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Good book on Galois groups

  1. Jun 26, 2014 #1
    I want to get a decent introduction into group theory and Galois groups. Can somebody recommend a good book that I can use for self-study? The book of Stewart - Galois Theory looks promising.
  2. jcsd
  3. Jun 26, 2014 #2
    Off the top of my head one thing that really stands out about Stewart's is the really thorough example of finding specific Galois groups & whatnot associated with [itex]x^4 - 2[/itex] over the rationals. It's not the only book that uses it as an example but in Stewart's it seems a lot more detailed than in others. I think I remember the rest being fairly user-friendly also. I guess there are worse books you could use for an intro. You might want to supplement with a book on group theory also.
  4. Jun 27, 2014 #3
    Thanks for your input. I'm thinking about supplementing this with the book 'abstract algebra' by Dummit and Foote.
    I noticed that Stewart also has a lot of exercises with worked out solutions that will be helpful in self-study.
  5. Jun 27, 2014 #4
    I haven't studied galois at all but I was browsing the cambridge books they use and this stood out for some reason. It may or may not be useful but I didn't see the harm in mentioning it. These are the books that are deemed appropriate for the Cambridge Maths tripos Galois Theory Course(third course taken to do with groups):

    E. Artin Galois Theory. Dover Publications (£6.99 paperback)
    I. Stewart Galois Theory. Taylor & Francis Ltd Chapman & Hall/CRC 3rd edition (£24.99)
    B. L. van der Waerden Modern Algebra. Ungar Pub 1949 (Out of print)
    S. Lang Algebra (Graduate Texts in Mathematics). Springer-Verlag New York Inc (£38.50 hardback) I. Kaplansky Fields and Rings. The University of Chicago Press (£16.00 Paperback)

    Stewart and Artin are both mentioned.

    Groups, Rings and Modules(second course taken):

    P.M.Cohn Classic Algebra. Wiley, 2000 (£29.95 paperback)
    P.J. Cameron Introduction to Algebra. OUP (£27 paperback)
    J.B. Fraleigh A First Course in Abstract Algebra. Addison Wesley, 2003 (£47.99 paperback)
    B. Hartley and T.O. Hawkes Rings, Modules and Linear Algebra: a further course in algebra. Chapman
    and Hall, 1970 (out of print)
    I. Herstein Topics in Algebra. John Wiley and Sons, 1975 (£45.99 hardback)
    P.M. Neumann, G.A. Stoy and E.C. Thomson Groups and Geometry. OUP 1994 (£35.99 paperback) M. Artin Algebra. Prentice Hall, 1991 (£53.99 hardback)

    Group Theory(first course taken - may be basic(?)):

    M.A. Armstrong Groups and Symmetry. Springer–Verlag 1988 (£33.00 hardback)
    † Alan F Beardon Algebra and Geometry. CUP 2005 (£21.99 paperback, £48 hardback).
    R.P. Burn Groups, a Path to Geometry. Cambridge University Press 1987 (£20.95 paperback)
    J.A. Green Sets and Groups: a first course in Algebra. Chapman and Hall/CRC 1988 (£38.99 paper-
    W. Lederman Introduction to Group Theory. Longman 1976 (out of print)
    Nathan Carter Visual Group Theory. Mathematical Association of America Textbooks (£45)

    This may be of some use...

    Again, sorry if it's absolutely worthless. :tongue:
  6. Jun 27, 2014 #5


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    Last edited by a moderator: May 6, 2017
  7. Jun 30, 2014 #6


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    the one from David Cox is a good read.
  8. Jul 2, 2014 #7
    Thanks for all your suggestions. The Cambridge list is definitely helpful, because for me it's sometimes difficult to see the difference in level between the different books. Cox' book also looks interesting. The book of Tignol also looks nice, I like the historical approach. The book of Artin seems to be a classic, but just looking at the pages strains my eyes.
    I am also checking some online material on galois theory, the one from Miles Reid looks good.
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