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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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Paul

Posts: 450
Registered: 7/12/10
Re: What difficulties encountered by beginners in abstract algebra?
Posted: Jan 7, 2013 5:48 PM
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On Monday, January 7, 2013 4:46:37 AM UTC, 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?
>

Difficulties with the basic concepts of abstraction and applying axioms, insisting on thinking merely with intuition. For example, some wrongly deny that for a group G, the subgroup generated by the empty set is the trivial subgroup. They argue (falsely) "Obviously, the empty set can't generate a group." Common questions like "Is the identity element in any group always equal to 1?" indicate a difficulty with thinking at the right level of abstraction. Many texts help with the necessary types of abstract thinking.

Paul Epstein



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
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William Elliot
1/7/13
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Dan Christensen
1/9/13
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William Elliot
1/10/13
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Shmuel (Seymour J.) Metz
1/10/13
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Michael Press
1/11/13
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Herman Rubin
1/11/13
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Michael Press
1/20/13
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Michael Press
1/7/13
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Paul
1/8/13
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Ken.Pledger@vuw.ac.nz
1/10/13
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Michael Press
1/9/13
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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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