On impulse about a month ago (and trying to use up a discount-coupon ;-), I purchased a little math reference volume at my local Barnes and Noble, entitled "Math In Minutes: 200 Key Concepts Explained in an Instant" by Paul Glendinning (or "Maths In Minutes" for the British version). Turns out it was published in 2012, even though I didn't see it 'til a few weeks back (as a British offering it may have taken awhile to reach the States).
Anyway, wasn't planning to mention it here, but occurs to me it might make an okay stocking stuffer for some budding math person on your holiday shopping list so I'll give it a plug. At about 5"x 5"x 1" it will literally fit in some oversized fireplace stockings! Amazon describes it, in part, thusly:
"...simple and accessible... introduction to 200 key mathematical ideas... described by means of an easy-to-understand picture and a maximum 200-word explanation… Compact and portable format -- the ideal, handy reference.""Ideal" is probably too strong a word, but definitely "handy." The format actually is reminiscent (in miniature) of Clifford Pickover's wildly-popular "The Math Book," in so much as there is generally a brief text on the left-hand page followed by a pertinent (black-and-white) picture on the right-hand page. Not as glossy or beautiful as Cliff's work, and the text is even thinner (indeed, rather superficial) than Pickover's, but the trade-off is a very portable, bite-size volume, that still touches a lot of ground. Also, unlike Pickover's strictly chronological format, the Glendinning offering categorizes its 200 ideas into broader topic areas:
- Sequences and series
- Functions and calculus
- Vectors and matrices
- Abstract algebra
- Complex numbers
- Spaces and topology
- Logic and proof
- Number theory
Again, it's not a great book you need to rush out and get for your own shelf, but perhaps a fun little reference/gift for some young mathematician you want to surprise.