Revision as of 05:44, 21 July 2010

The Purdue Research in Mathematics Experience (PRiME) is a program intended to support and document various research projects by students in mathematics at Purdue. It also exposes students to new resources available to them, such as Rhea, and Sage.

Participants

Anyone affiliated with Purdue willing to document project in mathematics is welcome to participate in PRiME. If you want to be added to the official list of participants below, just add yourself. The emphasis of PRiME is to expose the excitement of doing mathematics.

• Matt Davis (Purdue 10' Alumnus)
• James Ryan (Undergraduate Student)
• Jamie Weigandt (Graduate Student)

Projects

Matt Davis and Jamie Weigandt will be learning about the generalization of the ABC conjecture to number fields, and using the data in Cremona's tables of elliptic curves to write down atypical ABC triples over number fields of degree ≤6.

James Ryan will we working through William Stein's free online book Elementary Number Theory: Primes, Congruences, and Secrets

Schedule

Monday, July 12, 2010

• 7:30 - 9:30 in MSEE 393: PRiME Kickoff with the Nova Special on Fermat's Last Theorem

Wednesday, July 14, 2010

• Discussed material from chapter 1 of Stein's Book.

Thursday, July 15, 2010

• Discussed euclidean algorithm
• Started sage tutorial

Friday, July 16, 2010

• James Ryan will present the main result which makes the euclidean algorithm work.
• Matt, James, and Jamie will begin discussing Mazur's notices article about the ABC conjecture.
• Start an article about ABC triples

Wednesday, July 21, 2010

• Continue discussing Mazur's article.
• Introduction of the Erdos-Woods Problem

Research Focus Questions

• Is there an algorithm for deciding the Erdos-Woods Problem?
• If so, is this algorithm practical?
• Can we find *bad* Erdos-Woods examples?
• Can we find *really bad* Erdos-Woods examples?

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