|Three high school friends work through some difficult mathematical ideas in this book, recently translated into English from the Japanese original.
The author is apparently well known in Japan for his non-fiction books in computer science and mathematics, and the book jacket says this is his first novel. Actually, although I do think this is a wonderful book, I have trouble thinking of it as a "novel". Like the other books I have labeled as "didactic", it is really more of a textbook into which a few characters have been introduced for the purpose of making it more readable and understandable. At the beginning, the main character is a nerdy high school freshman who likes math and has no experience with girls. However, he soon meets the brilliant Miruka who understands math in a way he cannot and the vivacious Tetra, who begs him to help her with her math classes. There is a bit of romance, but not much plot aside from their attempts to solve the challenging problems that arise from their discussions and their teacher's assignments.
The mathematics in the book is pretty advanced, mostly circling around the connections between infinite sequences and series (e.g. generating functions), but touching also on calculus, combinatorics, number theory and other interesting topics. It is an ambitious agenda, and I think that "watching" as the characters struggle with the ideas may help many readers get through it. However, those same readers might benefit from reading a real textbook as well since this book's approach is a bit informal. (For example, after quickly learning the rule for differentiating a few functions without even knowing the definition of derivative, they proceed to take the derivatives of sums of these functions as corresponding sums of the derivatives. Of course, that is correct, but they have no reason to assume so and would be wrong had they tried the same simplistic idea with products. Yuki can get away with this sort of thing since it is the characters, and not he himself, who is saying it, but a math textbook would be expected to be more rigorous.)
In Japanese, it seems that there are quite a few sequels covering such topics as Fermat's Last Theorem and Galois Theory. In addition, there are comic book/manga versions of them as well!
Kudos to Tony Gonzalez, who is credited with translating this book into English (and co-founding the publishing house, Bento Books). One would have to know both languages and math pretty well to have completed this project.
And, speaking of Tony Gonzalez, he has just written to let me know about some other Math Girls books that are available:
Tony Gonzalez, Bento Books
Thank you for listing (and recommending!) my translation of Hiroshi Yuki's Math Girls on your website.
I'm embarrassed to say that I forgot to let you know when we published its sequel, Math Girls 2: Fermat's Last Theorem. That book follows the same template of Math Girls, but covers different areas of mathematics. This title is a bit more cohesive in its approach, with most topics touching on the knowledge needed for a somewhat in-depth description of Wiles's proof of FLT in the final chapter.
Today we also launched a new Math Girls spinoff series, aimed at readers who aren't quite ready for the mathematical content of the main series. The first volume is called Math Girls Talk About Equations and Graphs.
This and the other books in the series make no attempt at creating a plot, they're just conversations between the Math Girls characters about various topics in mathematics. I'm currently translating the second volume, Math Girls Talk About the Integers (which touches on topics from discrete math, and introduces proof by induction), and we hope to release that this fall. The third book in the series, Math Girls Talk About Trigonometry, was released in Japan last month, and we'll translate and publish that one as soon as possible.
An interesting and informative review of this book by Mari Abe and Mei Kobayashi appeared in the August 2012 issue of the AMS Notices.