Papers, Preprints and Books of Arthur Benjamin (in PDF
format)
Color scheme for paper themes:
Papers on combinatorics are RED.
Papers
on mathematical games are BLUE.
Papers
on miscellaneous topics are GREEN.
Back to my home
page...
PUBLISHED WORKS: (* Stars denote undergraduate co-authors)
- 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 Electornic 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]
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)
[
Word file] [ 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!)
* Stars denote undergraduate co-authors.
last updated April 5, 2015.
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