Dr. Robert Styer

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

CONTENTS:

 

Teaching schedule and current courses / office hours

Spring 2010  Math 5900 Senior Seminar

Office Hours:
     See syllabi on WebCT.  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

Some Past Course Info (including Math-Physics materials) (most newer material is buried within Web_CT interface)

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 unfinished introduction to harmonic series.        
        Geometric constructions with ruler and compass, or ruler, or compass.  Revised Sept 2009

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Research interests:

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 working with Reese Scott on 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 geometric series, harmonic series, some plane geometry; 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.  Here is my unsuccessful attempt on the palindrome problem.  Here is my 1981 thesis.

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.)

I have also worked on happy numbers, inspired by one of our senior seminar students in Spring 2008.  Here is info on consecutive happy numbers.

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Family

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. (older photo and more recent photo of us at the azalea garden, the location of an important date many years ago.)   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 two oldest children, Amy and Melanie, are in college studying biochemistry and animal sciences.  Joey and Andy are homeschooling for high school, and David is in the kindergarten program of the Pennsylvania CyberCharter School.  Of course, our youngest, Daniel, is not in school yet.  Amy enjoys playing violin, and Melanie plays flute.  Joey likes robotics and soccer and Boy Scouts and computer games and jazzy piano.  Andrew plays trumpet and likes drama and singing; his favorite activities are playing computer games or lying around reading a book. David likes trucks and planes and anything that moves.  We have a guinea pig and a rabbit and a betta fish.  

2008 trip to China to adopt David Chuan Jian Styer

2009 trip to adopt Daniel Liu Chao Styer

More Family Info

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Mathematical Links

Finding Math Facts

Fun Math Pages

Math Organizations

Math Software

Math Teaching Service Opportunities

Misc Math

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Miscellaneous Links

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Link Exchanges

 

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