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Topic: What difficulties encountered by beginners in abstract algebra?
Replies: 17   Last Post: Jan 20, 2013 6:16 AM

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William Elliot

Posts: 1,702
Registered: 1/8/12
Re: What difficulties encountered by beginners in abstract algebra?
Posted: Jan 7, 2013 4:48 AM
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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?



Date Subject Author
1/6/13
Read What difficulties encountered by beginners in abstract algebra?
Dan Christensen
1/6/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Porky Pig Jr
1/7/13
Read Re: What difficulties encountered by beginners in abstract algebra?
William Elliot
1/7/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Dan Christensen
1/9/13
Read Re: What difficulties encountered by beginners in abstract algebra?
William Elliot
1/10/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Shmuel (Seymour J.) Metz
1/10/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Michael Press
1/11/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Herman Rubin
1/11/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Michael Press
1/20/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Michael Press
1/7/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Paul
1/8/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Ken.Pledger@vuw.ac.nz
1/10/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Michael Press
1/9/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Michael Stemper
1/9/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Ken.Pledger@vuw.ac.nz
1/9/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Brian Q. Hutchings
1/20/13
Read Re: What difficulties encountered by beginners in abstract algebra?
Frederick Williams

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