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Math books for self study

  1. Dec 19, 2009 #1
    I study physics and i find math very interesting.

    I'm using Michael Spivak's "Calculus" and i think it's really good book.

    Spivak's book is great sample of book that i desire - it's for mathematicians, not for physicist, but you can understand it even if your not a mathematician.

    And it have problems that demand more than just using some kind of pattern (atleast it seems so, i solved just few).

    I'm looking for linear algebra book, abstract algebra and number theory book (for freshman).
    If this is book without problems, then i need one with problems too - but problems that require more than just using a pattern.

    And any other book that is as good as Spivak's Calculus.
     
  2. jcsd
  3. Dec 19, 2009 #2
    For linear algebra, I think if you like Spivak then you'll like Linear Algebra Done Right by Sheldon Axler. Another book I like is Linear Algebra by Hoffman and Kunze; apparently the book by Friedberg, Insel and Spence is similar but I have not read it myself.

    For abstract algebra I recommend Herstein's Topics In Algebra, which has challenging problems and excellent, clear exposition. Another book that's regularly recommended as is as challenging as Herstein is the book by Michael Artin: Algebra.

    Sorry I can't help you with number theory, I haven't studied it.
     
  4. Dec 22, 2009 #3
    For abstract and linear algebra, I recommend reading Algebra by Artin cover to cover. Artin provides crucial commentary that would provide some much needed intuition for you as you first grapple with the concepts. He also emphasizes concrete, elegant constructions over abstract, logical development. For instance, he develops much of group theory through an extended study of the group of motions of the Euclidean plane. It's a bizarre approach, and there are a number of standard topics that are left out in order to make room for the special topics. But it works exceptionally well provided you read it in the order Artin intended, i.e., cover to cover.

    I first learned rings from Herstein's Abstract Algebra. Then I read the chapter on rings in Artin's book and my views were fundamentally changed. The sections on quotient rings and adjunction of elements were particularly insightful.

    I took a course in number theory last semester, and we used Elementary Number Theory: Primes, Congruences, and Secrets by William Stein. It's a decent book, but it has an unusual focus on algebraic techniques despite discussing exclusively elementary number theory. I believe elementary number theory is best attacked from a variety of viewpoints, including both the algebraic and the analytic approaches. For this purpose, I think An Introduction to Number Theory by Everest and Ward is a really awesome book. It often gives multiple proofs of the same result using different techniques and perspectives. It's at the graduate-level, but I found it very easy to read. (Disclaimer: I've only read the first few chapters.) You can see a preview here: http://books.google.com/books?id=mG...resnum=5&ved=0CBwQ6AEwBA#v=onepage&q=&f=false
     
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