# √(-1)        r=1-sin(θ)      μαθ

This is the homepage of Robert Styer,
Department of Mathematics and Statistics, Villanova University,
800 Lancaster Avenue, Villanova, PA 19085-1699 USA
Office: Saint Augustine Center (SAC) 372
Phone: (610) 519 4845
Fax: (610) 519 6928
e-mail: robert  DOT styer AT  villanova  DOT  edu

Director of the Comprehensive Science Program

## Teaching

Office Hours:

See syllabi on Blackboard.  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

Pre 2000 Course Info (including old Math-Physics materials) (anything since about 2000 has the course material buried within Villanova's Blackboard interface)

Some Educational Modules I enjoyed making
Bouncing Balls Module: An introduction to geometric series, 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: Trisecting a Line Segment, LOCI Online Journal Feb 2010 link

Misc:

In Sept 2010 the Villanovans for Life campus group invited several professors to discuss how their prolife views intersect with their professional life; here is my one page statement (pdf, Word).

My favorite senior seminar class model

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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 (a musician/composer who does math on the side to relax!) on Diophantine equations research.
Here are some articles and other work we have done on exponential Diophantine equations.

I also enjoy creating educational modules:
Bouncing Balls Module: An introduction to geometric series, 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: Trisecting a Line Segment, LOCI Online Journal Feb 2010 link

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 an old unsuccessful attempt on the palindrome problem.  My 1981 thesis.

I have also worked on happy numbers, inspired by one of our senior seminar students in Spring 2008.  Some Info on consecutive happy numbers.  Another seminar student led to a paper on multiplicative persistence

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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. (quite old photo and another old photo of us at the azalea garden, the location of an important date many years ago.)   Peggy is a certified Wilson reading tutor.

We have six children.  Our oldest, Amy, is in grad school studying parasitology, and is engaged to Fadi Greene, who is finishing law school. Melanie works for the USDA as a food inspector.  Joe is married to Wei and working for CarMax doing some sort of finance work.  Andy is studying Energy and Environmental Policy at University of Delaware.   David is in fourth grade and our youngest, Daniel, is in second grade, with the Pennsylvania CyberCharter School.  David is high energy, and loves baseball, soccer, and all sports.  Daniel likes his friends in baseball and soccer, likes building with Legos, but really excels at always asking "why?".

Pictures on the right: 50th Styer Reunion 1998, below that is the Hill Reunion 2011.
My dad was one of 12, my mom one of 9, so lots of cousins!

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Finding Math Facts

Math Organizations

Math Software

• GeoGebra  (similar to Geometer's Sketchpad)
Geogebra applets
• Finite Group Behavior (subgroups and cosets of small groups)
• UBASIC (number theory software)
• HippoCampus has lots of material but in particular very nice web modules on calculus
• Khan Academy A large collection of videos (including calculus topics) that many people find helpful (though I find them algorithmic rather than intellectually exciting)
• MIT OpenCourseWare Some good calculus and linear algebra videos and practice exams, aimed at a typical MIT student (that is, above a normal human level!)
• Falstad has some nice math-physics applets

Fun Math Pages

Math Teaching Service Opportunities

Misc Math

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• Online shopping
URL:  http://www.marketamerica.com/sanusiglobal/
Note: this link is organized by one of my former (outstanding) students.
• CBB Christian Bookstore
URL
- www.christianbooksbibles.com

Description – “Christianbooksbibles.com is a leading retailer of Christian books, Bibles and more, helping you and your faith community grows closer to Christ.  With over 100,000 Christian resources such as Bible studies, Small Group curriculum, Sunday school lesson material, Christian fiction, Christian video, and more, we have all that you need!  With unbeatable prices and personalized customer service, CBB is your one stop for Christian resources. ChristianBooksBibles.com is more than a business, it is a ministry.  Let CBB walk with you on your journey of faith.”
Note:  My wife and I like their site.

• Math Lesson Plans Lesson Planet helps math teachers quickly find teacher-reviewed online math lesson plans and worksheets.

• The Peak Directory. (Visit: http://www.peakdirectory.com/cat/universities.html)
The Peak Directory was developed in 2005 as an online search aid with constantly updated categories and fresh topics. Our staff works diligently to create a database of links to the Web's best resources for some of the most sought after and researched topics. Unlike many directories, all of our links are hand selected by members of our staff. Our editors personally assess each submission and search for quality sites to include.

• Online Masters in Biotechnology: useful information on the biotech field and a comprehensive list of university programs.
• Online Christian Colleges  Over 100 accredited online Christian universities and colleges.
• Science Masters' Degree Programs  Masters in Science Degrees lead to excellent careers, and there are a variety of online options.
• OnlineMathDegrees.org  Online (Higher Ed) Math Programs and some info on math careers.
• Online Technology Degrees Two and Four Year Technology Degrees
• MastersDegreeOnline.org -- provides tons of information to current and prospective graduate students. We have over 20 subjects that are relevant for you and your readers. According to a report, compensation varies for different career fields. For example, a mathematics master's degree holder can make \$157,000 annually, while a high school teacher with a master's degree will make \$57,800.  Some degrees provide higher earning opportunities than others and this is why it would be worth considering your interests on the programs being offered to maximize the potential returns of enrolling in a Masters degree.

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08/20/2015 :