...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Monday, March 9, 2015

Single Digits... and Much, Much More

"Single Digits: In Praise of Small Numbers"  by Marc Chamberland

Several books in recent times have been comprised of "biographical" sketches of numbers... listing interesting tidbits/stories/facts about various integers or other significant numbers. So when an advance review copy of Marc Chamberland's "Single Digits: In Praise of Small Numbers" appeared in my mailbox, I thought to myself, "...seen this approach, been done before... yawwwn."
Getting into the volume though I was very pleasantly surprised! This compact (slightly over 200 pgs.) volume offers up different problems, puzzles, theorems, findings, conjectures on virtually every page. It's a veritable carnival for math geeks!! Yes, its chapters take you through the digits 1 through 9, as a skeletal framework for the book, but the chockfull content goes well, well beyond such simplicity. Indeed, as you're reading the fascinating contents herein you quickly lose sight of whatever tie-in a given chapter has to any "single digit."

Much of the material is not new, and is often classic. But a surprising amount is lesser, or even rarely, known subject matter. I feel safe in saying that both amateur and professional mathematicians alike will find new items of interest here -- LOTS of mathematics grist for thought and play -- with a heavy emphasis on geometry and algebra, and just a smidgen of topology, trig, or other math fields. The last couple of chapters, "8" and "9," are some of the shorter, but also deepest and most difficult chapters in the book.
Alexander Bogomolny has written a quick review of the volume and indicates the surprising breadth of subject matter included (while still only touching on a small sampling of the topics):

Indeed, there is so much real math packed in here I can't really recommend this work for a general audience, but only to those who are already enamored of math or have some good background with it.  This book is not for tepid math folks, but for diving into exhilaratedly with both feet!  There are around 115 topics listed in the table of contents, and of course some of those topics entail further topics.
The title and cover of the book don't really do it justice, nor hint at, the amount, richness, or variety of that mathematical fare inside. In fact, I fear a lot of lay readers, may pick this book up expecting a simpler treatment than what is within, while other mathematicians may not recognize, from the deceptively lightweight look of the book, what a fantastic, useful volume it is!  In short, it's a book I thought might only deserve a passing glance, but in fact is a welcome, splendid, fruitful addition to my math bookshelf. Reading it has left me with a LONG list of interesting things I want to explore further on Google... and oddly, these days, I'm not sure you can pay a book any higher compliment than that!

On Amazon, "Single Digits" is listed as due for June 1 release -- something to anticipate, and can be pre-ordered.

[ I'll note, lastly, that the author Marc Chamberland runs a YouTube site called "Tipping Point Math" here:  https://m.youtube.com/user/TippingPointMath? ]

1 comment:

  1. (the advantage of being in an English-speaking country... you get advance copies!)