EDUCATION

Ph.D. Mathematics (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

TEACHING SCHEDULE

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

Spring 2024

• DS 02.395.1, DS 02.695.3, T 5-7:45pm, Robinson 212
• Math 03.150.4 Discrete Math, TR 11am-12:15pm, Science 254
• Math 03.150.5 Discrete Math, MW 12:30pm-1:45pm, Science 128

Previous courses taught

MATHEMATICAL RESEARCH

Mathematical Interests:

• Current research projects: Visit my eXperimental Mathematics Laboratory (XML) website at to learn more about the following research programs:
  • Machine learning: this program involve projects that seek to employ machine learning to solve classification and computer vision problems.
  • Error-correcting codes for communication: this project seeks to construct insertion/deletion correcting codes for multi-symbol alphabets using number-theoretic techniques and develop encoding/decoding algorithms for such codes.
• Previous research projects

Research Publications

NOTE: Asterisk '*' indicates undergraduate student; caret '^' indicates graduate student

28. H. Nguyen, L. LaValva*, S. Ho, M. Khan*, N. Kaegi*, Optimal N-ary ECOC Matrices for Ensemble Classification, 2021 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1-8, doi: 10.1109/SSCI50451.2021.9660146. PDF (arXiv version)
27. H. Nguyen, M. Khan*, N. Kaegi*, S. Ho, J. Moore*, L. Borys*, L. LaValva*, Ensemble Learning using Error Correcting Output Codes: New Classification Error Bounds, 2021 IEEE 33nd International Conference on Tools with Artificial Intelligence (ICTAI), DOI 10.1109/ICTAI52525.2021.00114. PDF (arXiv version)
26. S. Ho, M. Marchiano*, S. Zockoll*, H. Nguyen, An Error-Correcting Output Code Framework for Lifelong Learning without a Teacher, 2020 IEEE 32nd International Conference on Tools with Artificial Intelligence (ICTAI), DOI: 10.1109/ICTAI50040.2020.00048.
25. Patrick F. Bray* and H. D. Nguyen, The Area of the Mandelbrot Set and Zagier's Conjecture, INTEGERS 18 (2018), A57. [PDF]
24. J. Rosado^, H. D. Nguyen, and L. Cao, Partitions of Equiangular Tight Frames, Linear Algebra and Its Applications 526 (2017), 95-120. DOI 10.1016/j.laa.2017.03.022. [PDF]
23. D. Bittner*, L. Cheong*, D. Gates*, and H. D. Nguyen, New Approximations for the Area of the Mandelbrot Set, Involve, a Journal of Mathematics 10-4 (2017), 555--572. DOI 10.2140/involve.2017.10.555. [PDF]
22. B. Logan* and H. D. Nguyen, Group Symmetries of Complementary Code Matrices, IEEE Trans. Aerospace and Electr. Systems 52 (October 2016), no. 5, 2255 - 2262. DOI 10.1109/TAES.2016.150478 [PDF]
21. G. E. Coxson and H. D. Nguyen, Doppler Tolerance, Complementary Code Sets, and the Generalized Thue-Morse Sequence, IET Radar, Sonar and Navigation 10 (December 2016), no. 9, 1603-1610. DOI 10.1049/iet-rsn.2015.0569 [PDF]
20. T. A. Le^ and H. D. Nguyen, New Multiple Insertion-Deletion Correcting Codes for Non-Binary Alphabets, IEEE Trans. Information Theory 62 (May 2016), no. 5, 2682-2693. DOI 10.1109/TIT.2016.2541139 [PDF]
19. H. D. Nguyen, A New Proof of the Prouhet-Tarry-Escott Problem, INTEGERS 16 (2016), #A1 (9 pp). [PDF]
18. H. D. Nguyen, A Generalization of the Digital Binomial Theorem, J. Integer Sequences 18 (2015), Article 15.5.7 (20 pp). [PDF]
17. H. D. Nguyen, A Mixing of Prouhet-Thue-Morse Sequences and Rademacher Functions, INTEGERS 15 (2015), #A14 (16 pp). [PDF]
16. G. E. Coxson, B. Logan*, and H. D. Nguyen, Row-Correlation Function: A New Approach to Complementary Code Matrices, Proceedings of 52nd Annual Allerton Conference on Communication, Control, and Computing, October 2014, 1357-1361. DOI 10.1109/ALLERTON.2014.7028613 [PDF]
15. H. D. Nguyen and L. Cheong, New Convolution Identities for Hypergeometric Bernoulli Polynomials, J. Number Theory 137 (2014), pp. 201-221. [PDF]
14. H. D. Nguyen, Generalized Binomial Expansions and Bernoulli Polynomials, INTEGERS 13 (2013), #A11 (13 pp). DOI 10.1515/9783110298161.149 [PDF]
13. A. Fabian* and H. D. Nguyen, Paradoxical Euler: Integrating by Differentiating, The Mathematical Gazette 97 (March 2013), No. 538, pp. 61-74. DOI 10.1017/S002555720000543X [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)
12. A. Hassen and H. D. Nguyen, Moments of Hypergeometric Zeta Functions, J. Algebra, Number Theory: Advances and Applications 7 (2012), No. 2, pp. 109-129. [PDF]
11. A. Hassen and H. D. Nguyen, A Zero-Free Region for Hypergeometric Zeta Functions, Intern. J. Number Theory 7 (2011), No. 4, pp. 1033-1043. DOI 10.1142/S1793042111004678 [PDF]
10. A. Hassen and H. D. Nguyen, Hypergeometric Zeta Functions, Intern. J. Number Theory 6 (2010), No. 1, pp. 99-126. DOI 10.1142/S179304211000282X . [PDF]
9. R. Booth* and H. D. Nguyen, Bernoulli Polynomials and Pascal's Square, Fibonacci Quarterly 46/47 (2008/2009), No. 1, pp. 38-47. [PDF]
8. A. Hassen and H. D. Nguyen, Hypergeometric Bernoulli Polynomials and Appell Sequences, Intern. J. Number Theory 4 (2008), No. 5, pp. 767-774. DOI 10.1142/S1793042108001754 . [PDF]
7. H. D. Nguyen, 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]
6. A. Hassen and H. D. Nguyen, The Error Zeta Function, Intern. J. Number Theory 3 (2007), No. 3, pp. 439-453. DOI 10.1142/S1793042107001000 [PDF]
5. H. D. Nguyen, 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]
4. H. D. Nguyen, Decay of KdV Solitons, SIAM Journal on Applied Mathematics, 63 (2003), No. 3, pp. 874-888. DOI 10.1137/S0036139902402695 [Postscript] [PDF]
3. A. Hassen and H. D. Nguyen, 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]
2. H. D. Nguyen, 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]
1. H. D. Nguyen, Weakly symmetric spaces and bounded symmetric domains, Transformation Groups 2 (1997), No. 4, pp. 351-374. [PDF]

Old Preprints

NOTE: Asterisk '*' indicates undergraduate student; caret '^' indicates graduate student

1. T. Mansour and H. D. Nguyen, A Digital Binomial Theorem for Sheffer Sequences, Preprint (2015). [PDF]
2. T. Mansour and H. D. Nguyen, A q-Digital Binomial Theorem, Preprint (2015). [PDF]
3. H. D. Nguyen, A Digital Binomial Theorem, Preprint (2014). [PDF]
4. D. Taggart* and H. D. Nguyen, Mining the Online Encyclopedia of Integer Sequences, Preprint (2012). [PDF]
5. H. D. Nguyen, Polar Isotropy Actions on Compact Weakly Symmetric Spaces, Preprint (2001). [PDF]
6. H. D. Nguyen, Tautochrones on Riemannian Manifolds, Preprint (1998). [PDF]

Educational Publications

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

Talks

1. Ensemble Learning using Error Correcting Output Codes: New Classification Error Bounds, 2021 IEEE 33nd International Conference on Tools with Artificial Intelligence (ICTAI), 11-2-2021.
2. Anomaly Detection and Zero-Shot Learning With Error-Correcting Output Codes, Vietnam-USA Joint Mathematics Meeting Quy Nhon, Vietnam, 6-13-2019.
3. Partitions of Steiner Equiangular Tight Frames, Joint Math Meetings Baltimore, CA, 1-16-2019.
4. A new efficient decoding algorithm for correcting multiple insertion or deletion errors in Helberg codes, Joint Math Meetings San Diego, CA, 1-13-2018.
5. On a series formula for the area of the Mandelbrot set and Zagier's conjecture, Mathfest Chicago, IL, 7-28-2017.
6. Filtering and Decoding Non-binary Tenengolts Codes Capable of Correcting Multiple Insertion/Deletion Errors, Joint Math Meetings Atlanta, GA, 1-7-2017.
7. The Digital Binomial Theorem for Sheffer Sequences, Mathfest Columbus, OH, 8-6-2016.
8. The Mathemagics of Error-Correcting Codes, South Jersey Math Alliance, 12-4-2015.
9. The Digital Binomial Theorem, Rowan Math Dept Colloquium, 3-23-2015.
10. A New Proof of the Prouhet-Tarry-Escott Problem, Joint Math Meetings, 1-11-2015.
11. A New Proof of the Prouhet-Tarry-Escott Problem, Rowan Math Dept Colloquium, 9-29-2014.
12. Digital Sequences and Doppler Tolerant Waveforms in Radar, Addis Ababa University, Ethiopia, 5-19-2014 (invited lecture)
13. The Prouhet-Thue-Morse Sequence and Doppler Tolerant Waveforms in Radar, Rowan Math Dept Colloquium, 3-31-2014.
14. New Convolution Identities for Hypergeometric Bernoulli Polynomials, Joint Math Meetings, 1-15-2014.
15. Identities to DIE For: Differentiating, Integrating, and Expanding Bernoulli Polynomials, Rowan Math Dept Colloquium, 3-27-2013.
16. Mining the OEIS: Ten Experimental Conjectures, Joint Math Meetings, 1-9-2013: [PDF]
17. Data Mining the OEIS for New Identities, MAA-NJ Section Spring Meeting 2012, 3-31-12: [PDF]
18. Head Bites Tail: Crunching Numbers to Match Integer Sequences, Rowan Math Dept Colloquium, 12-8-11: [PDF]
19. Experimental Mathematics and Data Mining: Extracting Identities from the Online Encyclopedia of Integer Sequences, Mathfest 2011, 8-4-11: [PDF]
20. Experimental Mathematics and Data Mining: Excavating the Online Encyclopedia of Integer Sequences for New Mathematical Identities, Rowan Math Dept Colloquium, 1-23-11: [PDF]
21. A Combinatorial Formula for Certain Two-Dimensional Sequences Related to Generalized Bernoulli Polynomials, Joint Math Meetings 2011, 1-9-11: [PDF]
22. Sums of Products of Hypergeometric Bernoulli Polynomials, MAA-NJ Section Meeting Spring 2010, 4-10-10: [PDF]
23. Foot to the Pedal: Constant Pedal Curves and Surfaces, Joint Math Meetings 2010, 1-13-10: [PDF]
24. Euler, Goldbach and Exact Values of Cosine, Euler Society Annual Conference 2009, 7-13-09: [PDF]
25. Discovering Bernoulli Number Identities Via Euler Maclaurin Summation, Joint Math Meetings 2009, 1-7-09: [PDF]
26. Bernoulli = Bernoulli: Discovering Bernoulli Number Identities via Euler-Maclaurin Summation, Rowan Math Dept Colloquium, 9-24-08 [PDF]
27. Paradoxical Euler or Integration by Differentiation: A Synopsis of E236, Euler Society Annual Conference 2008, 7-21-08 [PDF]
28. Translating Euler's Works: How to get your students' feet wet in undergraduate research, Joint Math Meetings 2008, 1-6-08 [PDF]
29. Pascal's Square: Determinants, Bernoulli Polynomials, and the Arithmetical Triangle, MathFest 2007, 8-5-07: [PDF]
30. Appell Sequences and Hypergeometric Bernoulli Polynomials, Joint Math Meetings 2007, 1-5-07: [PDF]
31. How Bernoulli Did It: Sums of Powers, Generating Functions, and Bernoulli Numbers, Rowan Math Seminar, 10-11-06: [PDF]
32. A Half-Marriage in Error: When Zeta Integrates a Gaussian, MAA-NJ Section Meeting Spring 2006, 4-8-06: [PDF]
33. Newton's "Greatest Blunder": His theorem on revolving orbits and failed calculation of lunar precession, Rowan Math Seminar, 3-1-06: [PDF]
34. The Search for Nothing: A zero-free region of hypergeometric zeta, Rowan Math Seminar, 10-5-05: [PDF]
35. Newton's Greatest Blunder, MathFest 2005, 8-5-05
36. Hypergeometric Zeta Functions, Joint Math Meetings, 1-5-05: [PDF]
37. Hypergeometric Zeta Functions, Rowan Math Seminar, 9-29-04
38. Solitons: From Canal Water Waves to Molecular Lasers, Philadelphia IEEE Night, 5-20-03

Positions

• Rowan Representative, New Jersey Big Data Alliance, 2018-Present
• Governor, MAA New Jersey Section, 2015-2018
• Chair, Department of Mathematics, Rowan University, 2007-2010
• Chair, MAA New Jersey Section, 2007-2009
• Vice Chair for Speakers, MAA New Jersey Section, 2003-2006
• Founding Director, Garden State Undergraduate Mathematics Conference (GSUMC), March 27, 2004
• Public Information Officer, MAA New Jersey Section, 2001-2003

TECHNOLOGY

SageMath Student Instruction Manual

• SageMath Advice for Calculus (PDF)
• SageMath Advice for Calculus - Examples (Sage file)

LINKS

• Rowan University
• UC Berkeley Math Dept.
• Mathematical Association of America (MAA)
• American Mathematical Society (AMS)

PERSONAL

• Personal website