Instructor: Ira Papick

Description: I am planning on offering a graduate level topics course in algebra focusing on polynomial applications in the secondary school curriculum.  The course will tentatively meet twice weekly on Tuesday/Thursday from 1- 2:15 PM (these days and times can be changed if necessary).

The course will be held in seminar format and the students taking the course will do much of the lecturing.  I will start the course with a series of lectures on general properties of polynomial rings.  Topics will include: division algorithm in polynomial rings, factorization in polynomial rings, elementary Galois theory, approximation theorems, Hilbert Basis Theorem and Hilbert Nullstellensatz, polynomials in graph theory, elementary results in algebraic curves, polynomials in linear algebra over commutative rings, polynomials in number theory, and other related topics.

The first student participation aspect of the course will involve a survey of polynomial results and applications in current high school textbooks. The students participating in the seminar will report on their findings in written and oral presentations.

The second student participation aspect of the course will involve searching the mathematics research literature for interesting and appropriate polynomial applications for secondary teachers. Again, the students participating in the seminar will report on their findings in written and oral presentations.

Prerequisite: The main prerequisite for the course is a graduate course in abstract algebra or permission of the instructor (Ira J Papick).  This course is specifically designed for doctoral students in Mathematics Education and/or graduate students in Mathematics with an interest in Mathematics Education.