WELCOME!
|
|
|
|
TEACHING
CURRENT SCHEDULE
Note: Students enrolled in my courses
should log into Blackboard for complete
access to course materials.
Fall 2008
- Math 01.507.01, Wed 6:30-9pm, Robinson 310
|
TIME/DAY |
MON |
TUE |
WED |
THU |
FRI |
|
2-3pm |
|
|
|
|
|
|
4-5:30pm |
OFFICE HOURS
|
|
|
||
|
5-6:30pm |
|
|
OFFICE HOURS
|
|
|
|
6:30-9pm |
|
|
Math 01.507.1 Differential Geometry Robinson 310 |
|
|
|
|
|
|
|
|
|
Note: I am also available by appointment. Feel free to also just stop by my office.
Ph.D. Math (1996),
B.S. Mathematics and B.S.
Electrical Engineering (1990),
MATHEMATICAL RESEARCH
My Interests:
- MSC: 22EXX Lie Groups, 53CXX Global Differential Geometry, 35Q51 Solitons, 11MXX (Zeta Functions)
- I am currently involved in the Student Translations of Euler’s Mathematics (STEM) Project. I am also collaborating with my colleague, Abdul Hassen, to study hypergeometric zeta functions, a generalization of the classical Riemann zeta function based on its integral definition, and their connections to Bernoulli polynomials. See the list of papers below.
- My other interests include 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).
- Euler,
Goldbach and Exact Values of Trigonometric Functions (with Elizabeth Volz), Preprint (2008). [PDF]
- Paradoxical
Euler: Integrating by Differentiating (with Andrew Fabian), Preprint (2008). [PDF]
- Bernoulli
Polynomials and Pascal’s Square (with Robert Booth), to appear in The Fibonacci Quarterly. [PDF]
- Hypergeometric
Bernoulli Polynomials and Appell Sequences (with Abdul Hassen), to appear in Intern. J. Number
Theory. [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]
- A Zero Free
Region for Hypergeometric Zeta Functions (with Abdul Hassen), Preprint
(2005). [PDF]
- Hypergeometric
Zeta Functions (with Abdul Hassen), to appear in Intern. J. Number Theory. [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), W. H. Freeman, 2009, ISBN:
1-4292-2578-5. 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
- 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
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
MATHEMATICAL EDUCATION
Projects
Proof Study (Math Seminar Course, Fall 2001)
- Math Survey: Understanding Proof (PDF)
- Proof Study: Gender Differences (PDF)
- Proof Questionnaire (PDF)
Introduction to Mathematical Reasoning (course proposal, Word document)
CUPM Curriculum Guide: Undergraduate Programs
and Courses in the Mathematical
Sciences
PROFESSIONAL ACTIVITIES
- Chair, MAA-NJ, 2007-2009
- Chair-elect, MAA-NJ, 2006-2007
- Vice Chair for Speakers, MAA-NJ, 2003-2006
- Conference Director, Garden State Undergraduate Mathematics Conference (GSUMC), March 27, 2004
- Public Information Officer, MAA-NJ, 2001-2003
TECHNOLOGY
Mathematica Student Tutorial Manuals
Projects
LINKS
PERSONAL