MAT5900--001, Fall 2006
Seminar in Research Experience (CRN 21289)

Instructors:
Dr. Timothy Feeman. Office: SAC 373; Phone and voice mail: (610) 519-4693;
e-mail: timothy.feeman@villanova.edu  Fax: (610) 519-6928;
Office hours: Mon. & Wed. 10:30 am to 12:00 pm; Tues. 11:30 am to 1:00 pm; and by appointment.

Dr. Osvaldo Marrero. Office: SAC 327; Phone and voice mail: (610) 519-4844;
e-mail: osvaldo.marrero@villanova.edu  Fax: (610) 519-6928;
Office hours: TBA and by appointment.

Research teams     Project I: presentation schedule   Guidelines for written reports

Research teams:  The research teams and assigned readings teams for your work in this course are as follows.

• L. Ahlschlager, C. Muller: Rectangles in rectangles, by John E. Wetzel
• R. Crane, L. Klatka, S. Rawlins: Invariants under group actions to amaze your friends, by Douglas E. Ensley
• K. Denby, T. Hallett, E. Pilong: Rootless matrices, by Bertram Yood
• S. Hartman, K. Soderlund, B. DeGeorge: Row coincidences in nonsingular binary matrices, by Osvaldo Marrero and Paul Pasles
• L.Donohue, J. O'Connor, K. Behnken: Encryption using a variant of the Turning-Grille method, by Stephen Fratini
• M. Donohue, H. Moy, L. Priebe: Apollonian cubics: An application of group theory to a problem in Euclidean geometry, by Paris Pamfilos and Apostolos Thoma

Project I: The presentation schedule for the first project is as follows. Each presentation should be about 20 minutes in length. All written reports are due by the end of class on Wednesday, October 18.

Monday, October 16.

• 1:30 - 1:50  M. Donohue, H. Moy, L. Priebe: Apollonian cubics
• 1:55 - 2:15  L. Ahlschlager, C. Muller: Rectangles in rectangles
• 2:20 - 2:40  L.Donohue, J. O'Connor, K. Behnken: Encryption

Wednesday, October 18.

• 1:30 - 1:50  S. Hartman, K. Soderlund, B. DeGeorge: Row coincidences
• 1:55 - 2:15  K. Denby, T. Hallett, E. Pilong: Rootless matrices
• 2:20 - 2:40  R. Crane, L. Klatka, S. Rawlins: Invariants under group actions

Guidelines for written reports. Your written report should include a description of the main problems or questions addressed in the paper that you read as well as a discussion of the author's motivation for considering these problems. Your report should include illustrations or examples that you worked out that help to explain or motivate the problems. Your report should discuss, in your own words, the chief mathematical tools, ideas, and approaches that were used in the paper to solve the problems. It is not necessary to recapitulate every detail of every proof; instead, try to give a feel for what the principal arguments and techniques were that were used. If you found portions of the author's argument to be difficult or confusing, you can say so in your report. Your report should also include a section that describes unanswered questions or problems that the paper raised in your thinking. (This section will serve as an introduction to your work in the second portion of this seminar.) Finally, your report must include a list of references, presented in the correct professional format. This list should include not only the paper itself but also any other sources you may have consulted in the process of reading and understanding the paper.

In sum, your report should

• describe, motivate, and illustrate the main questions addressed in the paper;
• discuss in your own words the principal mathematical techniques and approaches that were used in the paper to answer these questions;
• present some new questions for future research that arise from the reading;
• include a list of references.

last revised: 11-december-2006