Fun but serious mathematics books to gift advanced undergraduates.

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).

Answer

  • Check into Generatingfunctionology by Herbert Wilf.

    From the linked (author’s) site, the second edition is available for downloading as a pdf. There is also a link to the third edition, available for purchase.

    It’s a very helpful, useful, readable, fun, (and short!) book that a student could conceivably cover over winter break.


  • Another promising book by John Conway (et. al.) is The Symmetries of Things, which may very well be of interest to students.

  • One additional suggestion, as it is a classic well worth being placed on any serious student’s bookshelf: How to Solve It by Georg Polya.

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