This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
You should add ring modules,vector spaces,and algebras at least. Remag12@yahoo.com 05:42, 10 January 2006 (UTC)
Abstract algebra/Archive 1 ( | talk | history | protect | delete | links | watch | logs | views) was formerly listed as a good article, but was removed from the listing because the article lists none of its references or sources -- Allen3 talk 20:36, 18 February 2006 (UTC)
I took this up to review it just as it got coincidentally removed from the list. There should've been a Template:GAnominee placed at the top of this page when it was nominated, too. Oh well, here's my comments anyway.
This is, essentially, an important article, that should bring a clear and engaging overview of a field of mathematical activity. Many readers of the Mathematics article will, as their next port of call, fancy a dip into some of the various branches, and the Abstract Algebra article will sometimes be first stop - readers will be enticed by the image of a Rubik's Cube or the mention of root2.
I think that the article currently pitches to undergraduate mathematicians and higher, and that it remains quite opaque for readers with less experience than that. It specialises far too soon and makes few concessions to the more vivid elements of its subject. As it resides "near the front of" the mathematics Wikirealm, its duty is to offset its specialism with a much gentler pace, more informal language and vividity in the exposition. That said, the existing prose is very eloquent and much of it definitely deserves to remain.
The "Example" has a superb introductory sentence more suited to the whole article's introduction. The actual example assumes a lot of knowledge. I think that a more appropriate level of example would be (for instance) one in which several disparate objects are shown to have inverses relative to an identity. The notions of homomorphism and isomorphism so crucial to abstract algebra should also be expanded upon, preferably with an example.
Much more should be made of abstract algebra's branches. Prominent or thriving subdivisions such as group theory or boolean algebras should be expanded upon in an elementary and vivid way, most easily with examples. Or at the least, there should be pointers to tangible articles such as examples of groups. As it is, the history is generalised down into a single sentence, and the examples form a list of algebraic structures. Material currently in the introduction needs breaking off into sections, and I suspect some of it can go into "history", with a little expansion.
Examples of abstract algebra's usefulness need expanding upon.
Although vector spaces are listed, neither Linear algebra nor its relationship to abstract algebra are mentioned. The distinction of representation theory is not clear: what is concrete about it that distinguishes it from abstract algebra?
The references and external links are excellent.
I could not have passed the article. It is stable, factually accurate and neutral, but it is not yet sufficiently broad or comprehensible. Topology and Calculus are currently useful comparisons for this article. Please feel free to call upon me for my comments prior to resubmission. -- Vinoir 04:03, 27 April 2006 (UTC)
A recent edit commented out some text, unsure where it should go (if anywhere). Here it is.
Formal definitions of certain algebraic structures began to emerge in the 19th century. Abstract algebra emerged around the start of the 20th century, under the name modern algebra. Its study was part of the drive for more intellectual rigor in mathematics. Initially, the assumptions in classical algebra, on which the whole of mathematics (and major parts of the natural sciences) depend, took the form of axiomatic systems. Hence such things as group theory and ring theory took their places in pure mathematics.
Examples of algebraic structures with a single binary operation are:
More complicated examples include:
See algebraic structures for these and other examples.
I'm not an expert, but it seems that these links should still be present, if only at the end of the article. Geometry guy 02:24, 28 March 2007 (UTC)
"This grants the mathematician who has learned algebra a deep sight, and empowers him broadly." This sentence seems a little odd. I suppose that it's meant to convey the advantages of studying algebra, but what exactly is "deep sight", and how can you be broadly empowered? Can it be clarified, or should we remove it? Hermajesty 18:52, 14 January 2006 (UTC)
In the interest of improving this page, here are some proposed questions that I could imagine a reader of the article either coming here to find the answer, or being pleased to discover the information. Feel free to add questions. -- Jake 21:18, 5 October 2006 (UTC)
Theres something I can do but this is not one of them. Here are some examples: 15 meters to millimeters?, 3.5 tons to pounds?, 6800 seconds to hours? could anyone help me understand how th you get the answer for these? —Preceding unsigned comment added by 72.94.239.161 ( talk) 00:45, 15 September 2008 (UTC)
If I state "X is derived from Y", and quit then I am attempting to state a fact, and it deserves some citation if it is not general knowledge. If I state "X is derived from Y, and here is the evidence for it" then I have a thesis statement. If so, the citations are needed for the evidence I present ostensibly supporting my thesis. So the first [citation needed] is perhaps misplaced, since the ensuing portions of the article go to great lengths to support the thesis, unfortunately in "Early Group Theory" the citations needed are lacking. — Preceding unsigned comment added by 98.169.63.134 ( talk) 02:45, 14 January 2010 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 |
You should add ring modules,vector spaces,and algebras at least. Remag12@yahoo.com 05:42, 10 January 2006 (UTC)
Abstract algebra/Archive 1 ( | talk | history | protect | delete | links | watch | logs | views) was formerly listed as a good article, but was removed from the listing because the article lists none of its references or sources -- Allen3 talk 20:36, 18 February 2006 (UTC)
I took this up to review it just as it got coincidentally removed from the list. There should've been a Template:GAnominee placed at the top of this page when it was nominated, too. Oh well, here's my comments anyway.
This is, essentially, an important article, that should bring a clear and engaging overview of a field of mathematical activity. Many readers of the Mathematics article will, as their next port of call, fancy a dip into some of the various branches, and the Abstract Algebra article will sometimes be first stop - readers will be enticed by the image of a Rubik's Cube or the mention of root2.
I think that the article currently pitches to undergraduate mathematicians and higher, and that it remains quite opaque for readers with less experience than that. It specialises far too soon and makes few concessions to the more vivid elements of its subject. As it resides "near the front of" the mathematics Wikirealm, its duty is to offset its specialism with a much gentler pace, more informal language and vividity in the exposition. That said, the existing prose is very eloquent and much of it definitely deserves to remain.
The "Example" has a superb introductory sentence more suited to the whole article's introduction. The actual example assumes a lot of knowledge. I think that a more appropriate level of example would be (for instance) one in which several disparate objects are shown to have inverses relative to an identity. The notions of homomorphism and isomorphism so crucial to abstract algebra should also be expanded upon, preferably with an example.
Much more should be made of abstract algebra's branches. Prominent or thriving subdivisions such as group theory or boolean algebras should be expanded upon in an elementary and vivid way, most easily with examples. Or at the least, there should be pointers to tangible articles such as examples of groups. As it is, the history is generalised down into a single sentence, and the examples form a list of algebraic structures. Material currently in the introduction needs breaking off into sections, and I suspect some of it can go into "history", with a little expansion.
Examples of abstract algebra's usefulness need expanding upon.
Although vector spaces are listed, neither Linear algebra nor its relationship to abstract algebra are mentioned. The distinction of representation theory is not clear: what is concrete about it that distinguishes it from abstract algebra?
The references and external links are excellent.
I could not have passed the article. It is stable, factually accurate and neutral, but it is not yet sufficiently broad or comprehensible. Topology and Calculus are currently useful comparisons for this article. Please feel free to call upon me for my comments prior to resubmission. -- Vinoir 04:03, 27 April 2006 (UTC)
A recent edit commented out some text, unsure where it should go (if anywhere). Here it is.
Formal definitions of certain algebraic structures began to emerge in the 19th century. Abstract algebra emerged around the start of the 20th century, under the name modern algebra. Its study was part of the drive for more intellectual rigor in mathematics. Initially, the assumptions in classical algebra, on which the whole of mathematics (and major parts of the natural sciences) depend, took the form of axiomatic systems. Hence such things as group theory and ring theory took their places in pure mathematics.
Examples of algebraic structures with a single binary operation are:
More complicated examples include:
See algebraic structures for these and other examples.
I'm not an expert, but it seems that these links should still be present, if only at the end of the article. Geometry guy 02:24, 28 March 2007 (UTC)
"This grants the mathematician who has learned algebra a deep sight, and empowers him broadly." This sentence seems a little odd. I suppose that it's meant to convey the advantages of studying algebra, but what exactly is "deep sight", and how can you be broadly empowered? Can it be clarified, or should we remove it? Hermajesty 18:52, 14 January 2006 (UTC)
In the interest of improving this page, here are some proposed questions that I could imagine a reader of the article either coming here to find the answer, or being pleased to discover the information. Feel free to add questions. -- Jake 21:18, 5 October 2006 (UTC)
Theres something I can do but this is not one of them. Here are some examples: 15 meters to millimeters?, 3.5 tons to pounds?, 6800 seconds to hours? could anyone help me understand how th you get the answer for these? —Preceding unsigned comment added by 72.94.239.161 ( talk) 00:45, 15 September 2008 (UTC)
If I state "X is derived from Y", and quit then I am attempting to state a fact, and it deserves some citation if it is not general knowledge. If I state "X is derived from Y, and here is the evidence for it" then I have a thesis statement. If so, the citations are needed for the evidence I present ostensibly supporting my thesis. So the first [citation needed] is perhaps misplaced, since the ensuing portions of the article go to great lengths to support the thesis, unfortunately in "Early Group Theory" the citations needed are lacking. — Preceding unsigned comment added by 98.169.63.134 ( talk) 02:45, 14 January 2010 (UTC)