Papers
Here are some recent publications, a particularly good Masters Thesis, and selected not-so-recent publications:
- Cayley-Dickson Construction for Beginners: An Accessible Proof of Hurwitz's Sums Of Squares Theorem (with Adrian Rice), to appear in Mathematics Magazine.
- Why Hamilton Couldn't Multiply Triples (with Adrian Rice), College Mathematics Journal (CMJ) 52, #3 (2021), 185-192.
- Richard Guy, Bud Brown, and the Writing of The Unity of Combinatorics, The Pi Mu Epsilon Journal 15, #3 (Fall 2020), 129-137.
- Five Families around a Well: a new look at an old problem (with Matthew Crawford), CMJ 49, #3 (2018), 162-168.
- Commutativity and Collinearity: a historical case study of the interconnection of mathematical ideas. Part I (with Adrian Rice), Bulletin of the British Society for the History of Mathematics 31, #1 (2016), 1-14.
- Commutativity and Collinearity: a historical case study of the interconnection of mathematical ideas. Part II (with Adrian Rice), Bulletin of the British Society for the History of Mathematics 31, #2 (2016), 90-103.
- Saints And Scoundrels And Two Theorems That Are Really The Same, CMJ 46
(November 2015), 326-334.
- Many More Names of (7,3,1), Mathematics Magazine (Math. Mag.), 88
(April 2015), 103-120.
- Generalizing Gauss's Gem (with Marc Chamberland),
Amer. Math. Monthly 119, #7 (August-September 2012), 597-601.
- Why Ellipses Are Not Elliptic Curves (with Adrian Rice),
Math. Mag., 85 (June 2012), 163-174.
- Trigonometry Without Triangles (with Adrian Rice),
Math Horizons, 19, #2 (November 2011), 20-23.
- A Mathematical Trip to Princeton, Mathematical Intelligencer
32, #3 (Fall 2010), 35-37.
- Chocolate Key Cryptography (with Dale Bachman and Anderson Norton),
Mathematics Teacher 104 (September 2010), 100-104.
- A Conversation with Archimedes, Math Horizons,
17, #4 (April 2010), 22-24.
- Why is PSL(2,7) isomorphic to GL(3,2)? (with Nicholas Loehr), Amer. Math. Monthly 116, #8 (October 2009), 727-731.
- A Dozen Hat Problems (with James Tanton), Math Horizons 16, #4 (April 2009), 22-25.
- Kirkman's Schoolgirls Wearing Hats and Walking through Fields of Numbers (with Keith E. Mellinger), Math. Mag. 82 (February 2009), 3-15.
- Fibonacci's Forgotten Number (with Jason C. Brunson), CMJ 39 (March 2008), 112-120.
- Whodunit?, Math Horizons 14, #4 (April 2007), 25-26, 28-29.
- A Conversation with Lewis Carroll, Math Horizons 14, #2 (November 2006), 9-11.
- Hyperelliptic Curves with Compact
Parameters (with Bruce T. Myers and Jerome A. Solinas),
Designs, Codes, and Cryptography 36 (2005), 245-261.
- Phoebe Floats! , College
Mathematics Journal 36 (March 2005), 114-122.
- A Conversation with
Leonardo Pisano , Math Horizons 12, #3 (February
2005), 16-18.
- The Ancient World's Magical
Genius Thinks Big , Math Horizons 12, #2 (November
2004), 5-8.
- Configurations with Subset
Restrictions (with Theresa P. Vaughan), J.
Comb. Mathematics and Comb. Computing 48
(2004), 197-215.
- The Fabulous (11,5,2) Biplane,
Math. Mag. 77 (April 2004), 87-100.
- Three Connections to Continued
Fractions, Pi Mu Epsilon Journal 11 (2002),
353-362.
- Elliptic Curves from Mordell to
Diophantus and Back (with Bruce T. Myers), Amer. Math. Monthly 109 (August-September 2002), 639-649.
- The Many Names of (7,3,1),
Math. Mag. 75 (April 2002), 83-94.
- Cycles of Directed Graphs Defined
by Matrix Multiplication (mod n) (with Theresa P. Vaughan),
Discrete Mathematics 239 (2001), 109-120.
- Magic Squares, Finite Planes and Points
of Inflection on Elliptic Curves, CMJ 32 (September 2001), 260-267.
- Three Fermat Trails to Elliptic
Curves, CMJ 31(May 2000),
162-172.
- Square Roots from 1;24,51,10 to Dan
Shanks, CMJ 30 (March 1999), 82-95.
- An Introduction to the General Number Field Sieve, by Matthew Briggs (Masters Thesis, Virginia Tech, 1998).
- Directed Graphs Defined by
Arithmetic (mod n), Fibonacci Quarterly 35
(1997), 346-351.
- Periodic Seeded Arrays and Automorphisms of the Shift, Trans. Amer. Math. Soc. 339 (September 1993), 141-161.
