WELCOME!
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TEACHING SCHEDULE
Note: Students enrolled in my courses should log into Blackboard for access to course materials (requires Rowan username and password).
Spring
2013
- Math 03.150 Discrete Math,
MW 12:15-1:30pm, Robinson 201A
- Math 01.330 Real Analysis,
TR 12:15-1:30pm, Bunce 109
- Math 01.507 Differential Geometry,
T 6:30-9pm, Science 254
Ph.D.
Math (1996),
B.S.
Mathematics and B.S. Electrical Engineering (1990),
MATHEMATICAL RESEARCH
Mathematical
Interests:
- I am currently involved in
an experimental mathematics research project called Eureka, which 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. Other on-going research projects include
hypergeometric zeta functions and hypergeometric Bernoulli polynomials.
- My previous research projects include Student
Translations of Euler’s Mathematics (STEM),
solitons
(in particular understanding soliton interaction
in terms of particle decay and the corresponding interaction between ghost
particles) and 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).
- Mining the Online Encyclopedia of Integer Sequences (with Douglas Taggart), Preprint (2012). [PDF]
- Generalized Binomial Expansions and
Bernoulli Polynomials, INTEGERS: The Electronic J. of Combinatorial Number Theory 13 (2013), #A11, pp. 1-13. [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://www.maa.org/editorial/euler/HEDI%2060%20Curves%20and%20paradox.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]
- Euler, Goldbach and Exact
Values of Trigonometric Functions (with Elizabeth Volz), Preprint (2008). [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
- Polar
Isotropy Actions on Compact Weakly Symmetric Spaces, Preprint (2001). [PDF]
- 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]
- 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]
- Tautochrones on
Riemannian Manifolds,
Preprint (1998). [PDF]
- Weakly
symmetric spaces and bounded symmetric domains, Transformation Groups 2 (1997), No. 4, pp. 351-374. [PDF]
- Weakly
symmetric spaces and bounded symmetric domains, Ph.D. Thesis (1996). [Postscript]
[PDF]
Educational
Publications
- 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]
- 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]
Recent
Talks
- Data Mining the OEIS for New Identities, MAA-NJ Section Spring Meeting 2012,
3-31-12: [PDF]
- Head Bites
Tail: Crunching Numbers to Match Integer Sequences, Rowan Math Dept
Colloquium, 12-8-11: [PDF]
- Experimental
Mathematics and Data Mining: Extracting Identities from the Online
Encyclopedia of Integer Sequences, Mathfest
2011, 8-4-11: [PDF]
- Experimental
Mathematics and Data Mining: Excavating the Online Encyclopedia of Integer
Sequences for New Mathematical Identities, Rowan Math Dept Colloquium, 1-23-11: [PDF]
- A
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]
- The Search
for Nothing: A zero-free region of hypergeometric zeta, Rowan Math Seminar, 10-5-05: [PDF]
- Newton’s
Greatest Blunder, MathFest 2005, 8-5-05
- Hypergeometric
Zeta Functions, Joint Math Meetings, 1-5-05: [PDF]
- Hypergeometric
Zeta Functions, Rowan Math Seminar, 9-29-04
- Solitons:
From Canal Water Waves to Molecular Lasers,
Projects
Experimental Math Summer
Enrichment Program 2009
Student
Translations of Euler’s Mathematics (STEM)
Animated GIFs of solitons:
- KdV
1-soliton
- KdV
2-solitons
- SGE 1-soliton
- SGE 2-solitons
- Particle Decay of
KdV 2-solitons
- Particle Decay of
KdV 3-solitons
Java
applets of solitons:
Classification
Tables
PROFESSIONAL ACTIVITIES
- Chair, MAA-NJ,
2007-2009
- Chair-elect, MAA-NJ,
2006-2007
- Vice Chair for Speakers, MAA-NJ,
2003-2006
- Founding Director, Garden
State Undergraduate Mathematics Conference (GSUMC),
March 27, 2004
- Public Information Officer, MAA-NJ,
2001-2003
TECHNOLOGY
Mathematica
Student Tutorial Manuals
LINKS
- Rowan Math Dept.
- Rowan University
- UC Berkeley Math Dept.
- Mathematical Association of America (MAA)
- American Mathematical Society (AMS)
PERSONAL