Date: Jan 7, 2013 4:48 AM
Author: William Elliot
Subject: Re: What difficulties encountered by beginners in abstract algebra?

On Sun, 6 Jan 2013, wrote:
> On Sunday, January 6, 2013 11:46:37 PM UTC-5, Dan Christensen wrote:

> > I am working on some introductory notes for group theory. What
> > difficulties are typically encountered by math or science undergrads
> > in an introductory course on abstract algebra?

> The same kind of difficulties as moving from Calculus to Analysis. Need
> set theory, need some intro to logic and proofs.

What do you mean need an introduction to logic and proofs?
I learned logic and proofs during my high school sophomore year
in the Euclidean geometry class. Where are they these days?

> In fact, the same difficulties are encountered by those taking the
> course of Linear Algebra. With a mindset of Calculus, they don't realize
> it's quite a different ball game. No longer "just go ahead, apply some
> rules, do some number crunching, get the answer". So they expect to
> spend a few minutes right before the class start to do the homework, and
> of course they fail. What they must realize: need some time to think and
> absorb the problem. I went through all of that.

Learn to think? Don't they learn that in high school? Weird.
When I entered college, thinking was taken for granted.
Now we have to teach kids to be homo sapiens?

What's all the pre-algebra, pre-calculus, pre-math, pre-school
pre-stuff about? Does it teach anything or is it just various
sorts of kindergarten school?