This is the website for the 2010 MAA PREP course in Algebraic Number Theory. The MAA PREP is funded by the National Science Foundation (NSF grant DUE-0817071).
The Organizers
The PREP course will be lead by John Cullinan and Allison Pacelli.
Workshop Description
Number theory is an ideal setting for exciting students about mathematics, and for training students to do mathematics research. There are a large number of easily stated open problems in the field. In addition, students can generate examples, make conjectures, and prove theorems. This workshop is aimed at college and university faculty who wish to learn more about number theory, in particular, the area of algebraic number theory.
Algebraic number theory begins with the story of Fermat’s Last Theorem. In 1847, Lamé announced a complete proof of the theorem; unfortunately, his proof was incorrect because he was assuming that certain rings (the cyclotomic integers) were unique factorization domains, and this is not always the case. Although it was almost 150 more years until the theorem was proven, the field of algebraic number theory was born, in part, to address the issue of unique factorization.
Goals of the workshop:
1)Participants will learn how to use powerful software (freely available online) to supplement their teaching and enhance research projects.
2)Participants will be able to teach an undergraduate course in algebraic number theory (at either the sophomore/junior or senior capstone level), or supplement existing courses (including abtract algebra, number theory, and discrete math) with material from algebraic number theory.
3)Participants will be able to begin research projects in the area of algebraic number theory.
4)Participants will be able to involve undergraduates in algebraic number theory research projects.
No prior knowledge of the field is required to register for this workshop, however, comfort with basic abstract algebra is necessary. Participants will be expected to learn some material before the workshop begins; there will be also be a pre- assignment designed to familiarize participants with some of the software that we will be using during the workshop.
Important Information
The workshop will be held from June 28 to July 2 at Williams College in Bronfman Science Center. Food and accommodations are included in the workshop fee. Information on Accommodations can he found here. More information will be added as it becomes available.
Getting Here
Directions to Williams are located here. You can view a campus map here.
Daily Schedules
Each day will consist of a combination of lecture, groupwork, and presentations. The day will last roughly from 9am to 4pm, with a break for lunch. Wednesday will be a half-day giving participants a chance to explore and enjoy the area.
Computing
Computing will figure prominently in this course, both as a tool for exploring new topics, and for designing projects for use by undergraduates. You will be asked to do one of two things before arriving at the workshop: either install gp-pari directly onto your computer from this site (the program needs to be compiled; it's not hard, but requires some attention); or create an online account with sage here (you will need to set your sage notebook to gp). The advantage to using sage is that you can save your notebooks for future reference and it is an easy way to give demonstrations in class. The advantage to having gp-pari on your machine is that it runs faster.
Recreational Information
Participants will have access to the Williams College athletic facilities, including a 50 meter indoor pool, basketball courts, tennis courts, squash courts, fitness center, weight room, and track. There are many hiking trails within walking distance to campus as well. Nearby Attractions Include:
Sterling and Francine Clark Art Institute
MASS MoCA - Massachusetts Museum of Contemporary Art