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I am looking for fun, interesting mathematics textbooks which would make good studious holiday gifts for advanced mathematics undergraduates or beginning graduate students. They should be serious but also readable.

In particular, I am looking for readable books on more obscure topics not covered in a standard undergraduate curriculum which students may not have previously heard of or thought to study.

Some examples of suggestions I've liked so far:

  • On Numbers and Games, by John Conway.
  • Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups, by John Meier.
  • Ramsey Theory on the Integers, by Bruce Landman.

I am not looking for pop math books, Gödel, Escher, Bach, or anything of that nature.

I am also not looking for books on 'core' subjects unless the content is restricted to a subdiscipline which is not commonly studied by undergrads. (E.g. Finite Group Theory by Isaacs would be good, but Abstract Algebra by Dummit and Foote would not.)

  • 0
    How about Kassel's *Braid Groups*? http://www.amazon.com/Braid-Groups-Graduate-Texts-Mathematics/dp/1441922202/ref=reg_hu-rd_add_1_dp2012-12-24
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    How about *Fourier Analysis*, T.W. Korner, Cambridge University Press, 1988? (the "o" in "Korner" needs an umlaut, but I can't seem to get one there...)2012-12-24
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    What about the Princeton Companion? http://press.princeton.edu/titles/8350.html It would be excellent for someone at that stage of mathematical life2012-12-24
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    Just out of curiosity, does G.E.B. have a bad reputation among the actual maths community?2012-12-24
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    @JustinL. Actually I usually hear people speak well of it. It was just a good example of the type of thing I was not looking for.2012-12-25
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    I DO want to make a comment to the OP here-in the wee hours of Christmas day. Having reviewed Issacs' book for the MAA,it would be an EXTRAORDINARY undergraduate indeed who could read it beyond the first few chapters. This would be a second year graduate textbook at most institutions-the later chapters in particular are VERY demanding.So I think it isn't realistic to put this one on your list.2012-12-25

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