Hieu D. Nguyen

Department of Mathematics
Rowan University
Glassboro, NJ 08028
Phone: (856) 256-4500 Ext. 3886
Fax: (856) 256-4816
Office: Robinson 228N

Visit my eXperimental Mathematics Laboratory (XML) website


Note: Students enrolled in my courses should log into Blackboard for access to course materials (requires Rowan username and password).

Fall 2015

Previous courses taught


Ph.D. Math (1996), University of California - Berkeley (thesis advisor: Joseph A. Wolf)
Thesis: Weakly symmetric spaces and bounded symmetric domains [Postscript] [PDF]
B.S. Mathematics and B.S. Electrical Engineering (1990), University of Minnesota


Mathematical Interests:

Recent Preprints

NOTE: Asterisk '*' indicates undergraduate student

  1. A Digital Binomial Theorem for Sheffer Sequences (with Toufik Mansour), Preprint (2015). [PDF]
  2. Group Symmetries of Complementary Code Matrices (with Brooke Logan*), Preprint (2015). [PDF]
  3. A q-Digital Binomial Theorem (with Toufik Mansour), Preprint (2015). [PDF]
  4. New Multiple Insertion-Deletion Correcting Codes for Non-Binary Alphabets (with Tuan A. Le), Preprint (2015). [PDF]
  5. A Digital Binomial Theorem, Preprint (2014). [PDF]
  6. New Approximations for the Area of the Mandelbrot Set (with Daniel Bittner*, Long Cheong*, and Dante Gates*), Preprint (2014). [PDF]
  7. Doppler Tolerance, Complementary Code Sets, and the Generalized Thue-Morse Sequence (with Greg E. Coxson), Preprint (2014). [PDF]
  8. Euler, Goldbach and Exact Values of Trigonometric Functions (with Elizabeth Volz), Preprint (updated 2014; original version 2008). [PDF]
  9. Mining the Online Encyclopedia of Integer Sequences (with Douglas Taggart*), Preprint (2012). [PDF]

Research Publications

NOTE: Asterisk '*' indicates undergraduate student

  1. A New Proof of the Prouhet-Tarry-Escott Problem, to appear in INTEGERS. [PDF]
  2. A Generalization of the Digital Binomial Theorem, J. Integer Sequences 18 (2015), Article 15.5.7 (20 pp). [PDF]
  3. A Mixing of Prouhet-Thue-Morse Sequences and Rademacher Functions, INTEGERS 15 (2015), #A14 (16 pp). [PDF]
  4. Row-Correlation Function: A New Approach to Complementary Code Matrices (with Greg E. Coxson and Brooke Logan*), Proceedings of 52nd Annual Allerton Conference on Communication, Control, and Computing, October 2014, 1357-1361. [PDF]
  5. New Convolution Identities for Hypergeometric Bernoulli Polynomials (with Long Cheong*), J. Number Theory 137 (2014), pp. 201-221. [PDF]
  6. Generalized Binomial Expansions and Bernoulli Polynomials, INTEGERS 13 (2013), #A11 (13 pp). [PDF]
  7. Paradoxical Euler: Integrating by Differentiating (with Andrew Fabian*), The Mathematical Gazette 97 (March 2013), No. 538, pp. 61-74. [PDF] (This work was discussed in Ed Sandifer’s column, How Euler Did It, in October 2008 (Curves and Paradox): http://eulerarchive.maa.org/hedi/HEDI-2008-10.pdf)
  8. Moments of Hypergeometric Zeta Functions (with Abdul Hassen), J. Algebra, Number Theory: Advances and Applications 7 (2012), No. 2, pp. 109-129. [PDF]
  9. A Zero-Free Region for Hypergeometric Zeta Functions (with Abdul Hassen), Intern. J. Number Theory 7 (2011), No. 4, pp. 1033-1043. [PDF]
  10. Hypergeometric Zeta Functions (with Abdul Hassen), Intern. J. Number Theory 6 (2010), No. 1, pp. 99-126. [PDF]
  11. Bernoulli Polynomials and Pascal’s Square (with Robert Booth*), Fibonacci Quarterly 46/47 (2008/2009), No. 1, pp. 38-47. [PDF]
  12. Hypergeometric Bernoulli Polynomials and Appell Sequences (with Abdul Hassen), Intern. J. Number Theory 4 (2008), No. 5, pp. 767-774. [PDF]
  13. Rearing Its Ugly Head: The Cosmological Constant and Newton’s Greatest Blunder, American Mathematical Monthly 115 (May 2008), No. 5, pp. 415-430: http://www.maa.org/pubs/monthly_may08_toc.html [PDF]
  14. The Error Zeta Function (with Abdul Hassen), Intern. J. Number Theory 3 (2007), No. 3, pp. 439-453. [PDF]
  15. Soliton Collisions and Ghost Particle Radiation, Journal of Nonlinear Mathematical Physics 11 (2004), No. 2, pp. 180-198: http://www.sm.luth.se/~norbert/home_journal/electronic/v11n2.html [PDF]
  16. Decay of KdV Solitons, SIAM Journal on Applied Mathematics, 63 (2003), No. 3, pp. 874-888: http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000063000003000874000001&idtype=cvips&gifs=Yes   [Postscript] [PDF]
  17. Compact weakly symmetric spaces and spherical pairs, Proceedings of the American Mathematical Society 128 (2000), No. 11, pp. 3425-3433: http://www.ams.org/proc/2000-128-11/S0002-9939-00-05425-3/home.html [PDF]
  18. Characterizing weakly symmetric spaces as Gelfand pairs, Journal of Lie Theory 9 (1999), No. 2, pp. 285-291: http://www.emis.de/journals/JLT/vol.9_no.2/1.html [PDF]
  19. Weakly symmetric spaces and bounded symmetric domains, Transformation Groups 2 (1997), No. 4, pp. 351-374. [PDF]

Old Preprints

  1. Polar Isotropy Actions on Compact Weakly Symmetric Spaces, Preprint (2001). [PDF]
  2. Tautochrones on Riemannian Manifolds, Preprint (1998). [PDF]

Educational Publications

  1. Mathematica for Rogawski’s Calculus (with Abdul Hassen, Gary Itzkowitz, and Jay Schiffman), 2nd Edition, W. H. Freeman, 2011, ISBN-10: 1-4641-0178-6.  Table of contents [PDF]
  2. Linkages as Applied to Protein Folding (with James Factor), DIMACS Educational Module Series 08-1 (March 2008), http://dimacs.rutgers.edu/Publications/Modules/moduleslist.html [PDF]


  1. The Digital Binomial Theorem, Rowan Math Dept Colloquium, 3-23-2015.
  2. A New Proof of the Prouhet-Tarry-Escott Problem, Joint Math Meetings, 1-11-2015.
  3. A New Proof of the Prouhet-Tarry-Escott Problem, Rowan Math Dept Colloquium, 9-29-2014.
  4. Digital Sequences and Doppler Tolerant Waveforms in Radar, Addis Ababa University, Ethiopia, 5-19-2014 (invited lecture)
  5. The Prouhet-Thue-Morse Sequence and Doppler Tolerant Waveforms in Radar, Rowan Math Dept Colloquium, 3-31-2014.
  6. New Convolution Identities for Hypergeometric Bernoulli Polynomials, Joint Math Meetings, 1-15-2014.
  7. Identities to DIE For: Differentiating, Integrating, and Expanding Bernoulli Polynomials, Rowan Math Dept Colloquium, 3-27-2013.
  8. Mining the OEIS: Ten Experimental Conjectures, Joint Math Meetings, 1-9-2013: [PDF]
  9. Data Mining the OEIS for New Identities, MAA-NJ Section Spring Meeting 2012, 3-31-12: [PDF]
  10. Head Bites Tail: Crunching Numbers to Match Integer Sequences, Rowan Math Dept Colloquium, 12-8-11: [PDF]
  11. Experimental Mathematics and Data Mining: Extracting Identities from the Online Encyclopedia of Integer Sequences, Mathfest 2011, 8-4-11: [PDF]
  12. Experimental Mathematics and Data Mining: Excavating the Online Encyclopedia of Integer Sequences for New Mathematical Identities, Rowan Math Dept Colloquium, 1-23-11: [PDF]
  13. A Combinatorial Formula for Certain Two-Dimensional Sequences Related to Generalized Bernoulli Polynomials, Joint Math Meetings 2011, 1-9-11: [PDF]
  14. Sums of Products of Hypergeometric Bernoulli Polynomials, MAA-NJ Section Meeting Spring 2010, 4-10-10: [PDF]
  15. Foot to the Pedal: Constant Pedal Curves and Surfaces, Joint Math Meetings 2010, 1-13-10: [PDF]
  16. Euler, Goldbach and Exact Values of Cosine, Euler Society Annual Conference 2009, 7-13-09: [PDF]
  17. Discovering Bernoulli Number Identities Via Euler Maclaurin Summation, Joint Math Meetings 2009, 1-7-09: [PDF]
  18. Bernoulli = Bernoulli: Discovering Bernoulli Number Identities via Euler-Maclaurin Summation, Rowan Math Dept Colloquium, 9-24-08 [PDF]
  19. Paradoxical Euler or Integration by Differentiation: A Synopsis of E236, Euler Society Annual Conference 2008, 7-21-08 [PDF]
  20. Translating Euler's Works: How to get your students' feet wet in undergraduate research, Joint Math Meetings 2008, 1-6-08 [PDF]
  21. Pascal’s Square: Determinants, Bernoulli Polynomials, and the Arithmetical Triangle, MathFest 2007, 8-5-07: [PDF]
  22. Appell Sequences and Hypergeometric Bernoulli Polynomials, Joint Math Meetings 2007, 1-5-07: [PDF]
  23. How Bernoulli Did It: Sums of Powers, Generating Functions, and Bernoulli Numbers, Rowan Math Seminar, 10-11-06: [PDF]
  24. A Half-Marriage in Error: When Zeta Integrates a Gaussian, MAA-NJ Section Meeting Spring 2006, 4-8-06: [PDF]
  25. Newton’s “Greatest Blunder”: His theorem on revolving orbits and failed calculation of lunar precession, Rowan Math Seminar, 3-1-06: [PDF]
  26. The Search for Nothing: A zero-free region of hypergeometric zeta, Rowan Math Seminar, 10-5-05: [PDF]
  27. Newton’s Greatest Blunder, MathFest 2005, 8-5-05
  28. Hypergeometric Zeta Functions, Joint Math Meetings, 1-5-05: [PDF]
  29. Hypergeometric Zeta Functions, Rowan Math Seminar, 9-29-04
  30. Solitons: From Canal Water Waves to Molecular Lasers, Philadelphia IEEE Night, 5-20-03


Eureka Website

Experimental Math Summer Enrichment Program 2009

Student Translations of Euler’s Mathematics (STEM)

Soliton Radiation Website

Animated GIFs of solitons:

Java applets of solitons:

Classification Tables




Mathematica Student Tutorial Manuals