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

seriousbut alsoreadable.

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 notlooking 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 Theoryby Isaacs would be good, butAbstract Algebraby Dummit and Foote would not).

**Answer**

- Check into
by Herbert Wilf.*Generatingfunctionology*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
, which may very well be of interest to students.*The Symmetries of Things*

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

**Attribution***Source : Link , Question Author : Community , Answer Author : Community*