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Book of Algebra Problems

  1. Nov 12, 2006 #1
    Studying for the math GRE and I need source of abstract algebra problems. I have/understand all the theory books, just need to get quick at the basics!

    Are any of the Schaum's worthwhile?
    Abstract Algebra, ISBN 0071403272, 450 problems, bad Amazon reviews
    Modern Abstract Algebra, ISBN 0070026556, 425 problems
    Group Theory, ISBN 0070041245, "hundreds" of problems

    Any other suggestions?
  2. jcsd
  3. Nov 12, 2006 #2
    None of those. Get this
    http://www.amazon.com/Cracking-Math-Test-Graduate-Prep/dp/0375764917/sr=8-1/qid=1163377555/ref=pd_bbs_sr_1/102-6965815-5635368?ie=UTF8&s=books [Broken]

    It's more compact. The others have too much information and you don't have the time to learn so much right now. This book gets you through all the theory as quick as possible and it has practice problems similiar to those on the GRE. It's quite a bit to learn, but the book does a good job since it's very concise. You should focus on calculus. Goodluck.
    Last edited by a moderator: Apr 22, 2017 at 1:59 PM
  4. Nov 12, 2006 #3


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    Uh.. there's abstract algebra on the GRE?

    - Warren
  5. Nov 12, 2006 #4
    abstract algebra, graph theory..yup......math gre...
  6. Nov 12, 2006 #5


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    this from the gre website:

    The test consists of 66 multiple-choice questions,
    drawn from courses commonly offered at the under-
    graduate level. Although the Mathematics Test has
    been rescaled, the content of the test has not changed.
    Approximately 50 percent of the questions involve
    calculus and its applications —subject matter that can
    be assumed to be common to the backgrounds of
    almost all mathematics majors. About 25 percent of
    the questions in the test are in elementary algebra,
    linear algebra, abstract algebra, and number theory.
    The remaining questions deal with other areas of
    mathematics currently studied by undergraduates in
    many institutions.
    The following content descriptions may assist
    students in preparing for the test. The percentages
    given are estimates; actual percentages will vary
    somewhat from one edition of the test to another.
    Calculus — 50%
    Material learned in the usual sequence of elementary
    calculus courses — differential and integral calculus
    of one and of several variables — including calculus-
    based applications and connections with coordinate
    geometry, trigonometry, differential equations, and
    other branches of mathematics
    Algebra — 25%
    Elementary algebra: basic algebraic techniques and
    manipulations acquired in high school and used
    throughout mathematics
    Linear algebra: matrix algebra, systems of linear
    equations, vector spaces, linear transformations, char-
    acteristic polynomials, eigenvalues and eigenvectors
    Abstract algebra and number theory: elementary
    topics from group theory, the theory of rings and
    modules, field theory, and number theory
    Additional Topics — 25%
    Introductory real analysis: sequences and series of
    numbers and functions, continuity, differentiability
    and integrability, elementary topology of \0 and \0n
    Discrete mathematics: logic, set theory, combina-
    torics, graph theory, and algorithms
    Other topics: general topology, geometry, complex
    variables, probability and statistics, and numerical
    The above descriptions of topics covered in the test
    should not be considered exhaustive; it is necessary to
    understand many other related concepts.
  7. Nov 12, 2006 #6


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    the practice test had a few questions on subgroups of Z, groups of order 4, matrices of order 2 and 3, rational roots of polynomials, binomial coefficients, and a question on commutativity of rings.

    almost any algebra book, no matter how elementary would cover these thigns.
  8. Nov 13, 2006 #7
    Thanks for luck, but I'd rather not leave it up to that! I'm not applying to school this year, so I have some time before next April and November. I've been out of school for a while and although I've kept up with theory, my calculation abilities have definitely suffered.

    I've been using "Cracking the GRE" as the basis for my calculus review. I work through the relevant chapters to get a feel for the level/types of problems and my deficiencies. Then I pick up my copy of Stewart or my differential equations book and start solving problems. I last cracked these books as a freshman, but they've again found their use. Especially Stewart and his "Problems Plus" at the end of each chapter. These problems take longer than the types found on the GRE but are of similar level of difficulty.

    So I'm not really looking for a review of theory. It couldn't hurt to have that summary, but I'm really just looking for a book to practice the types/level of problems found on the GRE. Especially the number theory related algebra problems. It's one of the few branches of mathematics that just doesn't interest me (number theory that is).

    So again, not looking for theory or an elementary summary of results. Just a book with a good price per problem and figured one of those would be suitable.
  9. Nov 13, 2006 #8


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    there is an actual gre on their website.
  10. Nov 18, 2006 #9
    I guess I'm just generally frustrated with the dearth of preparation materials. I will post back in a couple of months with my review program and sources of problems I encounter. As with most things, it'll just take an outlay of a few bucks.
  11. Nov 18, 2006 #10
    I recommend:
    Exercises in Algebra: A Collection of Exercises in Algebra, Linear Algebra and Geometry (Algebra, Logic and Applications) by A.I. Kostrikin; Gordon and Breach Publ.
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