Real math! Romance! Karate! That's what the back of this unusual math book promises to its readers. Odd as it may seem to teach math with a comic book, The Manga Guide to Linear Algebra does a pretty good job of teaching the basics through comics and some light storytelling.
The book starts off with an introduction to the story's main characters. Reiji wants to learn martial arts so he can stop being a wimp. The head of the karate club, Tetsuo, agrees to let him join on one condition: he has to tutor Tetsuo's sister, Misa, in linear algebra. Most the book's instruction is given from the perspective of Reiji teaching Misa, and the story of Reiji's efforts to get stronger in karate and woo Misa are sprinkled in between the lessons.
I read this book from the perspective of someone who enjoyed and did well in linear algebra. I still use many of the basics today, but have not studied the minute details for a while. (For example, I haven't had to do Gaussian elimination in ages.) So I read this book as a bit of a refresher for myself, and tried to guess how easily someone new to the subject would grasp the concepts.
For my purposes, it was great. I definitely understood everything explained in the book, and even learned a few new tricks for solving problems. For new learners, I had some mixed feelings, but felt positively about it overall.
The comic book form worked really well for setting up an informal conversation for each lesson as Reiji explained the math to Misa. This allowed for more colloquial language and some back-and-forth questioning and discussion that you'd never include in a formal textbook. The illustrations were also helpful, allowing for extra imagery, even if just to set up a useful metaphor (such as a character using a broom for the sweeping concept in Gaussian elimination). The images were especially helpful when explaining vectors, which I thought was done particularly well.
On the other hand, the content was not as dense as a regular textbook. Most of the time I didn't think this mattered, especially since the book is openly intended to be supplementary. Even still, there were times I felt like a little extra explanation might help. This was especially true in the non-comic sections between chapters. For example, one discussed combinations and permutations through example, but I felt like I'd be kind of lost after just those few pages on the topic.
As for the story, it successfully got me interested in the characters and their well-being. I wanted Misa to do well in math, and I wanted Reiji to excel in karate. This did give some motivation for reading the math parts in order to get to the next piece of the story.
However, the story didn't really integrate much into the mathematical content beyond one character teaching another. Some examples did include the story's characters and one even related to karate, but really, the story could have been anything and it would have worked just as well. This isn't necessarily a bad thing, since engagement is a good reason to use story. But it would be neat to see an example where the story itself could actually help teach the content better than could be done without any story at all.
Overall, I really enjoyed this book and got through it surprisingly quickly. Despite any small weaknesses discussed above, I would wholeheartedly recommend it to students just learning the subject as well as anyone needing to brush up.