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)

  1. The Bisection Method: Which Root?
    The American Mathematical Monthly, Vol. 94, No. 9, pp. 861-863, November 1987.
    [ PDF file]
     
  2. Turnpike Structures for Optimal Maneuvers.
    Ph.D. Thesis, The Johns Hopkins University, Department of Mathematical Sciences, 1989.    Advisor: Alan J. Goldman.
    [ PDF file]
     
  3. 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]
     
  4. Another Way of Counting NN.
    (with Fritz Juhnke*)
    SIAM Journal on Discrete Mathematics, Vol. 5, No. 3, pp. 377-379, August 1992.
    [ PDF file]
     
  5. Optimization in Chemical Kinetics.
    (with Gordon J. Hogenson*)
    The UMAP Journal, Vol. 13, No. 1, pp. 17-24, Spring 1992.
    [ PDF file]
     
  6. Optimal Leapfrogging.
    (with Joel Auslander* and Daniel S. Wilkerson*)
    Mathematics Magazine (cover article), Vol. 66, No. 1, pp.14-19, February, 1993.
    [ PDF file]
     
  7. Optimal Blackjack Strategy with `Lucky Bucks'.
    (with Eric L. Huggins*)
    The UMAP Journal, Vol. 14, No. 4, pp. 309-318, Spring 1993.
    [ PDF file]
     
  8. 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]
     
  9. Optimal Klappenspiel.
    (with Derek L. Stanford*)
    The UMAP Journal (cover article), Vol. 16, No. 1, pp. 11-20, Spring 1995.
    [ PDF file]
     
  10. Sensible Rules for Remembering Duals--The S-O-B Method.
    SIAM Review, vol. 37, No. 1, pp. 85-87, 1995.
    [ PDF file]
     
  11. 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]
     
  12. Determinants of the Tournaments.
    (with Clifford A. McCarthy*)
    Mathematics Magazine, Vol. 69, No. 2, pp. 133-135, April 1996.
    [ PDF file]
     
  13. Combinatorics and Campus Security.
    The UMAP Journal (cover article), vol. 17.2, pp. 111-116, Summer 1996.
    [ PDF file]
     
  14. 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]
     
  15. Bounds on a Bug.
    (with Matthew T. Fluet*)
    The UMAP Journal, Vol 20, No. 1, pp. 5-9, 1999.
    [ PDF file]
     
  16. The Best Way to Knock 'm Down.
    (with Matthew T. Fluet*)
    The UMAP Journal, Vol 20, No. 1, pp. 11-20, 1999.
    [ PDF file]
     
  17. Magic ``Squares'' Indeed!
    (with Kan Yasuda*)
    The American Mathematical Monthly, Vol. 106, No. 2, pp. 152-156, February, 1999.
    [ PDF file]
     
  18. Unevening the Odds of `Even Up'.
    (with Jennifer J. Quinn)
    Mathematics Magazine, Vol 72, No. 2, pp. 149-150, 1999.
    [ PDF file]
     
  19. 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]
     
  20. Recounting Fibonacci and Lucas Identities.
    (with Jennifer J. Quinn)
    The College Mathematics Journal, Vol 30, No. 5, pp. 359-366, November, 1999.
    [ PDF file]
     
  21. Fibonacci and Lucas Identities through Colored Tilings.
    (with Jennifer J. Quinn)
    Utilitas Mathematica, Vol 56, pp. 137-142, November, 1999.
    [ PDF file]
     
  22. A Rational Solution to Cootie.
    (with Matthew T. Fluet*)
    The College Mathematics Journal, Vol 31, No. 2, pp. 124-125, March, 2000.
    [ PDF file]
     
  23. Paths to a Multinomial Inequality.
    (with Jennifer J. Quinn)
    Ars Combinatoria, Vol 55, pp. 117-122, 2000.
    [ PDF file]
     
  24. 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]
     
  25. 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]
     
  26. 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]
     
  27. What's Best?
    (with Matthew T. Fluet*)
    The American Mathematical Monthly, Vol 107, No. 6, pp. 560-562, June-July, 2000.
    [ PDF file]
     
  28. 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]
     
  29. 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]
     
  30. 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]
     
  31. 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]
     
  32. 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]
     
  33. 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]
     
  34. 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]
     
  35. 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]
     
  36. 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]
     
  37. 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]
     
  38. 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]
     
  39. 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]
     
  40. 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]
     
  41. 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]
     
  42. 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]
     
  43. 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]
     
  44. Counting on Determinants.
    (with Naiomi T. Cameron)
    The American Mathematical Monthly, Vol 112, No. 6, pp. 481-492, June-July 2005.
    [ PDF file]
     
  45. 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]
     
  46. Pythagorean Primes and Palindromic Continued Fractions.
    (with Doron Zeilberger)
    INTEGERS: The Electronic Journal of Combinatorial Number Theory, 5(1), #A30, 2005.
    [ PDF file]
     
  47. Revisiting Fibonacci and Related Sequences.
    (with Jennifer J. Quinn)
    Mathematics Teacher, Vol 99, No. 5, pp. 357-361, December 2005/January 2006.
    [ PDF file]
     
  48. 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]
     
  49. Self-Avoiding Walks and Fibonacci Numbers.
    The Fibonacci Quarterly, Vol. 44, No. 4, pp. 330-334, November 2006.
    [ PDF file]
     
  50. Summing Cubes by Counting Rectangles
    (with Jennifer J. Quinn and Calyssa Wurtz*)
    The College Mathematics Journal, November 2006.
    [ PDF file]
     
  51. A Combinatorial Solution to Intertwined Recurrences.
    (with Michael D. Hirschhorn)
    The Australasian Journal of Combinatorics, Vol 37, pp. 101-116, 2007.
    [ PDF file]
     
  52. 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]
     
  53. 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]
     
  54. 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]
     
  55. 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]
     
  56. 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]
     
  57. 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]
     
  58. 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]
     
  59. 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]
     
  60. 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]
     
  61. 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]
     
  62. 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]
     
  63. 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]
     
  64. Counting on Chebyshev Polynomials
    (with Daniel Walton*)
    Mathematics Magazine, Vol. 82, No. 2, pp. 117-126, April 2009.
    [ PDF file]
     
  65. 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]
     
  66. 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]
     
  67. 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]
     
  68. 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]
     
  69. 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]
     
  70. 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]
     
  71. 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]
     
  72. 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]
     
  73. Third and Fourth Binomial Coefficients
    (with Jacob N. Scott*)
    The Fibonacci Quarterly, Vol. 49, No. 2, pp. 99-101, May 2011.
    [ PDF file]
     
  74. 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]

  75. 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]

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

  77. 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]

  78. Counting on r-Fibonacci Numbers
    (with Curtis R. Heberle*)
    The Fibonacci Quarterly, Vol. 52, Number 2, pp. 121-128, May 2014.
    [ PDF file]

  79. Combinatorial Proofs of Fibonomial Identities
    (with Elizabeth Reiland*)
    The Fibonacci Quarterly, Vol. 52, Number 5, pp. 28-34, December 2014.
    [ PDF file]


  80. A Bijective Proof of a Derangement Recurrence
    (with Joel Ornstein*)
    to appear in The Fibonacci Quarterly, 2017.
    [ PDF file]

  81. Factoring Numbers with Conway's 150 Method
    to appear in The College Mathematics Journal, 2017.

  82. The BINGO Paradox
    (with Ben Weiss)
    to appear in Math Horizons, 2017.


Book Reviews, Problem Solutions, and Letters:

  1. Aspects of Combinatorics (by Victor Bryant) and Excursions in Calculus. (by Robert M. Young)
    SIAM Newsletter, (Discrete Mathematics Activity Group), Winter, 1994.
     
  2. 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]
     
  3. Across the Board: The Mathematics of Chessboard Problems. (by John J. Watkins)
    The Mathematical Intelligencer, Vol. 27, No. 2, 2005.
    [ PDF file]
     
  4. Letter to the Editor: Sury's Parent of Binet's Formula.
    Mathematics Magazine, Vol 78, No. 2, p. 97, April 2005.
    [ PDF file]
     
  5. Q.954 and A.954, Quickie Problem and Solution.
    (with Michel Bataille)

    Mathematics Magazine, Vol 78, No. 4, October 2005.
    [ PDF file]
     
  6. Proof Without Words: Alternating Sums of Odd Numbers.
    Mathematics Magazine, Vol 78, No. 5, p. 385, December 2005.
    [ PDF file]
     
  7. Solution to Problem 1751, A Combinatorial Identity.
    (with Andrew Carman*)

    Mathematics Magazine, Vol 80, No. 4, pp.309-310, October 2007.
    [ PDF file]
     
  8. Reader Reflections (Division by 1001).
    (with Patrick Vennebush)

    Mathematics Teacher, Vol 104, No. 5, p. 332, December 2010/January 2011.
    [Word file] [PDF file]

  9. 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]

  10. 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]

  11. Math Bite: Multiplying by 9.
    (with Rohan Chandra*)

    The College Mathematics Journal, Vol 47, No. 4, pp.281, September 2016.
    [ pdf file]

Other Papers:

  1. Mathematical Magic for Skeptics.
    (with Michael B. Shermer)
    Skeptical Inquirer, Vol. 18, No. 1, pp. 52-62, Fall 1993.
     
  2. Enumerating Backgammon Positions: The Perfect Hash.
    (with Andrew M. Ross*)
    Interface, Vol. 16, No. 1, pp. 3-10, Spring 1997.
    [ PDF file]
     
  3. Math Major Wins College Jeopardy.
    Math Horizons, pp. 24-26, April 1999.
     
  4. A Better Way to Memorize Pi: The Phonetic Code.
    Math Horizons, p. 17, February 2000.
     
  5. The Mathematical Web.
    (with Jennifer J. Quinn)
    Math Horizons, pp. 27-29, February, 2001.
     
  6. Proof With Words: 2 + 11 - 1 = 12.
    Mathematics Magazine, Vol. 74, No. 2, p. 98, April 2001.
    [Word file]
     
  7. Mathematical Constance (a poem dedicated to Constance Reid).
    The American Mathematical Monthly, Vol. 108, No. 5, p. 423, May 2001.
    [Word file]
     
  8. Math Major, Math Major (a song).
    Math Horizons, p. 28, September 2001.
    [ Word file]
     
  9. 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]
     
  10. Double Birthday Magic Square
    M-U-M (The Magazine for the Society of American Magicians), pp. 68-69, August 2006.
    [pdf file]
     
  11. 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]

  12. 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]
     
  13. 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:

  1. Teach Your Child Math.
    (with Michael B. Shermer)
    McGraw Hill, New York, 177 pages, 1991. (Out of Print.)
     
  2. 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.)
     
  3. 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!)
     
  4. 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.)
     
  5. Biscuits of Number Theory.
    (co-edited with Ezra B. Brown)
    Mathematical Association of America, Dolciani Series, Washington DC, 311 pages, 2009. (Order here!)

  6. The Art of Mental Calculation: Addition & Subtraction
    (with Natalya St. Clair)
    self-published with createspace.com, 60 pages, 2014. (Order here!)

  7. The Fascinating World of Graph Theory
    (with Gary Chartrand and Ping Zhang)
    Princeton University Press, Princeton NJ, 322 pages, 2015. (Order here!)
      
  8. 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):

  1. The Joy of Mathematics.
    The Teaching Company, Chantilly, VA (24 thirty minute lectures on DVD), 2007. (Order here!)

  2. Discrete Mathematics.
    The Teaching Company, Chantilly, VA (24 thirty minute lectures on DVD), 2009. (Order here!)
     
  3. The Secrets of Mental Math
    The Teaching Company, Chantilly, VA (12 thirty minute lectures on DVD), 2011. (Order here!)

  4. The Mathematics of Games and Puzzles: From Cards to Sudoku
    The Teaching Company, Chantilly, VA (12 forty-five minute lectures on DVD), 2013. (Order here!)


     

* Stars denote undergraduate co-authors.



last updated April 5, 2015.
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