Should I try to change the way Abstract Algebra is taught at my university? If so, how?

manpreet Best Answer 2 years ago

[This (soft) question should be Community Wiki.]

Background:

A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the material presented in this course would be somewhat different from the things I had learned previously (including subjects like calculus, linear algebra, logic, graph theory, et cetera). I also knew Abstract Algebra is a very broad subject, and many modern subjects are rooted in its matter, including Algebraic Geometry, Algebraic Topology, Algebraic Number Theory, and many more subjects.

I would be disappointed, however. The course was hard. I didn't mind that (I suspected it would). I didn't mind others being naturally better at it than me (as I'm not a particularly talented mathematician).

I do think that I could have learned the material better if it would be presented in a different matter, though. Every student received a little booklet, containing course notes. All material was in there. I felt that the material was presented in quite a dense manner. I like to see a lot of worked examples of new material I'm learning, but there weren't many in there. I guess the booklet covered in 135 pages about the same material the abstract algebra book by Dummit and Foote covers in about 223 pages. I guess a somewhat bigger "reference book", like Dummit and Foote's or Fraleigh's book, would serve me better.

Furthermore, we had to do a lot of exercises from the booklet. Each week, we had to hand in assignments, consisting of exercises in the booklet. Everything went pretty fast. Your work would be checked and graded, but the "ideal" solutions would not be shown on, for example, a webpage. I also found that disappointing, because I often learn a lot from worked solutions to exercises I do not (completely) understand.

In the end, I barely passed the course and decided that I would not follow more abstract algebra courses in the future. This was "Abstract Algebra I". Next year, there were optional courses called "Abstract Algebra II" and "Abstract Algebra III". These courses contain subject matter on Rings, Fields, Galois Theory, Ideals, and more. This meant that, along with about half of my classmates who also would not be attending these further courses, I wouldn't learn about these interesting subjects.

Sure, I can buy some "easy" introductory abstract algebra book (like Pinter's) and work my way through it, but I doubt it's the "real deal" and I will understand the material as well as my classmates who will follow "Abstract Algebra II" and "Abstract Algebra III".

I think this way, many talent is wasted. The abstract algebra courses feel a bit like a rat race, in which only the very best survive (until the end of algebra III). I don't think this is o.k. . It seems to me that the notions developed abstract algebra could aid you in the study of other subjects that may not be explicitely related to abstract algebra.

Questions:

Should I even bother trying to change the way abstract algebra is currently taught at my university? Do you think these complaints are legitimate? Or should I stop whining and accept abstract algebra just isn't for me, nor ever will be?

If you think these complaints are, at least to a certain extend, legitimate, I wonder how you think I should tell my university professors to do things differently.

Just to be clear: I think I won't benefit from the changes made in the way this subject is taught at our university (if any changes are to be made at all), since by then I probably will have already finished my bachelor's degree. So this question is intented for future students.

manpreet 2 years ago