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I am a high schooler with a deep interest in mathematics, which is why I have self-studied Linear Algebra and have begun my self-study in Differential Equations. As I am a man who likes to plan ahead, I'm pondering what field of mathematics to plunge into once I've finished DE's. I am thinking of Abstract Algebra: it has always sounded mystical and intruiging to me for some reason. I have a couple of questions regarding AA:

  • What exactly is Abstract Algebra? What does it study? Please use your own definition, no wikipedia definition please.

  • What are its applications? Does it have a use for example in physics or chemistry, or is it as abstract as its name suggests?

  • Would it be a logical step for a high schooler to self-study abstract algebra after studying LA and DE's, or is there a field of (post-high school) math 'better' or more useful to study prior to abstract algebra?

  • What are some good books, pdfs, open courseware etc. on abstract algebra? links and names please.

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    Don't plan that far ahead. Sounding mystical doesn't really make it mystical. Some people go to Disneyland and get everything they expected, others go and find themselves underwhelmed. Don't decide too early in life what you are going to be.2012-10-26
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    possible duplicate of [Good abstract algebra books for self study](http://math.stackexchange.com/questions/54839/good-abstract-algebra-books-for-self-study)2012-10-26
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    This comment is wrong on so many levels, I need more than 600 characters. First of all, I just want to self-study, that doesn't mean I'll spend my life doing it. Also, too early in life? I have 2 more years to go until university, now's the right time to 'decide', whatever that may mean. Also, if I get disappointed, I can stop whenever I want, it's not like an unbreakable commitment I make to the field if I decide to read something about it. Also, I expect to finish DE in a year or so, so it's not that far ahead..2012-10-26
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    you might study number theory before looking at abstract. For a first read of abstract I like Galilean's text. You can get an old edition for a couple bucks. Linear algebra is sufficient preparation for that book. See http://books.google.com/books/about/Contemporary_Abstract_Algebra.html?id=CnH3mlOKpsMC2012-10-26
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    @rschwieb This is *not* a duplicate of that question (there are currently 3 votes to close it as such). This question asks things that are not a part of that question. Please be more careful with close votes. Answers to questions like these can prove very valuable to students. This is one of the few places on the net that students can receive informed replies to such questions (and perhaps is the *only* place some folks have access to such expertise).2012-10-26
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    @BillDubuque Will you own up to the precedent and consequences of insisting on keeping every duplicate-with-new-question-tacked-on unclosed? Closures are not bans, you know... they're just a signal that the question needs work.2012-10-26
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    @rschwieb I actually agree to Bill, this does not seem to be a duplicate..2012-10-26
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    @rschwieb Hyperbole aside, the question you linked is *very far* from being a duplicate. It concerns only (part of) the 4th of the OP's questions. One should not be in any rush to close such questions. We are here to *share* mathematical knowledge, not to inhibit such.2012-10-26
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    I **strongly** recommend Pinter's *A Book of Abstract Algebra*. http://www.amazon.com/Book-Abstract-Algebra-Edition-Mathematics/dp/0486474178 It's cheap, it's eminently readable, and it has great problems (with solutions!). It's extremely accessible to an undergraduate or advanced high schooler.2012-10-26
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    @EdGorcenski Will I have to have knowledge of proof-writing, or is that included in the book?2012-10-26
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    @AbstractAlgebra Your question may garner more respect if you change the title to something more serious. The current title may start some folks off on the wrong foot. Alas, a sense of humor is not a *universal* property - even for *algebraists!* $ $ [update: title is now changed, originally it was "Abstract Algebra for Dummies"]2012-10-26
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    I disagree with closing this question.2012-10-26
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    @AbstractAlgebra Pinter has some problems to demonstrate properties, which is just a very basic notion of "proof." His presentation of the material serves as a good tutorial for the basics of how to write proofs. In any case, the problems for entry-level topics in abstract algebra are little more than definition-pushing types of proofs anyways.2012-10-26
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    @BillDubuque I still await (and am not holding my breath for) the answer to my question that I asked you.2012-10-26
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    @EdGorcenski So all in all you would recommend this for someone who has no prior knowledge of proof-writing and abstract algebra (I have of course encoutered some proof-writing in Linear Allgebra, but nothing too impressive)2012-10-26
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    Yes, I would. It is a good introduction to both abstract algebra and abstract thinking. And, for $10 on Amazon, you really cannot go wrong.2012-10-26
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    @rschwieb (and others) The meta site (not the main site) is the proper place to discuss meta issues. Please browse meta or post a new question on meta if you wish to discuss meta issues such as viewpoints on closure.2012-10-26
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    @BillDubuque Fair enough. While we're at it, now is a good time to ask if there's any machinery to withdraw votes. I too disagree with myself on closing this question.2012-10-26
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    @rschwieb That would be nice, but SE doesn't give us any way to undo close votes, afaik. Thanks for keeping an open mind on such. I think many folks waver back and forth on these matters. My views on closure have changed considerably from two years ago.2012-10-26

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