The Joy Of X: A Guided Tour Of Math, From One To Infinity, by Steven Strogatz
For some reason, math has always intimidated a great many people, and that intimidation, taught by parents to children or teachers to students, has done a great deal of harm to the people of the United States, who as a result lack basic mathematical literacy in many cases and thus economic literacy or an ability to understand much about how the world works. The author has devoted himself in this book to showing some delightful aspects of the history of mathematics in a way that seeks to make the subject as a whole a great deal less intimidating. As someone who is generally fond of math, I do not really understand why it intimidates so many people, given that we at least implicitly use a great deal of math that becomes entirely too difficult when we try to use it explicitly, but the author does a great job of writing a witty and amusing book full of short chapters that deal with a great many aspects of mathematics and how it relates to the lives of people, and in the process this is the sort of book that could encourage a great many people to be far less frightened of math.
This book is about 250 pages and it is divided into thirty chapters in six parts. After a short preface, the first six chapters in the first part deal with numbers (I), looking at the upsides and downsides to numbers (1), treating numbers concretely (2), subtraction and negative numbers (3), the cummutative property (4), division (5), and the populist implications of the place value system (6). After that there are five chapters on relationships (II), specifically on algebra (7), complex numbers (8), word problems (9), the quadratic formula (10), and functions (11). After this comes five chapters on shapes (III) that deal with geometry and intuition (12), proofs (13), conic sections (14), sine waves (15), and limits (16). After this comes five chapters on change (IV) that discuss differential calculus (17), integral calculus (18), e (19), the three-body problem (20), and vector calculus (21). The fifth section discusses data (V), with chapters on distribution curves (22), probability theory (23), and linear algebra (24). Finally, the last part of the book discusses the frontiers of math (VI), namely prime numbers (25), group theory (26), möbius strips (27), differential geometry (28), calculus (29), and infinity (30). After these chapters the book ends with acknowledgments, notes, credits, and an index.
The author, in this book, shows some drawings but manages not to be too frightening to most readers through the dense sort of equations that plague many books about math. Yet the approach of the author is a sound one in looking at what sort of problems are solved via different aspects of math. The discussion of relevance here is not merely tacked on to the discussion of what others would find boring, but is at the heart of the book. The author has a clear joy for the subject of mathematics in its variety and seeks to convey that excitement and that joy to the reader. There are clearly some readers who may be susceptible to thinking joyfully about mathematics, not least in areas like conic sections where what is seemingly bizarre and obscure ends up connecting to each other nicely . And in understanding what mathematics can help someone to do and know better, the rest of the language is not nearly as daunting as it would otherwise be.
 I have a fondness for conic sections because one of them, the parabola, is defined as the set of all points that are equidistant from a focus and a line called a directrix, which was a title in a role playing game world I created with a onetime friend of mine.