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).
- 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.