Tanya Khovanova's Fun Math Book Reviews:

For Kindergarten and elementary school, and probably some adults.

"Imagine" by Norman Messenger has beautiful pictures, each one a sort of puzzle, joke, optical illusion, or the like. As a bonus, at the corners of every page there is a math puzzle for older children.

For kids, starting from kindergarten

While "The Book of Classic Board Games" by Klutz Press is not exactly a math book, it is a most excellent posession. This book details 15 board games, with complete rules, and, more importantly, boards for all of them. The book also comes with a set of pieces, so that one can play all the games contained in it right away.

The games in this book are classics. They have all stood the test of time, most having existed and been popular for centuries, and some even for millenia. All these games are easy to learn, yet have deep (sometimes very deep) strategies. A definitely enjoyable experience, for children as well as adults.

For kids, starting from kindergarten, and adults

"The Magic Show" by Mark Setteducati has the unique (as far as I know) property of being a self-presenting magic show. The book has various tabs and wheels and things, which one pulls or rotates to make things happen. The interesting part is that the tricks tend not to invlove subterfuge on the book's part, but are rather mathematical in nature. The book is fun to go through, and it is educational to figure out how the tricks work.

For kids in elementary school and middle school

"Cool Math" by Christy Maganzini. The name is apt -- the math presented here really is cool. Appropriate for children just slightly past the stage of being able to count to a million and to multiply.

I taught at School Plus, and later discovered that the contents of this book coincided precisely with my program. That is, me and the author of this book have the same taste for coolness.

This book constitutes a chilrden's version of MathAlive, a cool math class at Princeton University.

For kids starting middle school and adults

"A Super-Sneaky, Double-Crossing, Up, Down, Round & Round Maze Book" by Larry Evans is an excellent book of mazes. Each maze is very different from the others, and each one is a work of art.

Grades 5-8

I conducted a Math Party for the benefit of a Princeton Charter School fundraising auction. "Solve This" by James S. Tanton was the best book for it. Particularly appropriate for kids who do Mathcounts.

This is a book of activities rather than exercises, it is most appropriate either for a group to do together, or for someone who wants to show something to their friends.

For kids and adults.

"Masters of Deception" by Al Seckel is the most mathematical art book I've ever seen. Naturally this book contains chapters with painting by Dali and Escher, but it also includes many others: ambigrams by Scott Kim, anamorphoses by Istvan Orosz and many optical illusions and impossible figures by other. I brought this book home and my family had to cancel all our plans as we can't put aside this book until we finished it. I like art when it is not only beautiful, but also makes me puzzled.

Beginning of the book: 8 and up, Ending of the book: 20 and up

"The Riddle of Scheherazade" by Raymond Smullyan is an excellent book of logic puzzles. Unlike some puzzle books, the puzzles in this one build in difficulty.

"What is the Name of this Book?" by Raymond Smullyan is similarly structured, containing a progression of logic puzzles, running from the classic "You have two coins with total value 15c. One of them is not a nickel. What are they?" to Godel's Incompleteness Theorem.

Raymond Smullyan is, in my opinion, the best author of logic books of all time. He knows his stuff very well, and has an excellent sense of humor. He has written a great many books, on logic and on the Tao. His perspective on the latter is very interesting because it is the perspective of a logician.

Feel free to search through Amazon for Raymond Smullyan.

Age: 9 and up

"Aha! Gotcha" by Martin Gardner is about paradoxes. It presents a great many of them, complete with amusing pictures, and it dissects and discusses each paradox in non-technical terms. Great fun if you are not acquainted with paradoxes, and potentially enlightening even if you are. My 11-year-old son has read this book more than ten times.

Martin Gardner is the classic author of recreational mathematics books. He has written a huge amount of stuff --- brainteasers, hexaflexagons, discussions of the structure of the universe... you name it. One particularly good example is "Classic Brainteasers" on the right. Go ahead and search Amazon for Martin Gardner. You're likely to find something to your taste.

Ages: 9 and up

In "Logic puzzles" by Mark Fowler we have a good collection of logic puzzles, which together contain the clues to a "superpuzzle." The "superpuzzle" provides a unifying thread to the book's puzzle collection, and encourages enough interest to actually solve the individual puzzles in it.

For kids, starting from middle school and adults

"Walter Wick's Optical Tricks" by Walter Wick is a book of optical illusions. The fascinating thing about this book, though, is that all the illusions are presented as photographs. There are pictures (real, no photo editing!) of impossible shapes, objects floating in midair, and other fascinating optical tricks. The book encourages the reader to think about how each photograph was taken --- try it!

You might recognize Walter Wick's spectacular photography, if you've seen his photo-work in "I spy" series.

For non-beginner chess players

"The Chess Mysteries of Sherlock Holmes" by Raymond M. Smullyan is not your typical chess puzzle book. Instead of asking you to find a mate in three steps or to win material, this book offers entirely different challenges. For example, it offers a position, tells you that it was obtained legally, and then asks you to find the last two moves, or sometimes, it gives you a position with one piece missing, and asks you to place it (again, assuming that the position was reached after a legally played game of chess). After this book, you see chess in an entirely different light, and you think about things that never came to mind before.

"The Chess Mysteries of the Arabian Knights" by Raymond M. Smullyan is similar to the previous book, but the puzzles are more difficult.

For adults.

PopCo by Scarlett Thomas is a fiction book that discusses mathematics. It describes prime numbers, Fibonacci numbers and the Monty Hall problem as part of its narrative. I had a strange feeling reading the math parts of this novel. It felt that the descriptions were not thorough enough for people who do not know math, but were not needed at all for people who do know math.

I have to mention that there are some mistakes. For example, she refers to this statement from a Cretan — "All Cretans are liars" — as a paradox. There is nothing paradoxical about it if the speaker is a liar and not all Cretans are liars. In standard math literature it is usually assumed that all people living on the same island are either liars or truth-tellers. In this case, if we assume that, then the above statement becomes a paradox.

The author repeatedly cites classic math books and theories without understanding them. Because of that, Scarlett Thomas doesn't mention some implicit assumptions, leading her to make mistakes. There are also arithmetic mistakes.

If you don't care about the mathematical details, or if you do care and can see through the mistakes yourself, you might enjoy this book. For me, it was fun to read.

For adults.

I always wanted to find mathematical papers which applied mathematical ideas to sex, love and marriage. "Mathematics and Sex" by Clio Cresswell does this. There is a certain element of the book that I strongly dislike. The author embeds formulae into the text, without explaining the meaning of each variable. I think that this is a very bad taste in mathematical writing. At the same time, however, these formulae can be completely eliminated. It seems to me that the only goal of the formulae is to impress the reader, as to how complicated the subject looks.

Even if the formulae are ignored, the results and goal of each formula are still explained clearly in words. Also, there is a good list of references to actual mathematical papers.

For adults.

"The Music of the Primes" by Marcus du Sautoy describes the history of the hunt for a proof of the Riemann Hypothesis. The author is a mathematician, and it is clear that he knows what he is talking about. Furthermore, the second part of the book is dedicated to the modern research of the Riemann Hypothesis, and some of the people described in this, I know personally. This added a personal touch to my experience in reading the book.

For high school kids preparing for competitions, and adult math puzzle lovers.

In "Mathematical puzzles" Peter Winkler collected the best math problems you would like to do if you prepare for Math Olympiads. To do these problems you do not require math knowledge beyond high school, but you require inventiveness and creativity. Peter has a great taste and his collection contains all the most beautiful math puzzles.

In "Mathematical puzzles" Peter Winkler collected the best math problems you would like to do if you prepare for Math Olympiads. To do these problems you do not require math knowledge beyond high school, but you require inventiveness and creativity. Peter has a great taste and his collection contains all the most beautiful math puzzles.

The book "International Mathematical Olympiad 1959-1999" by Istvan Reiman contains all the problems from the first 40 IMOs together with solutions. It is a must for every student preparing for IMO. This book sometimes provides two different solutions, in rare cases -- three or four. There are also remarks discussing some generalizations.

I like how "The Art and Craft of Problem Solving" by Paul Zeitz is structured. The problems are grouped around ideas and strategies. First an idea or a strategy is presented, then some examples are discussed. Then there are a lot of problems and exercises.

There are no solutions -- only hints to selected problems. I think it is important to work with at least one book with a lot of problems and no solutions. This way those of us who are impatient have a chance to think without succumbing to the urge to check the solution.

"The USSR Olympiad Problem Book" was the olympiad Bible when I was in high school. The legend was: if you were allowed to have only one book to prepare that this was the one.

This book is restricted to only arithmetic and algebra problems. It has 320 problems and the choice of problems is classical -- it covers all the bases in arithmetic and algebra olympiad ideas.

"Mathematical Olympiad Challenges" by Titu Andreescu is organized by ideas. For each idea there are several examples and then problems. Solutions in the back. This book is similar in its structure to the book of Paul Zeitz, but more advanced.

The downside is that you can guess that the author is not a native English speaker.

The standard geometry course in the US is not enough to prepare for math competitions. If you want to win, you have to devote a big part of your time to geometry. "Lines and Curves: A Practical Geometry Handbook" is a very special geometry book. It presents geometry in motion. This dynamic approach is very unusual and very engaging. The explanations are interlaced with problems of increasing difficulty. There are a lot of problems, and they are tastefully chosen.

"Geometry Revisited" is a fun book. It has a section for every important geometry theorem and problem needed at the competitions. For example, it has the nine-point circle section and the section about "The Buttefly" problem.