Welcome to my Math Page.  Math 132 students click here.

 

Math Projects

Generators and Relations for Groups of Order 32

Generators and Relations for Groups of Order 64

Words for some missing groups from the ATLAS

Math Papers

Finite Groups with Planar Subgroup Lattices

 

Math Biography

I always had an interest in math growing up and expected to be a mathematician.  I excelled in math in public school.  I’ve noticed that for the most part, people think that mathematicians only do the type of math they are familiar with.  In elementary school, people assume that mathematicians are really good at multiplying large numbers.  In middle school, people assume that mathematicians are really good at solving for x.  In high school and early college, people assume mathematicians are really good at integrating ridiculous functions. 

In 10^th grade, I had a physics teacher, Jim Sly, who really motivated me to delve deeper into math.  Thanks in part to him and a book my dad got from Evangel University where he worked, I learned the basics of Calculus that year and a little bit of Differential Equations, Linear Algebra and Complex Analysis the next year.  I ended up with a 4 on the AP Calculus BC exam that year, and got a 5 the following year (after I actually took Calculus).  Jim also introduced me to Les Reid at Southwest Missouri State University. In order to prepare for the AHSME in 1999, he suggested I sit in on the upper-division combinatorics class that Les taught.  The following summer I sat in on an Introduction to Abstract Algebra course that focused mainly on ring theory.  My senior year, I spent most of the time in Calculus learning many subjects independently.  I also got 13 college credits, 10 for a Calculus-based physics class and 3 for Differential Equations.  The next summer I sat in on Linear Algebra at SMSU.

I entered Evangel University as a sophomore with 37 credits, thanks to the classes I took my senior year and 24 AP credits.  I took about 18 credit hours per semester with a maximum of 21.5 one semester.  Thanks to that and taking two years of summer school, I completed my bachelor’s degree in two years.  In addition, one semester I took the second graduate Abstract Algebra class at SMSU.  I also worked on two papers while there, both of which were presented at Kappa Mu Epsilon conventions.  The first was called “Quadratic Varieties” and examined the idea of conic sections in higher dimensions.  This was published in the Fall 2001 edition of KME’s publication, The Pentagon.  The second was called “The Planarity of Hasse Lattices” and served as the inspiration for my masters thesis.  It completely determined when the lattice of a cyclic group can be drawn on the plane without edges crossing.  This ended up winning an award for the top three papers at the convention.

I started my masters degree at SMSU in Fall of 2002.  I got my first major experience with teaching here.  I taught one semester of Math 101 and three semesters of Math 102.  Both are basic algebra courses.  Here I took courses in algebra, analysis (both real and complex), statistics, coding theory, number theory, topology, differential equation theory and combinatorics.  I started work on my masters thesis in the summer of 2003.  Les and I decided to purse the topic of the planarity of general subgroup lattices.  We didn’t expect to be able to answer the question for all groups, but we eventually did just that.  Abelian groups and p-groups were completed that summer.  In the fall semester of that year, we completed solvable groups whose order is the product of three or more distinct primes and all non-solvable groups.  Groups whose order is the product of two distinct primes took up the majority of the work, but was more-or-less finished by the end of the spring semester.  The original thesis was approximately 70 pages double-spaced.  For publication, we cut the size down to 20 pages, single-spaced.  This article is scheduled to appear soon in the Journal of Algebraic Combinatorics.  A PDF of this paper can be found above.

I am currently a graduate student here at Wash U and am teaching three discussion sections of Calculus 2.  My main interests lie in group theory.  I have auxiliary interests in algebraic topology, combinatorics and graph theory. 

 

Math Links

Les Reid’s Homepage--My former advisor and current co-author.

MiKTeX--For typesetting math documents

WinEdt--A very good TeX editor.

The Primes Page--Information about ridiculously large prime numbers.

Dave Rusin’s Page--An outstanding math atlas

The Atlas of Finite Group Representations--Information about many different groups.

Math World--A very large online math encyclopedia.

GAP--A program for all things related to groups

David Green’s Page--Information about p-groups.