Just a few quick book blurbs today....
1) Geometry is being emphasized less these days in secondary school curriculums, even disappearing in some cases. As someone who loved geometry that seems ashamed, though I understand the reasons for it. If only we lived in a Euclidian universe the importance of geometry would remain. But we don't, and your interest in Alfred Posamentier's (with Robert Geretschlager) latest book, "The Circle," will largely depend on your enamorment with geometry (I have a review copy of it; not due for general release 'til latter August).
A few years ago Posamentier was out with "The Secrets of Triangles," a fantastic overview of the geometry of that ubiquitous figure, and now he follows that with this treatment for the triangle's curvier cousin, the circle, in all its glory (triangles make plenty of appearances in this volume as well).
In his usual style, Posamentier sends a firehose of interesting ideas, examples, theorems, problems, etc. at the reader. You can virtually start with any chapter and be assured an interesting ride... as long as you have a yen for geometry. The book contains constructions, "art and architecture," history, and paradoxes, along with an abundance of plane geometry facts/problems/theorems.
2) Avner Ash and Robert Gross's "Summing It Up" is a much more advanced lesson in math, specifically number theory.
Like the Posamentier book this one abounds with examples and specific cases, but that's the only similarity. This is actually the third book from Ash and Gross, and it is focused on modular forms, a very hot topic since Wiles' proof of Fermat's Last Theorem as well as increased interest from the Langlands Program. Though it starts at a more elementary level the book builds toward ideas in number theory that will be difficult for the casual math reader to follow in the second half of the volume. As such it is not so much a "popular" read as an academic-like treatment of, or introduction to, some advanced math. 200 pages of rich, dense reading for the uninitiated. Certainly worth it if number theory is your particular area of interest or you've been wanting an intro to modular forms.
This MAA review of the book offers more details and will give you a better sense of whether or not you're prepared to tackle the subject matter involved:
3) Lastly, and I'm waaaaay late to the party on this one, but just now finishing Nate Silver's 2012 bestseller, "The Signal and the Noise." (Somehow, every time I thought of reading it, other books got in the way.) Anyway, I love this volume; far more interesting and wide-ranging than I realized it would be. A good introduction to Bayesian statistics, but covers a lot of other ground as well. So if by any chance you too passed it up along the way for some reason, I recommend it, especially since this is an election year and of course parts of it pertain especially to election/voter analysis.
Three completely different books, new, old, and forthcoming, that may satisfy very different tastes and levels of math background.
We are passed the halfway point for this year, and usually by now I already have an idea what my favorite math-read of the entire year may turn out to be. This year no single volume stands out for me though above others, so we'll see what the second half of the year brings along.
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