# √(-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
e-mail: robert  DOT styer AT  villanova  DOT  edu

Director of the Comprehensive Science Program
Info about the Laboratory Sciences minor

## Teaching

Office Hours:

See syllabi on Blackboard.  I prefer meeting by appointment (call or email me anytime to set up a time)

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:

My favorite senior seminar class model

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).

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## Research interests:

I am interested in analytic and elementary number theory. My thesis involved Hecke theory over number fields. 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  (student presentation nicely summarizing the proofs)

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.

Article in SIAM NEWS October 1997 on industrial mathematics  pdf

Research Productivity and Pareto's Law, in the Fall 2003 The Department Chair pdf

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 explored multiplicative persistence

Around 2005 a group headed by MaryAngela Papalaskari developed a Magic School which taught STEM ideas to high school students using Harry Potter as the hook.  These papers contain some information about this.

Papalaskari, M. A., Hess, K. L., Lagalante, A. F., Nadi, N., Styer, R. A., Way, T. P., Weinstein, R. D. (2007). Work in Progress: Engineering the Magic School - Creativity and Innovation in Context. 37th ASEE/IEEE Frontiers in Education Conference.

Papalaskari, M. A., Hess, K., Kossman, D., Metzger, S., Phares, A. J., Styer, R. A., Titone, C., Way, T. P., Weinstein, R. D., Wunderlich, F. J. (2006). PIVOTS: Service Learning at the Science, Theatre & Magic Boundary. 36th ASEE/IEEE Frontiers in Education Conference, 18-23.

In 2021-2022 I had the privilege of helping with a "gamefication" computer science teaching grant which resulted in this paper: Dicheva, D., Cassel, L., Styer, R., Dichev, C., Guy, B., Irwin, K. (2022). An Empirical Study of the Effects of Virtual Currency on Learners in Out of Class Practicing. In: Hilliger, I., Muņoz-Merino, P.J., De Laet, T., Ortega-Arranz, A., Farrell, T. (eds) Educating for a New Future: Making Sense of Technology-Enhanced Learning Adoption. EC-TEL 2022. Lecture Notes in Computer Science, vol 13450. Springer, Cham. https://doi.org/10.1007/978-3-031-16290-9_6   https://link.springer.com/chapter/10.1007/978-3-031-16290-9_6

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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 eight children.  Amy is married to Fadi Greene and is a biochemistry professor at Albright, with three children.  Melanie works for the USDA as a food inspector.  Joe is married to Wei, with 2 children, and works for Capital One.  Andy works for the Veteran's Administration. David is in twelfth grade and Daniel is in ninth.  The twins, Sahari and Mariah, are eleven.

An interesting Styer family history blog:
https://styerstories.family.blog/author/dopplichdutchman/

Pictures on the right: 50th Styer Reunion 1998 (on grass), Hill Reunion 2011 (at Camp Epachiseca).
My dad was one of 12, my mom one of 9, so I have lots of cousins!

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Finding Math Facts

Math Organizations

Math Software

• GeoGebra
• Group Explorer (subgroups and cosets of small groups)
• 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
• MathMatize has very nice "quiz game" setup with nice questions to review math content (I liked the linear algebra section)

Fun Math Pages

Math Teaching Service Opportunities

Misc Math

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• Online shopping site (an alum showed me this)
URL:  http://www.marketamerica.com/sanusiglobal/
Note: this link is organized by one of my former (outstanding) students.
• Math Lesson Plans Lesson Planet helps math teachers quickly find teacher-reviewed online math lesson plans and worksheets.

• 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.
• OnlineMathDegrees.org  Online (Higher Ed) Math Programs and some info on math careers.
• Faith Giant, for those who want to grow in faith.

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12/05/2023 :