Color scheme for paper themes:

Papers on combinatorics are RED.

Papers on mathematical games are BLUE.

Papers on miscellaneous topics are GREEN.

* Stars denote undergraduate co-authors.

## Published Works

**The Bisection Method: Which Root?***The American Mathematical Monthly*, Vol. 94, No. 9, pp. 861-863, November 1987.

[PDF file]**Turnpike Structures for Optimal Maneuvers***Ph.D. Thesis, The Johns Hopkins University, Department of Mathematical Sciences, 1989.*Advisor: Alan J. Goldman.

[PDF file]**Graphs, Maneuvers, and Turnpikes***Operations Research,*Vol. 38, No. 2, pp. 202-216, March/April 1990.

This paper was awarded the George Nicholson Prize from the Operations Research Society of America in 1988.

[PDF file]**Another Way of Counting***N*^{N}

(with Fritz Juhnke*)*SIAM Journal on Discrete Mathematics*, Vol. 5, No. 3, pp. 377-379, August 1992.

[PDF file]**Optimization in Chemical Kinetics**

(with Gordon J. Hogenson*)*The UMAP Journal*, Vol. 13, No. 1, pp. 17-24, Spring 1992.

[PDF file]**Optimal Leapfrogging**

(with Joel Auslander* and Daniel S. Wilkerson*)*Mathematics Magazine*(cover article), Vol. 66, No. 1, pp.14-19, February, 1993.

[PDF file]**Optimal Blackjack Strategy with ‘Lucky Bucks’**

(with Eric L. Huggins*)*The UMAP Journal*, Vol. 14, No. 4, pp. 309-318, Spring 1993.

[PDF file]**Localization of Optimal Strategies in Certain Games**

(with Alan J. Goldman)*Naval Research Logistics*, Vol. 41, No. 5, pp. 669-676, August 1994.

[PDF file]**Optimal Klappenspiel**

(with Derek L. Stanford*)*The UMAP Journal*(cover article), Vol. 16, No. 1, pp. 11-20, Spring 1995.

[PDF file]**Sensible Rules for Remembering Duals–The S-O-B Method***SIAM Review*, vol. 37, No. 1, pp. 85-87, 1995.

[PDF file]**How Do I Marry Thee? Let Me Count the Ways!**

(with Cherlyn Converse and Henry A. Krieger)*Discrete Applied Mathematics*, 59, pp. 285-292, 1995.

[PDF file]**Determinants of the Tournaments**

(with Clifford A. McCarthy*)*Mathematics Magazine*, Vol. 69, No. 2, pp. 133-135, April 1996.

[PDF file]**Combinatorics and Campus Security***The UMAP Journal*(cover article), vol. 17.2, pp. 111-116, Summer 1996.

[PDF file]**Strong Chromatic Index of Subset Graphs**

(with Jennifer J. Quinn)*The Journal of Graph Theory,*Vol. 24, No. 3, pp. 267-273, 1997.

[PDF file]**Bounds on a Bug**

(with Matthew T. Fluet*)*The UMAP Journal*, Vol 20, No. 1, pp. 5-9, 1999.

[PDF file]**The Best Way to Knock ‘m Down**

(with Matthew T. Fluet*)*The UMAP Journal*, Vol 20, No. 1, pp. 11-20, 1999.

[PDF file]**Magic “Squares” Indeed!**

(with Kan Yasuda*)*The American Mathematical Monthly,*Vol. 106, No. 2, pp. 152-156, February, 1999.

[PDF file]**Unevening the Odds of “Even Up”**

(with Jennifer J. Quinn)*Mathematics Magazine*, Vol 72, No. 2, pp. 149-150, 1999.

[PDF file]**Why the Player Never Wins in the Long Run at LA Blackjack**

(with Michael Lauzon* and Christopher Moore*)*The UMAP Journal*, Vol 20, No. 2, pp. 127-138, Summer 1999.

[PDF file]**Recounting Fibonacci and Lucas Identities**

(with Jennifer J. Quinn)*The College Mathematics Journal*, Vol 30, No. 5, pp. 359-366, November, 1999.

[PDF file]**Fibonacci and Lucas Identities through Colored Tilings**

(with Jennifer J. Quinn)*Utilitas Mathematica*, Vol 56, pp. 137-142, November, 1999.

[PDF file]**A Rational Solution to Cootie**

(with Matthew T. Fluet*)*The College Mathematics Journal*, Vol 31, No. 2, pp. 124-125, March, 2000.

[PDF file]**Paths to a Multinomial Inequality**

(with Jennifer J. Quinn)*Ars Combinatoria*, Vol 55, pp. 117-122, 2000.

[PDF file]**Phased Tilings and Generalized Fibonacci Identities**

(with Jennifer J. Quinn and Francis E. Su)*The Fibonacci Quarterly*, Vol 38, No. 3, pp. 282-288, June-July 2000.

[PDF file]**Counting on Continued Fractions**

(with Jennifer J. Quinn and Francis E. Su)*Mathematics Magazine*, Vol 73, No. 2, pp. 98-104, April, 2000.

[PDF file]**Random Approaches to Fibonacci Identities**

(with Gregory M. Levin, Karl Mahlburg*, and Jennifer J. Quinn)*The American Mathematical Monthly*, Vol 107, No. 6, pp. 511-516, June-July, 2000.

[PDF file]**What’s Best?**

(with Matthew T. Fluet*)*The American Mathematical Monthly*, Vol 107, No. 6, pp. 560-562, June-July, 2000.

[PDF file]**Fermion-Boson Transformation in Fractional Quantum Hall Systems**

(with John J. Quinn, Arkadius Wojs, and Jennifer J. Quinn)*Physica E*, Vol. 9, No. 4, pp. 701-708, April 2001.

[PDF file]**Optimal Token Allocations in Solitaire Knock ‘m Down**

(with Matthew T. Fluet* and Mark E. Huber)*The Electronic Journal of Combinatorics*, Vol 8, No. 2, pp. 1-8, #R2, 2001.

[PDF file]**Composite Fermions and Integer Partitions**

(with Jennifer J. Quinn, Arkadius Wojs, and John J. Quinn)*Jounal of Combinatorial Theory, Series A*, Vol 95, 390-397, 2001.

[PDF file]**Transformation of Statistics in Fractional Quantum Hall Systems**

(with John J. Quinn, A. Wojs, and Jennifer J. Quinn)*Physica E*, Vol 11, pp. 182-185, 2001.

[PDF file]**A Stirling EnCOUNTer with Harmonic Numbers**

(with Greg O. Preston* and Jennifer J. Quinn)*Mathematics Magazine*, Vol. 75, No. 2, pp. 95-103, April 2002.

[PDF file]**Analysis of the N-Card Game Le Her**

(with Alan J. Goldman)*Journal of Optimization Theory and Applications*, Vol 114, No. 3, pp. 695-704, September, 2002.

[PDF file]**Two Quick Combinatorial Proofs of “the sum of the cubes”**

(with Michael E. Orrison)*The College Mathematics Journal*, Vol 33, No. 5, pp. 406-408, November, 2002.

[PDF file]**The Fibonacci Numbers — Exposed More Discretely**

(with Jennifer J. Quinn)*Mathematics Magazine*, (cover article), Vol 76, No. 3, pp. 182-192, June 2003.

[PDF file]**A Probabilistic View of Certain Weighted Fibonacci Sums**

(with Judson D. Neer*, Daniel E. Otero, and James A. Sellers)*The Fibonacci Quarterly*, Vol 41, No. 4, pp. 360-364, August, 2003.

[PDF file]**A Combinatorial Approach to Hyperharmonic Numbers**

(with David Gaebler* and Robert Gaebler*)*INTEGERS: The Electronic Journal of Combinatorial Number Theory*, Vol 3, pp. 1–9, #A15, 2003.

[PDF file]**Linear Recurrences Through Tilings and Markov Chains**

(with Christopher R.H. Hanusa* and Francis E. Su)*Utilitas Mathematica*, Vol 64, pp. 3-17, November 2003.

[PDF file]**Fibinomial Identities**

(with Jennifer J. Quinn and Jeremy A. Rouse*)*Applications of Fibonacci Numbers, Volume 9*, (Frederic T. Howard, ed.), Kluwer Academic Publishers, pp. 19-24, 2004.

[PDF file]**Recounting Binomial Fibonacci Identities**

(with Jeremy A. Rouse*)*Applications of Fibonacci Numbers, Volume 9*, (Frederic T. Howard, ed.), Kluwer Academic Publishers, pp. 25-28, 2004.

[PDF file]**Proofs that Really Count: The Magic of Fibonacci Numbers and More**

(with Jennifer J. Quinn)*Mathematical Adventures for Students and Amateurs,*(David F. Hayes and Tatiana Shubin, editors), Spectrum Series of MAA, pp. 83-98, 2004.

[PDF file]**A (Not So) Complex Solution to a^2 + b^2 = c^n**

(with Arnold M. Adelberg and David I. Rudel*)*Mathematics Magazine,*Vol 77, No. 4, pp. 300-302, October 2004.

[PDF file]**Combinatorial Proofs of Fermat’s, Lucas’s, and Wilson’s Theorems**

(with Peter G. Anderson and Jeremy A. Rouse*)*The American Mathematical Monthly,*Vol 112, No. 3, pp. 266-268, March 2005.

[PDF file]**Counting on Determinants**

(with Naiomi T. Cameron)*The American Mathematical Monthly,*Vol 112, No. 6, pp. 481-492, June-July 2005.

[PDF file]**Recounting the Odds of an Even Derangement**

(with Curtis D. Bennett and Florence Newberger)*Mathematics Magazine,*Vol 78, No. 5, pp. 387-390, December 2005

[PDF file]**Pythagorean Primes and Palindromic Continued Fractions**

(with Doron Zeilberger)*INTEGERS: The Electronic Journal of Combinatorial Number Theory*, 5(1), #A30, 2005.

[PDF file]**Revisiting Fibonacci and Related Sequences**

(with Jennifer J. Quinn)*Mathematics Teacher*, Vol 99, No. 5, pp. 357-361, December 2005/January 2006.

[PDF file]**Combinatorial Interpretations of Spanning Tree Identities**

(with Carl R. Yerger*)*Bulletin of the Institute for Combinatorics and its Applications,*Vol 47, pp. 37-42, 2006.

[PDF file]**Self-Avoiding Walks and Fibonacci Numbers***The Fibonacci Quarterly*, Vol. 44, No. 4, pp. 330-334, November 2006.

[PDF file]**Summing Cubes by Counting Rectangles**

(with Jennifer J. Quinn and Calyssa Wurtz*)*The College Mathematics Journal*, November 2006.

[PDF file]**A Combinatorial Solution to Intertwined Recurrences**

(with Michael D. Hirschhorn)*The Australasian Journal of Combinatorics*, Vol 37, pp. 101-116, 2007.

[PDF file]**Fibonacci Deteminants — A Combinatorial Approach**

(with Naiomi T. Cameron and Jennifer J. Quinn)*The Fibonacci Quarterly*, Vol. 45, No. 1, pp. 39-55, February 2007.

[PDF file]**A Combinatorial Proof of Vandermonde’s Determinant**

(with Gregory P. Dresden)*The American Mathematical Monthly*, Vol. 114, No. 4, pp. 338-341, April 2007.

[PDF file]**The Probability of Relatively Prime Polynomials**

(with Curtis D. Bennett)*Mathematics Magazine*, (cover article), Vol. 80, No. 3, pp. 196-202, June 2007.

[PDF file]**Recounting Determinants for a Class of Hessenberg Matrices**

(with Mark A. Shattuck)*INTEGERS: The Electronic Journal of Combinatorial Number Theory*, Vol. 7, #A55, pp. 1–7, 2007.

[PDF file]**Estimating Winning Probabilities in Backgammon Races**

(with Andrew M. Ross and Michael Munson)*Optimal Play: Mathematical Studies of Games and Gambling*, (Stewart N. Ethier and William R. Eadington, editors), Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno, pp. 269–291, 2007.

[PDF file]**Paint it Black — A Combinatorial Yawp**

(with Jennifer J. Quinn, James A. Sellers, and Mark A. Shattuck)*Mathematics Magazine*, Vol. 81, No. 1. pp. 45-50, February 2008.

[PDF file]**The 99th Fibonacci Identity**

(with Alex K. Eustis* and Sean S. Plott*)*The Electronic Journal of Combinatorics*, R34 (A Fibonacci number!), February 25, 2008.

[PDF file]**An Alternate Approach to Alternating Sums: A Method to Die For**

(with Jennifer J. Quinn)*The College Mathematics Journal*, Vol. 39, No. 3. pp. 191-201, September 2008.

[PDF file]**Tiling Proofs of Recent Sum Identities Involving Pell Numbers**

(with Sean S. Plott* and James A. Sellers)*The Annals of Combinatorics*, Vol. 12, No. 3, pp. 271–278, October 2008.

[PDF file]**Recounting the Sums of Cubes of Fibonacci Numbers**

(with Timothy A. Carnes* and Benoit Cloitre)*Congressus Numerantium, Proceedings of the Eleventh International Conference on Fibonacci Numbers and their Applications*, (William Webb, ed.), Vol 194, pp. 45-51, 2009.

[PDF file]**When does (F_m)^L divide F_n? A Combinatorial Solution**

(with Jeremy A. Rouse*)*Congressus Numerantium, Proceedings of the Eleventh International Conference on Fibonacci Numbers and their Applications*, (William Webb, ed.), Vol 194, pp. 53-58, 2009.

[PDF file]**A Combinatorial Approach to Fibonomial Coefficients**

(with Sean S. Plott*)*The Fibonacci Quarterly*, Vol. 46/47, No. 1, pp. 7-9, February 2008/2009.

See also Errata: Vol 48, No. 3, pp. 276, August 2010.

[PDF file] [Errata]**Counting on Chebyshev Polynomials**

(with Daniel Walton*)*Mathematics Magazine,*Vol. 82, No. 2, pp. 117-126, April 2009.

[PDF file]**Compression Theorems for Periodic Tilings and Consequences**

(with Alex Eustis* and Mark Shattuck)*The Journal of Integer Sequences*, Vol. 12, Article 09.6.3, 2009.

[PDF file]**Combinatorial Trigonometry with Chebyshev Polynomials**

(with Larry Ericksen, Pallavi Jayawant, and Mark Shattuck)*Journal of Statistical Planning and Inference, Proceedings of the 6th International Conference on Lattice Path Combinatorics,*, Vol. 140, pp. 2157-2160, 2010.

doi:10.1016/j.jspi.2010.01.011

[PDF file]**Combinatorially Composing Chebyshev Polynomials**

(with Daniel Walton*)*Journal of Statistical Planning and Inference, Proceedings of the 6th International Conference on Lattice Path Combinatorics,*Vol 140, pp. 2161-2167, 2010.

doi:10.1016/j.jspi.2010.01.011, 2010.

[PDF file]**Catalan Determinants — A Combinatorial Approach**

(with Naiomi T. Cameron, Jennifer J. Quinn and Carl R. Yerger*)*Congressus Numerantum, Proceedings of the Twelfth Conference on Fibonacci Numbers and their Applications,*(William Webb, ed.), Vol. 200, pp. 27-34, 2010.

[PDF file]**The Lucas Triangle Recounted***Congressus Numerantum, Proceedings of the Twelfth Conference on Fibonacci Numbers and their Applications,*(William Webb, ed.), Vol. 200, pp. 169-177, 2010.

[PDF file]**Fibonacci Identities Derived from Path Counting in Automata**

(with Dale Gerdemann)*Congressus Numerantum, Proceedings of the Thirteenth Conference on Fibonacci Numbers and their Applications,*(Florian Luca and Pante Stanica, eds.), Vol. 201, pp. 237-256, 2010.

[PDF file]**An Amazing Mathematical Card Trick***The Mathematical Intelligencer*, Vol. 32, Number 2, pp. 37-41, Summer 2010.

doi:10.1007/s00283-009-9123-1

[PDF file]**Sums of Evenly Spaced Binomial Coefficients**

(with Bob Chen* and Kimberly Tucker)*Mathematics Magazine*, Vol. 83, No. 5, pp. 370-373, December 2010.

[PDF file]**Third and Fourth Binomial Coefficients**

(with Jacob N. Scott*)*The Fibonacci Quarterly*, Vol. 49, No. 2, pp. 99-101, May 2011.

[PDF file]**The Combinatorialization of Linear Recurrences**

(with Halcyon Derks* and Jennifer J. Quinn)*The Electronic Journal of Combinatorics,*Vol. 18(2), P12, Zeilberger Issue, June 11, 2011.

[ PDF file]**Combinatorics of Two Toned Tilings**

(with Phyllis Chinn, Jacob N. Scott*, and Greg Simay)*The Fibonacci Quarterly*, Vol. 49, No. 4, pp. 290-297, November 2011.

[PDF file]**Squaring, Cubing, and Cube Rooting***The College Mathematics Journal*, Vol. 43, Number 1, pp. 58-63, January, 2012.

[PDF file]**Challenging Magic Squares for Magicians**

(with Ethan J. Brown*)*The College Mathematics Journal*, Vol. 45, Number 2, pp. 92-100, March 2014. (This paper was reprinted in*The Best Writing in Mathematics 2015,*edited by Mircea Pitici, Princeton University Press, pp. 26-37, 2015.

[PDF file]**Counting on r-Fibonacci Numbers**

(with Curtis R. Heberle*)*The Fibonacci Quarterly*, Vol. 52, Number 2, pp. 121-128, May 2014.

[PDF file]**Combinatorial Proofs of Fibonomial Identities**

(with Elizabeth Reiland*)*The Fibonacci Quarterly*, Vol. 52, Number 5, pp. 28-34, December 2014.

[PDF file]**A Bijective Proof of a Derangement Recurrence**

(with Joel Ornstein*)*Proceedings of the 17th International Conference on Fibonacci Numbers and Their Applications,*pp. 28-29, December 2017.

[PDF file]**The BINGO Paradox**

(with Joseph Kisenwether and Ben Weiss)*Math Horizons*, Vol. 25, Number 1, pp. 18-21, September 2017.

Also appeared in*The Best Writing on Mathematics, 2018,*Mircea Pitici, Editor, Princeton University Press, pp. 108-116, 2019.

[PDF file]**Challenging Knight’s Tours**

(with Sam K. Miller*)*Math Horizons (cover article),*Number 3, Vol. 25, pp. 18-21, February 2018.

[PDF file]**Factoring Numbers with Conway’s 150 Method***The College Mathematics Journal*, Vol. 49, No. 2, pp. 122-125, March 2018.

[PDF file]**BINGO Paradoxes**

(with Barry A. Balof, Jay Cordes, and Joseph Kisenwether)

to appear in*Mathematics of Various Entertaining Subjects (MOVES),*Princeton University Press, 2019.**The Long and Short of Benford’s Law***Math Horizons*, Number 4, Vol. 25, pp. 8-9, April 2019.

[PDF file]**Unified Tiling Proofs of a Family of Fibonacci Identities**

(with Joshua Crouch* and James Sellers)*The Fibonacci Quarterly*, Vol. 57, Number 1, pp. 29-31, February 2019.

[PDF file]**A Tiling Interpretation of q-Binomial Coefficients**

(with Jonathan J. Azose*)*Fibonacci Quarterly,*Number 2, Vol. 58, pp. 99-125, May 2020.

[PDF file]**Counting on Euler and Bernoulli Number Identities**

(with John Lentfer* and Thomas C. Martinez*)*Fibonacci Quarterly,*Number 5 (Special Open Access Issue), Vol. 58, pp. 30-33, December 2020.

[PDF file]**A Tiling Interpretation of a Generalized Zeckendorf Theorem**

(with John Lentfer)*Integers: The Electronic Journal of Combinatorial Number Theory,*Volume 22, #A104, November 2022.

[PDF file]**Counting on Hosoya’s Triangle**

(with Daniela Elizondo)*The Fibonacci Quarterly,*Vol. 60, Number 5, pp. 47-55, December 2022.

[PDF file]

## Book Reviews, Problem Solutions, and Letters

**Aspects of Combinatorics (by Victor Bryant) and Excursions in Calculus. (by Robert M. Young)***SIAM Newsletter*, (Discrete Mathematics Activity Group), Winter, 1994.**Discrete Mathematics: Elementary and Beyond. (by L. Lovasz, J. Pelikan, and K. Vesztergombi)***The American Mathematical Monthly*, Vol 111, No. 7, pp. 636-638, August-September, 2004.

[PDF file]**Across the Board: The Mathematics of Chessboard Problems. (by John J. Watkins)***The Mathematical Intelligencer*, Vol. 27, No. 2, 2005.

[PDF file]**Letter to the Editor: Sury’s Parent of Binet’s Formula***Mathematics Magazine*, Vol 78, No. 2, p. 97, April 2005.

[PDF file]**Q.954 and A.954, Quickie Problem and Solution.**

(with Michel Bataille)*Mathematics Magazine*, Vol 78, No. 4, October 2005.

[PDF file]**Proof Without Words: Alternating Sums of Odd Numbers***Mathematics Magazine*, Vol 78, No. 5, p. 385, December 2005.

[PDF file]**Solution to Problem 1751, A Combinatorial Identity**

(with Andrew Carman*)*Mathematics Magazine*, Vol 80, No. 4, pp.309-310, October 2007.

[PDF file]**Reader Reflections (Division by 1001)**

(with Patrick Vennebush)*Mathematics Teacher*, Vol 104, No. 5, p. 332, December 2010/January 2011.

[Word file] [PDF file]**Solution to Problem 952, A Binomial Coefficient Identity**

(with Lizard Reiland*)*The College Mathematics Journal*, Vol 43, No. 3, pp.260-261, May 2012.

[PDF file]**Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks (by Persi Diaconis and Ron Graham)***SIAM Review*, Vol. 54, No. 3, pp. 609-612, 2012. (Featured Review)

[PDF file]**Math Bite: Multiplying by 9**

(with Rohan Chandra*)*The College Mathematics Journal*, Vol 47, No. 4, pp.281, September 2016.

[PDF file]

## Other Papers

**Mathematical Magic for Skeptics**

(with Michael B. Shermer)*Skeptical Inquirer*, Vol. 18, No. 1, pp. 52-62, Fall 1993.**Enumerating Backgammon Positions: The Perfect Hash**

(with Andrew M. Ross*)*Interface*, Vol. 16, No. 1, pp. 3-10, Spring 1997.

[PDF file]**Math Major Wins College Jeopardy***Math Horizons*, pp. 24-26, April 1999.**A Better Way to Memorize Pi: The Phonetic Code***Math Horizons*, p. 17, February 2000.**The Mathematical Web**

(with Jennifer J. Quinn)*Math Horizons*, pp. 27-29, February, 2001.**Proof With Words: 2 + 11 – 1 = 12***Mathematics Magazine*, Vol. 74, No. 2, p. 98, April 2001.

[Word file]**Mathematical Constance (a poem dedicated to Constance Reid)***The American Mathematical Monthly*, Vol. 108, No. 5, p. 423, May 2001.

[Word file]**Math Major, Math Major (a song)***Math Horizons*, p. 28, September 2001.

[Word file]**Mathematical Magic***Bridges: Mathematical Connections in Art, Music, and Science; Conference Proceedings 2004*, (Reza. Sarhangi and Carlo Sequin, Eds.), pp. 259–263, 2004.

[Word file]**Double Birthday Magic Square***M-U-M (The Magazine for the Society of American Magicians)*, pp. 68-69, August 2006.

[PDF file]**Ta Da! (A magical math Pop Quiz)***The New York Times (Education Life Section)*, pp. 32-33, Sunday, January 3, 2010

Online version on December 30, 2009

[web link]**Backgammon: Game On!***The Best Kind of College: An Insiders’ Guide to America’s Small Liberal Arts Colleges,*edited by Susan McWilliams and John E. Seery, SUNY Press, pp. 65-67, 2015.

[PDF file]**Magic in the Classroom***Bridges: Mathematical Connections in Art, Music, and Science; Conference Proceedings 2004*, (Reza. Sarhangi and Carlo Sequin, Eds.), pp. 259–263, 2015.

## Books

*Teach Your Child Math*

(with Michael B. Shermer)

McGraw Hill, New York, 177 pages, 1991. (Out of Print.)*Mathemagics: How to Look like a Genius Without Really Trying*

(with Michael B. Shermer)

McGraw Hill (Book-of-the-Month-Club Selection), New York, 218 pages, 1993, 1998. (Out of Print. Updated as*Secrets of Mental Math.*)*Proofs That Really Count: The Art of Combinatorial Proof*

(with Jennifer J. Quinn)

Mathematical Association of America, Dolciani Series, Washington DC, 208 pages, 2003.

(Order here!)*Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks*

(with Michael B. Shermer; translated into more than 10 languages!)

Random House, New York, 279 pages, 2006. (This is an updated version of*Mathemagics*.)*Biscuits of Number Theory*

(co-edited with Ezra B. Brown)

Mathematical Association of America, Dolciani Series, Washington DC, 311 pages, 2009.

(Order here!)*The Art of Mental Calculation: Addition & Subtraction*

(with Natalya St. Clair)

self-published with createspace.com, 60 pages, 2014.

(Order here!)*The Fascinating World of Graph Theory*

(with Gary Chartrand and Ping Zhang)

Princeton University Press, Princeton NJ, 322 pages, 2015.

(Order here!)*The Magic of Math: Solving for x and Figuring Out Why*

Basic Books, New York, NY, 336 pages, 2015. (A*New York Times Bestseller!*

## DVD Courses (from *The Great Courses*)

*The Joy of Mathematics*

The Great Courses, Chantilly, VA (24 thirty minute lectures on DVD), 2007.

(Order here!)*Discrete Mathematics*

The Great Courses,, Chantilly, VA (24 thirty minute lectures on DVD), 2009.

(Order here!)*The Secrets of Mental Math*

The Great Courses,, Chantilly, VA (12 thirty minute lectures on DVD), 2011.

(Order here!)**The Mathematics of Games and Puzzles: From Cards to Sudoku**

The Great Courses, Chantilly, VA (12 forty-five minute lectures on DVD), 2013.

(Order here!)**Math and Magic**

The Great Courses, Chantilly, VA (12 thirty minute lectures on DVD), 2018.

(Order here!)