enrolled in my courses should log into Blackboard
for access to course materials (requires Rowan username and password).
- Math 01.330 Real Analysis,
MW 2-3:15pm, Robinson 227
- Math 03.160 Discrete Structures,
TR 11-12:15pm, James 2105
- Math 03.160 Discrete Structures,
TR 3:30-4:45pm, Robinson 310
Previous courses taught
Math (1996), University of California - Berkeley (thesis advisor: Joseph A. Wolf)
- Thesis: Weakly symmetric spaces and bounded symmetric domains [Postscript]
Mathematics and B.S. Electrical Engineering (1990), University of Minnesota
- Current research projects: I am currently involved in
Visit my eXperimental Mathematics Laboratory (XML) website at to learn more
about the following projects:
- Partitions of frames: this project seeks to construct partitions of
frames whose spectral norms satisfy bounds specified in the recent work of Marcus, Spielman, and Srivastava on their positive
solution of the Kadison-Singer problem.
- Error-correcting codes: 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.
- Complementary code matrices (CCM): this project seeks to search and classify complementary code matrices,
which generalize Hadamard matrices and Golay pairs, and find new applications in the field of communications.
- Area of the Mandelbrot set: this project seeks to approximate the area of the Mandelbrot set by improving the upper bound
of 1.72 obtained by Ewing and Schober using complex analysis.
- Previous research projects:
- Eureka: this project seeks to mine the Online Encyclopedia
of Integer Sequences for new mathematical identities. See my preprint
listed below (under 'Research Papers'), recent talks listed below (under ‘Talks’),
or visit my Eureka website
for more information.
Translations of Euler’s Mathematics (STEM)
(in particular understanding soliton interaction
in terms of particle decay and the corresponding interaction between ghost
- Lie groups and differential geometry, where I have studied
weakly symmetric spaces (a generalization of Elie Cartan's symmetric spaces) and tried to
understand their connections to a well known circle of ideas: Gelfand
pairs, spherical pairs, spherical varieties, commutativity
of invariant differential operators, multiplicity-free actions (both in
the sense of representation theory and symplectic geometry).
NOTE: Asterisk '*' indicates undergraduate student
- A Digital Binomial Theorem for Sheffer Sequences (with Toufik Mansour), Preprint (2015). [PDF]
- A q-Digital Binomial Theorem (with Toufik Mansour), Preprint (2015). [PDF]
- A Digital Binomial Theorem, Preprint (2014). [PDF]
- Mining the Online Encyclopedia of Integer Sequences (with Douglas Taggart*), Preprint (2012). [PDF]
NOTE: Asterisk '*' indicates undergraduate student
- New Approximations for the Area of the Mandelbrot Set (with Daniel Bittner*, Long Cheong*, and Dante Gates*), to appear in Involve. [PDF]
- Group Symmetries of Complementary Code Matrices (with Brooke Logan*), to appear in IEEE Trans. Aerospace and Electr. Systems. [PDF]
- Doppler Tolerance, Complementary Code Sets, and the
Generalized Thue-Morse Sequence
(with Greg E. Coxson), to appear in IET Radar, Sonar and Navigation.
- New Multiple Insertion-Deletion Correcting Codes for Non-Binary Alphabets (with Tuan A. Le), IEEE Trans. Information Theory 62 (May 2016), no. 5, 2682-2693. [PDF]
- A New Proof of the Prouhet-Tarry-Escott Problem,
INTEGERS 16 (2016), #A1 (9 pp).
- A Generalization of the Digital Binomial Theorem, J. Integer Sequences 18 (2015), Article 15.5.7 (20 pp). [PDF]
- A Mixing of Prouhet-Thue-Morse Sequences and Rademacher
Functions, INTEGERS 15 (2015), #A14 (16 pp).
- 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.
- New Convolution Identities for Hypergeometric Bernoulli Polynomials (with Long Cheong*), J. Number Theory 137 (2014), pp. 201-221. [PDF]
- Generalized Binomial Expansions and
Bernoulli Polynomials, INTEGERS 13 (2013), #A11 (13 pp). [PDF]
- 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)
- Moments of Hypergeometric Zeta Functions (with Abdul Hassen), J. Algebra, Number Theory: Advances and Applications 7 (2012), No. 2, pp. 109-129. [PDF]
- A Zero-Free Region for Hypergeometric Zeta
Functions (with Abdul Hassen), Intern. J. Number Theory 7 (2011), No. 4, pp. 1033-1043. [PDF]
- Hypergeometric Zeta Functions (with
Abdul Hassen), Intern. J. Number Theory 6 (2010), No. 1, pp. 99-126. [PDF]
- Bernoulli Polynomials and Pascal’s Square (with Robert Booth*), Fibonacci
Quarterly 46/47 (2008/2009),
No. 1, pp. 38-47. [PDF]
- Hypergeometric Bernoulli Polynomials and Appell Sequences (with Abdul Hassen), Intern. J.
Number Theory 4 (2008), No. 5, pp. 767-774. [PDF]
- 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]
- The Error Zeta Function (with Abdul Hassen), Intern. J.
Number Theory 3 (2007), No. 3,
pp. 439-453. [PDF]
- 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]
- 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]
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
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
symmetric spaces and bounded symmetric domains, Transformation Groups 2 (1997), No. 4, pp. 351-374. [PDF]
Isotropy Actions on Compact Weakly Symmetric Spaces, Preprint (2001). [PDF]
- Tautochrones on
Preprint (1998). [PDF]
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]
- 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
- The Mathemagics of Error-Correcting Codes, South Jersey Math Alliance, 12-4-2015.
- The Digital Binomial Theorem, Rowan Math Dept Colloquium, 3-23-2015.
- A New Proof of the Prouhet-Tarry-Escott Problem, Joint Math Meetings, 1-11-2015.
- A New Proof of the Prouhet-Tarry-Escott Problem, Rowan Math Dept Colloquium, 9-29-2014.
- Digital Sequences and Doppler Tolerant Waveforms in Radar, Addis Ababa University, Ethiopia, 5-19-2014 (invited lecture)
- The Prouhet-Thue-Morse Sequence and Doppler Tolerant Waveforms in Radar, Rowan Math Dept Colloquium, 3-31-2014.
- New Convolution Identities for Hypergeometric Bernoulli Polynomials, Joint Math Meetings, 1-15-2014.
- Identities to DIE For: Differentiating, Integrating, and Expanding Bernoulli Polynomials, Rowan Math Dept Colloquium, 3-27-2013.
- Mining the OEIS: Ten Experimental Conjectures, Joint Math Meetings, 1-9-2013:
- Data Mining the OEIS for New Identities, MAA-NJ Section Spring Meeting 2012,
- Head Bites
Tail: Crunching Numbers to Match Integer Sequences, Rowan Math Dept
Colloquium, 12-8-11: [PDF]
Mathematics and Data Mining: Extracting Identities from the Online
Encyclopedia of Integer Sequences, Mathfest
2011, 8-4-11: [PDF]
Mathematics and Data Mining: Excavating the Online Encyclopedia of Integer
Sequences for New Mathematical Identities, Rowan Math Dept Colloquium, 1-23-11: [PDF]
Combinatorial Formula for Certain Two-Dimensional Sequences Related to
Generalized Bernoulli Polynomials, Joint Math
Meetings 2011, 1-9-11: [PDF]
- Sums of
Products of Hypergeometric Bernoulli Polynomials, MAA-NJ Section Meeting Spring 2010, 4-10-10: [PDF]
- Foot to the
Pedal: Constant Pedal Curves and Surfaces, Joint Math Meetings 2010, 1-13-10: [PDF]
- Euler, Goldbach and Exact Values of Cosine, Euler Society Annual Conference 2009, 7-13-09: [PDF]
- Discovering Bernoulli
Number Identities Via Euler Maclaurin Summation, Joint
Math Meetings 2009, 1-7-09: [PDF]
- Bernoulli = Bernoulli:
Discovering Bernoulli Number Identities via Euler-Maclaurin
Summation, Rowan Math Dept Colloquium, 9-24-08 [PDF]
- Paradoxical Euler or
Integration by Differentiation: A Synopsis of E236,
Euler Society Annual Conference 2008, 7-21-08 [PDF]
- Translating Euler's
Works: How to get your students' feet wet in undergraduate research, Joint Math Meetings
2008, 1-6-08 [PDF]
- Pascal’s Square: Determinants,
Bernoulli Polynomials, and the Arithmetical Triangle,
MathFest 2007, 8-5-07: [PDF]
- Appell Sequences and Hypergeometric
Bernoulli Polynomials, Joint Math Meetings 2007, 1-5-07: [PDF]
- How Bernoulli Did It: Sums of
Powers, Generating Functions, and Bernoulli Numbers, Rowan
Math Seminar, 10-11-06: [PDF]
- A Half-Marriage in Error: When
Zeta Integrates a Gaussian, MAA-NJ Section Meeting Spring
2006, 4-8-06: [PDF]
- Newton’s “Greatest Blunder”: His theorem on revolving orbits and
failed calculation of lunar precession,
Rowan Math Seminar, 3-1-06: [PDF]
- The Search
for Nothing: A zero-free region of hypergeometric zeta, Rowan Math Seminar, 10-5-05: [PDF]
Greatest Blunder, MathFest 2005, 8-5-05
Zeta Functions, Joint Math Meetings, 1-5-05: [PDF]
Zeta Functions, Rowan Math Seminar, 9-29-04
From Canal Water Waves to Molecular Lasers, Philadelphia IEEE
- Governor, MAA New Jersey Section,
- Chair, Department of Mathematics, Rowan University,
- Chair, MAA New Jersey Section,
- Vice Chair for Speakers, MAA New Jersey Section,
- Founding Director, Garden
State Undergraduate Mathematics Conference (GSUMC),
March 27, 2004
- Public Information Officer, MAA New Jersey Section,
Student Instruction Manual