This is the homepage of Robert Styer (picture)
Department of Mathematical Sciences, Villanova University,
800 Lancaster Avenue, Villanova, PA 19085-1699 USA
Office: Saint Augustine Center (SAC) 367
Phone: (610) 519 4845
Fax: (610) 519 6928
e-mail: robert DOT styer AT villanova
DOT edu
Spring 2008: Math 1505 Calculus II, Math 2600 Foundations
Office Hours:
I prefer meeting by appointment (call or email
me anytime to set up a time)
Learning
Resources
Math Learning and Resource Center
Writing Center
Citrixweb
Gateway
Past Course Info (including Math-Physics materials)
Some Educational Modules I enjoyed making
Bouncing Ball
Module (old version) An introduction to geometric series.
The complete updated version has been published in the Journal
of Online Mathematics and its Applications, Volume 7, 2007.
Tower of Blocks and
Harmonic Series Module An introduction to harmonic series.
Trisecting a Line Segment
Geometric constructions with ruler and compass, or
ruler, or compass.
I am interested in analytic and elementary number theory. My thesis involved Hecke theory over number fields. For some years I worked on conjectures by Imre Katai in additive and multiplicative number theory.
I have been helping Reese Scott with Diophantine equations research. Here are some articles and other work we have done on exponential Diophantine equations.
As a byproduct of the senior seminar in Fall 96, one of the students, Amy Eschleman, got me interested in the "ones" problem. The problem is to use the symbols 1, +, x, (, and ) to represent a number with the least number of ones. For instance, 6 = (1+1)x(1+1+1) uses five ones to represent six. 11 = 1+(1+1)(1+1+1+1+1) represents 11 with only eight ones. If we let f(n) be the least number of ones needed to express n, then some questions are: is f(n) <4 log(n)/log(3)? If p is a prime, is f(p) = 1+f(p-1)? Is f(2p) = min{1+f(2p-1), 2+f(2p-2)}? and many similar questions. This problem has all the hallmarks of many frustrating number theory problems. It is easy to state, and it interweaves addition and factorization in a way that makes probability arguments attractive but proofs hard to find. I have no hope of finding any proofs, but hope to find counterexamples to those conjectures which might be wrong. So perhaps if we calculate f(n) up to the millions or billions we might find possible counterexamples. So far, however, I have failed and perhaps there is not a counterexample. (See Richard Guy's book Unsolved Problems in Number Theory published by Springer for info on many more great problems.)
I also have been trying to create educational modules on basic calculus topics such as geometric series and harmonic series. (See links under Courses.) And here is a paper on Three: Lines, Triangles and the Trinity written for the November 2001 Experiences of God in the Disciplines Sophia Papers conference. Here is a review I wrote of the excellent Ordinary Differential Equations educational software ODE Architect.
An interesting treatment of the problem of Quantum Measurement has been worked out by a MIT graduate and colleague of mine and can be found on the arxiv preprint server, Problems of Quantum Measurement. A published announcement on Quantum Entanglement has appeared. (separate page for Quantum Measurement.)
Here is info on consecutive happy numbers, inspired by a senior seminar student talk in Fall 2007.
My wife Peggy has a degree in early childhood education from Ohio State, and sees Ohioans as the epitome of goodness. She is intelligent; in our premarital counseling personality test, Peggy scored 70 percent on the abstract reasoning, while I scored 30 percent (together we are 100%!). She has a sanguine personality, and we all too often talk till the wee hours of the morning. (photo of us at azalea garden.) Peggy tutors algebra and is a certified Wilson reading tutor, by the way, so if you need an algebra or a certified Wilson reading tutor, contact us!
Our oldest child, Amy, is now at college studying biochemistry and violin performance. Melanie, Joey and Andy are in the Pennsylvania CyberCharter School.
Amy enjoys playing violin. She also likes science; in May 2003 she was privileged to compete at the International Science Fair in Cleveland, Ohio, and May 2004 went as an observer to the Portland Oregon ISEF. Melanie loves reading, and also loves to go outside on her own to daydream, or to play games with her friends. In the fall of 2007 she organized a Shakespeare practice on Friday afternoons for Much Ado About Nothing to be performed in January. Melanie plays flute. She loves the 4H sheep projects, and she dog-sits to make money. Joey likes soccer and Boy Scouts and computer games and jazzy piano. Andrew plays trumpet and likes to sing around the house; his favorite activities are playing computer games or lying around reading a book. We have a guinea pig and a rabbit.
Finding Math Facts
Math Organizations
Math Software
Misc Math
