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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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Dan Christensen

Posts: 2,439
Registered: 7/9/08
Re: What difficulties encountered by beginners in abstract algebra?
Posted: Jan 7, 2013 9:37 AM
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On Monday, January 7, 2013 4:48:55 AM UTC-5, William Elliot wrote:
> 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?
>


Studies have shown that proof-writing skills learned in one branch of mathematics such as geometry may not be easily transferred to other branches such as abstract algebra and analysis.

F. A. Ersoz (2009) suggests that the many informal "axioms" of Euclidean geometry, as usually taught, are based largely on personal intuition and imagination (p. 163). While this may serve as a productive basis for some discussion, it can blur the boundary between the formal and informal, and lead to confusion as to what constitutes a legitimate proof in other domains (branches) of mathematics.

Ersoz also suggests that introductory geometry courses seldom present many of the methods of proof used in more abstract courses ? methods like proofs by induction, contrapositive or contradiction (p. 164). http://140.122.140.1/~icmi19/files/Volume_1.pdf

Dan


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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