Preliminary syllabus

Here is the first paragraph of original syllabus submitted to UMass governance when the course was approved.

This course is a rigorous introduction to abstract algebra focusing on structures and problems relevant to the secondary mathematics curriculum: elementary number theory, rings of polynomials and rational expressions, factorization in Euclidean domains, field extensions, and Euclidean constructions.
It's a pretty good first approximation to what we will cover. But I expect to digress from it pretty often as we find out collectively where our interests and talents lie.

Style

Here's a letter from a prospective student, and my answer - it provides some idea of what I have in mind.


 > From: a prospective classmate
 > To: eb@cs.umb.edu
 > Subject: Re: Math 560 at UMass Boston - update
 > Date: Thu, 22 Dec 2005 07:44:43 -0800 (PST)
 > 
 > Hello Mr. Bolker,
 >    
 >   I am very interested in taking your
 >   course this semester.  I have some questions...Will we be writing
 >   papers in this course or is it a mainstream/axiomatic math
 >   course?  Will we be discussing curriculum development for
 >   secondary ed?  I am asking these questions because I may be
 >   taking a full-course load in order to include this class-that's
 >   (4) classes.  And my life is already too busy with full time work 
 >   and family  obligations.

I don't think you'll be "writing papers". There will be some homework
assignments like those in a regular math course (work problems, prove
theorems). But I wouldn't describe it as "mainstream axiomatic". I'm
as interested in thinking about how to think about mathematics as I am
in just teaching you more mathematics.

Part of the class I think I want to run as a seminar, with students
taking turns presenting material they've prepared on topics related
to but not central to the official syllabus.

If it works out for the students I may encourage small group projects
- but that might be difficult for people working full time and meeting
only once a week at school.

I don't plan to do anything explicit about secondary ed curriculum
development, since I really don't know enough to be of help. But I do
intend to ask the class regularly how the mathematics we're covering
might affect what happens in the high school classroom - that's
something I want to learn. The answers will guide what we do in the
course as it progresses.

I expect the course to be lots of fun - and lots of work. I'd like to
have you in it - but don't know whether I can honestly encourage you
to commit the time. Clearly your family and your job have (and should
have) prior claim on your time. But I don't want to discourage you
either ... 

Prerequisites

There are no formal prerequisites for this course. You should love mathematics, and be reasonably experienced at it.

Where and when?

The course meets Tuesday from 5:30 to 8:30 with a short break in the middle. The official room is W01-0030. Not my first choice. No windows, and not a good room for mathematics since it has just one small blackboard.

Fortunately, I have been able to arrange matters so that we can (almost always) use the Dean's conference room, in the Dean's office on the second floor of Wheatley.