## Book Review: The Manga Guide To Linear Algebra

The Manga Guide To Linear Algebra, by Shin Takahashi and Iroha Inoue

After having read this book and finding it greatly enjoyable as well as informative, I think that the Manga guides to other subjects are likely to be of interest to me as well.  By putting a layer between the admittedly somewhat dry and dull material of linear algebra and the reader, the book allows the reader to put themselves in the shoes of Misa, an appealing young woman who struggles with the subject and wants to know how practical it is and how to understand the material for her college math class.  And looking at this book as an entrance into the series as a whole, it is worthwhile to add one layer between the reader and the raw material of mathematics (or science), given that the interest in the plot itself allows the material to be more interesting because of the context that it is in.  It is only a wonder that this sort of approach has not been taken before because of its obvious appeal for those who are interested in both manga as well as math and science and who seek to leverage narrative and story to make mathematics and science easier to appreciate

At its core, this is a book that deals with three people with complex motivations.  We have Reiji, a freshman at a university who is a bit of a weakling but devoted to getting stronger through the mastery of karate.  We have Tetsuo, who is powerful at karate but (spoiler alert) not too bright when it comes to math, and we have Tetsuo’s younger sister Misa, a beautiful freshman girl who Reiji tutors in mathematics thanks to a deal he makes with Tetsuo.  The frame story of their interactions, and the growing attraction that Reiji and Misa feel for each other, as well as Reiji’s attempts to prove himself to be strong takes place in the midst of instruction about linear algebra, where Reiji gives Misa (and the reader) various instruction on linear algebra in eight chapters, starting with an overview of linear algebra (1), moving on to the fundamentals of implication, equivalence, set theory, functions, combinations, and permutations (2), an introduction to matrices, matrix calculations, and special matrices (3), more matrices, including determinants and Cramer’s rule (4), vectors and vector calculations (5), linear independence, bases, dimensions, and coordinates (6), linear transformations and matrix rank (7), and eigenvalues and eigenvectors (8).  The instruction fits snugly with the story of karate and romance that surrounds it and makes for a compelling vehicle for mathematics instruction and its practicality.

What does one get out of this particular book?  It is a compelling mixture of technical material, which is deadly dull when one looks at it on its own, with a fascinating story and beautiful artwork.  And that combination is one that would likely translate to a lot of other materials as well.  This book, and the series it belongs to, is evidence of at least a few things, namely the importance of learning math and science and the difficulty many people in learning the material and sustaining interest in it unless it is packaged in the right way.  Some people might be offended by this sort of thing, but as someone who finds it more worthwhile to learn and to encourage learning than to complain about the sort of form that the learning is bundled with, I don’t see any reason to complain personally, except to wish that these had been around earlier.  Still, the story itself demonstrates the relationship between math knowledge and other skills, and demonstrates how it is that nerdy people can leverage their willingness to work hard at difficult subjects beyond math and science alone, which is useful information even for those who know the material already.