The 2008 Arizona Summer Program will be an exciting 4-week research experience for undergraduates interested in Computational Group Theory and its applications (partially taking place at the Biosphere). There will be several lecture series given by experts covering the various areas of computational Group theory accomponied by hands-on lab sessions using the free Computer Algebra system GAP. Students will work in teams of 3 or 4 on projects inspired by current problems in the area of computational Group theory and its applications. The lecture series will cover the following topics:

- Permuation groups
- Matrix groups
- Finitely presented groups
- Coding Theory
- Cryptography
- Representation Theory of finite Groups

Teams will be formed on the basis of interests and mathematical skills. Each team will be mentored by a faculty member and a graduate student, and will give regular oral reports on its progress to the whole group of participants and mentors. Students will prepare a poster describing their work and present it in a poster session held at the end of the program.

The program will also include lectures or workshops on the following topics:

- Introduction to GAP
- How to give a presentation using LaTeX and Beamer
- How to write a resume and how to prepare for graduate school
- An overview of graduate programs across the country
- Presentations by developers of Computer Algebra software.

The program will also feature field trips and other enrichment activities, such as:

- The Arizona Sonora Desert Museum
- Kitt Peak Observatory
- Mount Graham
- Karchner Caverns
- Chiricuahua Mountains
- Local companies: IBM, optics, or nanotech companies, Raytheon

- Dates: June 30 - July 25, 2008
- Location: The University of Arizona, Tucson Arizona
- Housing: Students will be housed at no cost and will be given an allowance for food.
- Stipend: Students will receive a stipend of $1200 and an allowance for travel expenses.
- Eligibility: The program is open to undergraduates and to students who will graduate in Spring 2008. To be eligible, students must be US citizens or permanent residents and have some background in mathematics (see below).

To apply, send these documents:

- An application form
- A brief statement (1-2 pages) about your interest in the program, what you hope to contribute, and what you hope to get out if it.
- Undergraduate transcripts (unofficial copies are ok)
- A list of mathematics courses and other possibly relevant courses with mathematical content. For each course, list the instructor, the textbook, the topics covered, and your grade.
- A letter of recommendation from someone who knows your mathematical talents. (Your referee might find these hints useful.)

to this address:

Arizona Summer Program 2008 Department of Mathematics University of Arizona Tucson, AZ 85721

postmarked on or before **February 15, 2008**.

Students should have had solid courses in Linear Algebra and preferable also in abtract Algebra. Some experience with mathematical software (such as GAP, Maple, or Mathematica) will be helpful but not essential. The ability to work independently and in teams is crucial.

If you have questions, please contact us at `klux@math.arizona.edu`