Tom
Edgar
I have been a faculty member at Pacific Lutheran University for twelve years. Before moving to Tacoma, I received a PhD at the University of Notre Dame studying Coxeter groups with Matthew J. Dyer. Previously, I completed a Masters degree at Colorado State University working with Anton Betten, and I did my undergraduate work at Dickinson College. My mathematical interests lie in the relationship between representation theory and combinatorics of Coxeter Groups. I am also interested in partial orders, combinatorial number theory, and integer sequences. More recently, I have become interested in visualization of mathematics (in particular so-called Proofs Without Words). I am currently the editor for the MAA publication Math Horizons.
Teaching : Fall 2021
Fall 2021 Drop-in Office Hours
- MWF 12:30pm - 1:30pm
- Th 1:30pm - 2:30pm
- By appointment (in-person or via Zoom)
Scholarship
Publications
- Balanced and Unbalanced: Physical proofs of the mean inequalities (to appear Mathematics Magazine, 2021)
- Visual sums of integers in polygonal arrays (to appear College Math Journal, 2021)
- Euler bricks: visually (to appear Mathematics Magazine, 2021)
- Visual triangular number identities from positional number systems (College Math Journal, 2021)
- Visual decompositions of polygonal numbers (College Math Journal, 2020)
- A visual proof of Gregory's theorem (Mathematics Magazine, 2019)
- A factorial card trick (Math Horizons, 2019)
- "Sum" visual rearrangements of the alternating harmonic series (College Math Journal, 2019)
- The First 100 Issues (Math Horizons, 2018)
- Roger Nelsen's Books, so far (College Math Journal, 2018)
- Counting binomial coefficients divisible by a prime power (American Mathematical Monthly, 2018)
- Staircase series (Mathematics Magazine, 2018)
- Happiness is integral, but not rational (Math Horizons, 2017)
- A visual validation of Viete's verification (College Math Journal, 2017)
- A confused electrician uses Smith normal form (Mathematics Magazine, 2016)
- Cryptographic word search (Math Horizons, 2014)
- Dominance orders on Natural Numbers (Mathematics Magazine, 2014)
- Proof without words: binomial coefficients modulo p (Mathematics Magazine, 2019)
- Proof without words: sums of even and odd powers (Mathematics Magazine, 2019)
- Proof without words: Abel's transformation (Mathematics Magazine, 2018)
- Proof without words: Rearranged alternating harmonic series (College Math Journal, 2018)
- Proof without words: series of perfect powers (Mathematics Magazine, 2017)
- Proof without words: a recursion for triangular nums (Mathematics Magazine, 2017)
- Proof without words: factorial sums (Mathematics Magazine, 2016)
- Proof without words: matchstick triangles (College Math Journal, 2016)
- Proof without words: The avg. of sq. pyr. and tri. is tetra. (Mathematical Gazette, 2016)
- Proof without words: 4/9+(4/9)^2+(4/9)^3+... = 4/5 (Mathematics Magazine, 2016)
- Proof without words: sums of reciprocals of binomial coeffs. (Mathematics Magazine, 2016)
- A Visual Tour of Identities for the Padovan Sequence (Mathematical Intelligencer, 2021)
- Some Combinatorics of factorial base representations (J. Int. Seq., 2020)
- Combinatorics of Zeckendorf representations (Involve, 2019)
- Consecutive factorial base Niven numbers (Fibonacci Quarterly, 2018)
- On the number of hyper m-ary partitions (Integers, 2018)
- Digital representations of rows of Pascal's Triangle with no entries divisible by a fixed prime power (PME, 2017)
- Approximating the Fibonacci sequence (Integers, 2016)
- The distribution of the number of parts of m-ary partitions (Rocky Mountain Journal of Mathematics, 2017)
- Extending some Fibonacci--Lucas relations (Fibonacci Quarterly, 2016)
- Multiplicative functions and their generalized binomial coefficients and Catalan numbers (J. Int. Seq., 2016)
- Totienomial coefficients (Integers, 2014)
- Finite projective geometries and linear codes (Master's Paper, 2004)
- Dihedral Symmetric Spaces (Note di Matematica, 2014)
- Universal reflection subgroups (Communications in Algebra, 2013)
- Characterization of hyperbolic Coxeter systems (Journal of Group Theory, 2011)
- Reduced expressions (Journal of Group Theory , 2010)
- Sets of reflections defining twisted Bruhat orders (Journal of Algebraic Combinatorics, 2007)
- Dominance and regularity in Coxeter groups (Ph.D. Dissertation)
- Many proofs that 1+2+3+...+n = n(n+1)/2 (a joint project initiated by Enrique Treviño)
- Combinatorics of rational base representations (from summer 2014 research)
- On the family of automatic normal forms for Coxeter groups (adapted from my dissertation)
- Dominance over N (written by Tyler Ball and Daniel Juda during 2012 summer research)
Math Horizons
For the calendar years 2020-2024, I am the editor of Math Horizons, the undergraduate magazine of the Mathematical Association of America.
From the Math Horizons website: Math Horizons is intended primarily for undergraduates interested in mathematics. Our purpose is to introduce students to the world of mathematics outside the classroom. Thus, while we especially value and desire to publish high quality exposition of beautiful mathematics we also wish to publish lively articles about the culture of mathematics. We interpret this quite broadly - we welcome stories of mathematical people, the history of an idea or circle of ideas, applications, fiction, folklore, traditions, institutions, humor, puzzles, games, book reviews, student math club activities, and career opportunities and advice.
Want to read Math Horizons? All MAA members get free electronic access to the magazine - just log in through the MAA website. Non-members can read all past issues (1993-present) on the Taylor & Francis site or at JSTOR. There are also free articles available online:
- MAA's Trevor Evans Award winning articles (given to authors of exceptional Math Horizons articles).
- An assortment of sample articles.