The Math Book by DK (2019, ISBN 978-1-4654-8024-8)

This book provides an overview of Mathematics. The coverage is historical, it basically describes mathematics in terms of its history. The first entry is Positional Numbers (how numbers are represented, with a discussion of Babylonians and Cuneiform numbers, etc.) The last entry is about the Poincare Conjecture.

If you know nothing about mathematics, then this book provides a good overview. Even if you know a lot about mathematics, you might enjoy the brief historical sketches.

Purchased from Amazon on 2020-11-28 for 19.29$

Beyond Infinity by Eugenia Cheng (2017, ISBN 978-0-465-09481-3)
Subtitle-- An Expedition To The Outer Limits Of Mathematics.

A book for the general reader about infinity and set theory. Well written. Slow at first, but I found the later chapters more interesting. Contains many drawings explaining various aspects of the subject.

Purchased at Barnes on 2017-6-22 for 27.00$

Visions Of Infinity by Ian Stewart (2013, ISBN 978-0-465-02240-3). Subtitled-- The Great Mathematical Problems. I like books about Infinity, however as the subtitle might suggest this book isn't so much about Infinity as it is about various math problems that mathematicians have struggled with over the centuries. Even though it isn't much about Infinity it is still very good.
Some of the problems discussed are Goldbach Conjecture, Squaring the Circle, Four Color Theorem, Kepler Conjecture, Mordell Conjecture, Fermat's Last Theorem, etc. This book is aimed at the general reader, however, the subject is complex and so may be a harder read depending on the reader's math background and interests. The author does a good job of explaining the problems and the attempts to solve them. Purchased from Powell's books on 7-6-2013 for $26.99. 

Calculating The Cosmos by Ian Stewart (2016, ISBN 978-0-465-09610-7)
Subtitle-- How Mathematics Unveils The Universe.

Talks about the mathematics of astrophysics from gravity to multiverse.  Excellent read. Despite the title, there is very little math. The book mostly talks about the math used to calculate various things.

Received as Christmas present 2016.

Beautiful Geometry by Eli Maor and Eugen Jost. (2014, ISBN 978-0-691-15099-4.)
51 chapters of interesting mathematics. Each chapter contains one mathematical idea or theorem. Each chapter also contains one or more drawing(s) that illustrate the idea or theorem.
Purchased from Amazon on 1-19-2014, for $20.79

The Story of Mathematics by Richard Mankiewicz (2000, ISBN 0-691-08808-X)
This is a history of mathematics. It is a high level summary, probably intended for people who are not mathematics or science oriented, but are interested in learning some of the history. The book does not cover any of the details of the areas it discusses. There are lots of interesting pictures and quotes.
Purchased  2001-7-20.

In Pursuit of the Unknown by Ian Stewart, 2012, ISBN 978-0-465-02973-0. Subtitle: 17 Equations That Changed the World. This book has a label on the back the says Mathematics, but I think it should be labelled Physics, etc. It is really more about the subjects of the equations than the mathematics. Subjects discusses include Pythagora's Theorem, Logarithms, Calculus, Newton's Law of Gravity, Square Root of Minus One, Euler's Formula for Polyhedra, Normal Distribution, Wave Equation, Fourier Transform, Navier-Stokes Equation, Maxwell's Equations, Second Law of Thermodynamics, Relativity, Schrodingers Equation, Information Theory, Chaos Theory and Black-Scholes Equation.
If you are interested in how mathematics is used in the real world, I think this is a good introduction. It is well written, informative and I think entertaining. Sadly there is no list of books for further reading.
 Purchased from Amazon on 2013-3-7 for $20.51.

The Glorious Golden Ratio by Alfred S. Posamentier.  2012, ISBN 978-1-61614-423-4. If you are interested in Mathematics then you'll love this book. The golden ratio is a number which occurs in geometry over and over again. The golden ratio is also related to the Fibonacci and Lucas numbers. This book discusses how to construct the golden ratio, how it has been used in the past and gives many examples of it in geometry. Purchased at Powells books, on 1-21-2012, for $27.00.

The Pythagorean Theorem by Alfred S. Posamentier.  2010, ISBN 978-1-61614-181-3. Subtitled: The Story of Its Power and Beauty.
The cover shows a "Pythagorean Tree" constructed from layers of Pythagorean triangles with squares on their sides. (Discussed in chapter 7.) This book is similar to the book by Eli Maor, but covers topics not discussed in that other book. Both books are worth reading.
Purchased from amazon.com, 10-5-2010, for $19.71.

The Man of Numbers by Keith Devlin. 2011, ISBN 978-0-8027-7812-3. Subtitled: Fibonacci's Arithmetic Revolution. This book is about Leonardo of Pisa aka Fibonacci. The book is well written. However, not much is known about Fibonacci, so it is a bit thin. The book describes Fibonacci's contribution to the western world as one of making the Hindu-Arabic number system more available to merchants and bankers in medieval Italy. Fibonacci did this through his book Liber Abbaci (the Book of Calculation). The book introduces the Hindu-Arabic numbers and how to do calculations with them. It does this mostly by presenting story problems that would be easy to understand or were relevant to the merchants of that time. The book also introduces algebraic ideas concerning how to solve story problems. Today the name Fibonacci is associated with Fibonacci Numbers. This because this number sequence appears in Liber Abbaci (see page 404, Liber Abaci, translated by L. E. Sigler) in a story about rabbits. The story, like the many other stories in the book, is intended as a way to use the number system to do math problems and not as a treatise on rabbit biology (or Fibonacci numbers either.) Purchased at Powell's books, 9-6-2011 for $25.00.

The Fabulous Fibonacci Numbers by Alfred S. Posamentier and Ingmar Lehmann. 2007, ISBN 978-1-59102-475-0.
This book discusses the Fibonacci numbers. It gives some of their history and many of the areas of mathematics and science that are touched by this number series. Also, discusses the Lucas numbers and the Golden Ratio. If you enjoy mathematics and numbers then you'll love this book. My only complaint is that the proofs of some of the statements were placed in an appendix instead of inline with the statements. Purchased 10-30-2007 at Powell's, for $28.

The Golden Section by Scott Olsen. 2006, ISBN 978-0-8027-1539-5. Subtitled Nature's Greatest Secret. Also, on the cover in small hard (for me) to read print it says "the essential guide to the deepest mystery on earth" and "a little book about the secret of life." This is a little book. It is not tiny, but it is smaller than most hard covers. The entire "Wooden Book" series is the same size. This book has many fine drawings illustrating the various subjects described. The book has 26 chapters and seven appendix. The chapters are each two pages long, with one page of text and one page of drawings. The subject is mostly "phi" (the Greek letter "phi" is used as a symbol for the number) an algebraic irrational number that appears frequently in nature. "phi" is approximated by the ratio of succeeding Fibonacci numbers 8/5,13/8, 21/13, etc. It is these Fibonacci numbers that usually are found. "phi" itself is given by the expression (1+sqrt(5))/2. The decimal value is approximately 1.6180339... While this book is mathematical in some of its content it is mostly mystical ideas related to how the numbers occurs in many places. I found this book very interesting to read and if I find the time may read it again. The text however is very terse, each chapter just scratches the surface of an idea before it goes on to another. If you are interested in "phi", but don't have a lot of time, then this book will introduce you the subject. You may find that when you have learned some about "phi" you will want to learn more. Golden Section is sometimes called Golden Ratio.

Facts on File - Calculus Handbook by Eli Maor. 2005, ISBN 0-8160-6229-3. This a reference book intended for students of calculus. There is a six page historical introduction to calculus. This followed by four sections of reference material. The first is a Glossary that defines many terms related to calculus, trigonometry, analytic geometry and strangely economics and finance. The second section contains Biographies of various mathematicians, third is a section of Chronology that lists significant events in the history of mathematics and finally the fourth section has some tables listing various facts about trigonometry and calculus.
The glossary is hard to read from beginning to end because it is an A-Z dictionary of math terms. It isn't intended to be read that way, but instead as a place for the student to look up terms. The other sections can be read from beginning to end or just those parts that the reader is interested in.

Trigonometric Delights by Eli Maor. 1998, ISBN 0-691-05754-0. This book is about Trigonometry. This is not a text book on trigonometry. I would say that to really appreciate this book the reader should have had some prior understanding of trigonometry and maybe some calculus. However, if you are interested in mathematics then you will probably enjoy this book. It is well written. It starts with the early history of mathematics that probably lead to trigonometry and follows the thread of history and how trigonometry as a science was employed at various times to solve problems.
Purchased at Powell's Books, 7-31-2002 for $23.50.

e, The Story of a Number by Eli Maor. 1994, ISBN 0-691-03390-0. This is a good book. I have read it twice now. The number "e" has the approximate value of 2.7182818284..., but cannot be written down precisely because it is an irrational number. This book covers a wide variety of topics related to "e", from the invention of logarithms, to "e" and complex numbers. The book doesn't assume the reader knows calculus, however calculus level math is discussed and explained.

The Pythagorean Theorem by Eli Maor. 2007, ISBN 987-0-691-12526-8. Subtitled: A 4000 Year History. Excellent book. I really enjoyed reading this. The subject is handled correctly and the author doesn't shy away from doing real math, ie, providing theorems and their proofs. However, the book is mostly about the history of this idea and how it has come to be used in various areas of mathematics and science. I will be reading his other books soon. Purchased at Powell's books on 7-27-2007, 24.95.

Infinity and the Mind, by Rudy Rucker. ISBN 0-691-00172-3. This is an excellent introduction to some complex ideas. Probably the reader who has little or no exposure to these ideas will find this book very difficult. Chapter titles are Infinity, All the Numbers, The Unnameable, Robots and Souls, The One and the Many, The Transfinite Cardinals, Godel's Incompleteness Theorems. I enjoyed this book (I have read it three times), but I find the Unnameable and the sections on Large Cardinals and Incompleteness difficult to understand.

The Mystery of the Aleph by Amir D. Aczel. ISBN 1-56858-105-X. The subtitle is Mathematics, the Kabbalah, and the Search for Infinity. This book is about the history of infinity. It is less technical than the David Foster Wallace book. Like that other book this one is mostly about Georg Cantor, but also covers Zeno (and other Greeks), Galileo, Gödel, Cohen and others. The book is well written and easy to read. The explanations of the more technical parts of the story are a bit over simplified, but still enjoyable for someone interested in this subject. This book plays up the idea that the study of infinity causes insanity.

Everything and More: A Compact History of ∞, By David Foster Wallace. ISBN 978-0-393-32629-1. This a really good book. A bit eccentric in style, but it works because the subject, infinity, is so complex. The story is mainly of Cantor's work in the modern theory of infinity, but it covers stuff from all periods of history, e.g., Zeno and other ancient Greeks to European mathematics of the 1600's and the discovery of Calculus (Leibniz and Newton.)
This book touches on many complex mathematical ideas, but doesn't get too bogged down with proofs, etc.

The Man Who Counted by Malba Tahan. ISBN 0 86241 883 6. The is a great little book. It is about a Persian man Beremiz Samir (the man who counted) and an Arab and some of the adventures they have. Each adventure involves some sort of mathematical problem,which Beremiz cleverly solves. This was an interesting book to read, especially if you are interested in mathematical puzzles.