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.
> 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 ...
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.