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, porky_pig_jr@my-deja.com 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?