
O Operations Research
P Relates to a paper
Teaching (Teaching Statement)
  • UCA MATH 1392 (2013)
    Trigonometry
  • UCA MATH 2330 (2014)
    Discrete Structures I: essentially an introduction to the foundation of mathematics. Logic, sets, induction, etc
  • UCA MATH 2335 (2013, 2014x2)
    Transition to advanced mathematics: essentially introduction to proofs and the foundation of mathematics.
  • UCA MATH 3320 (2013, 2014x2)
    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. Combinatorics, probability, formal languages and grammars, deterministic finite state machines, graph theory, modular arithmetic and RSA.
  • Duke Talent Identification Program (2012, 2013, 2014)
    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.
    Spy 101: Cryptology and Number Theory. Very similar to the above course, except we did a little more in cryptanalysis and covered quite a few special topics related to espionage and computing.
    Mobius Strips, Klein Bottles, and Fractals: the Mathematics of Distortion. Topics covered very basic point set topology, non-Euclidean geometry, very basic knot theory, very basic fractal analysis, and computational algebraic geometry (Groebner bases)
  • 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.
  • 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.
Applied Projects
  • 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.

  • Discrete Simulation
    Designed a discrete model for a biological epidemic in the mathematical sciences building at Clemson University. Implemented in Java

  • Symbolic Calculator
    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.

  • Data Analysis
    Performed an expository analysis of the Department of Transportation crash data for vehicular crashes in 2007. Implemented in SAS using a single database.

  • Regression Analysis
    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
    • Sandbox computer
      I built a computer and plan to use it to experiment with things on a system that has nothing important
    • This website
      I've tried to make this website both easy to navigate and maintain. I had to learn a little javascript to make the +/- boxes work, and PHP to write the repetitive html code. You don't see the PHP because I wrote it to output the final html webpage for me. Eventually I want to tie it in to a database too, but I haven't learned how to do that yet.
    • 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)
Synergistic activities and historical experiences
Faculty:
  • Math Club Advisor
  • "Science nights" at local schools (I've only done one so far, but I hope to get more involved with this)
Graduate:
  • Seminar Organizer, Graduate Student Seminar
  • Treasurer, Society of Industrial and Applied Mathematics
  • Mentor for undergraduates in two summer REUs
  • Wikipedian, 2000+ contributions
  • Lab Instructor, College Algebra
  • Teaching Assistant, Algebraic Structures
Undergraduate:
  • Student teacher
  • Mathematics tutor
  • Lab Instructor
  • Competitive programmer
  • Liaison between student organizations
  • Social events committee
  • Bible study leader
Secondary
  • Teen Court defense attorney for juveniles
  • Robotics competition participant
Funding History
  • Faculty Advancement Grant, Associated Colleges of the South
  • Travel grant, American Mathematical Society
  • Professional enrichment grant, Clemson University Graduate Student Government
  • Stipend for mentoring REU students
  • Travel support, Clemson University Department of Mathematical Sciences
Awards
  • SIAM Student Chapter Certificate of Recognition, SIAM and Clemson University Department of Mathematical Sciences, 2012
  • Outstanding Citizenship Award, Clemson University Department of Mathematical Sciences, 2011
  • Outstanding Masters Student, Clemson University Department of Mathematical Sciences, 2009
  • The Reference Desk Barnstar, Wikipedia, 2008
  • Hernandez Award, UCF Department of Mathematics, 2007
  • Order of Pegasus Nominee, UCF
  • Outstanding Tutor Award, UCF Department of Mathematics, 2007
  • Advanced Calculus Award, UCF Department of Mathematics, 2006
Documents
Last updated: 09/10/14