## Wednesday, November 23, 2011

### Math Girls: A Novel Way to Learn Some Deep Math

I asked for a review copy, but I can't even wait until I finish it to tell you about this marvelous book. Math Girls was published just yesterday. (How I love the internet, let me count the ways!) My thanks to Robert Talbert for his blog post on the book, and to Bento Books for sending me a review copy so I can satisfy my desire for immediate gratification. You can download a sample (first two chapters) from Bento Books here.

Math Girls has gone through 18 printings in Japan, and the English translation has just been released. There are lots more books in the series, but those of us who don't read Japanese will have to wait for those.

Here's a bit for flavor:

When you’re doing math, you’re the one holding the pencil, but that doesn’t mean you can write just anything. There are rules. And where there are rules, there’s a game to play—the same game played by all the great mathematicians of old. All you need is some fresh paper and your mind. I was hooked.

I had assumed it was a game I would always play alone, even in high school. It turned out I was wrong.

Our protagonist, a high school student, is intrigued by Miruka, an elusive girl at his school who gives him challenging math problems to ponder:
“Forget about the matrices for now,” she said. “Here’s a problem for you.”

Problem 3-1
Give a general term an in terms of n for the following sequence:
n     0 1  2 3 4 5   6  7···
an    1 0 −1 0 1 0 −1 0 ···
“Think you can you do it?” she asked.
“Sure, that’s easy. All you’re doing is going back and forth between 1, 0, and −1. Sort of. . . oscillating between them.”
“That’s all you see?”
“Am I wrong?”
“Not wrong, exactly. Go ahead and give me a generalization.”

And our protagonist (I don't know his name yet) helps another student, Tetra, with her math. So you get to see the same ideas played out at higher and lower levels. When Miruka kicked Tetra's chair out from under her, I had to skip the math to find out what would happen next between the characters. I'm not sure the storyline will make complete sense to me, but I am so loving it!

Tony, the rep from Bento books made a request:
If you blog about Math Girls, please be sure to let your readers know that this is a pretty advanced book. We’ve had many inquiries from parents looking for fun books for their middle school and younger children who love math, but Math Girls is probably best suited to, at a minimum, talented high school juniors and seniors who want to go beyond what they’re likely to be exposed to in a high school curriculum. The “sweet spot” for our readership will probably be first or second year college math majors who are looking for a more relaxed treatment of some of the stuff that they’re plunging into.

I'm counting the math lovers on my holiday gift list, and planning to buy each of them a copy. I'll be reading the rest of the book on the plane to Seattle this evening. And I'll let you know soon whether the adult content extends past the math.

===

It's Friday now. I just finished. My review copy is a pdf, and I need a paper copy to study the math. I just bought 4 copies; one for me, and 3 for the math lovers in my life. (Oops! I just thought of someone else I need to get it for.)

The topic I'm most interested in studying more closely is called the "Basel problem". It asks for an exact sum (in closed form) of the series . I knew the answer, but had no idea, until I read Math Girls, how it was derived. I've started to see it, and I love what I'm seeing through the mist. The coolest thing is how connected it is to what I'm teaching in Calculus II.

The only complaint I have about the mathematical exposition is when derivatives are given with no real explanation in chapter 9. I think that could have been fleshed out a bit more.

I would highly recommend this book for anyone at the level of pre-calculus and above who enjoys math. (There is no adult content besides the math.)