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I also have an analagous page for toys.
I also love ballroom dancing and have a page with reviews of dance movies and dance exercise DVDs.
My friends have periodically asked me to recommend books that could help advanced children improve their mathematics. So, I have pulled together this resource list of particularly good math books for kids, along with my comments on why they are so good. I've linked as many of these as I could to their pages on Amazon.com. As a note, those links take you to Amazon.com, where you will be subject to their policies and procedures. I take no responsibility for what happens to you over there :-)
Since I work with very advanced children, you need to take that into account when you see my age recommendations.
For kindergarten and elementary school, and probably some adults "Imagine" by Norman Messenger |
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For kids, starting from kindergarten, and for adults While "The Book of Classic Board Games" by Klutz Press The games in this book are classics. They have all stood the test of time, most having been popular for centuries, and some even for millennia. All these games are easy to learn, despite having deep (sometimes very deep) strategies. Both children and adults will enjoy this book. |
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For kids, starting from kindergarten, and for adults "The Magic Show" by Mark Setteducati |
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For kids in elementary and middle school The name of "Cool Math" by Christy Maganzini I used to teach at School Plus, and later discovered that the contents of this book coincided precisely with my program. That is, the author of this book and I have the same sense of coolness. This book constitutes a children's version of MathAlive, a math class at Princeton University that is also cool. |
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For kids starting middle school, and for adults "A Super-Sneaky, Double-Crossing, Up, Down, Round & Round Maze Book" by Larry Evans |
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Grades 5-8 I conducted a Math Party for the benefit of a
Princeton Charter School fundraising auction. "Solve This" by James S. Tanton Solve This is a book of activities — rather than exercises — that work well for a group effort or for an individual who wants to show off to their friends. |
These books can be enjoyed by kids and adults at the same time.
For kids and adults "Masters of Deception" by Al Seckel |
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Beginning of the book: 8 and up. End of the book: 20 and up "The Riddle of Scheherazade" by Raymond Smullyan "What is the Name of this Book?" by Raymond Smullyan Raymond Smullyan is, in my opinion, the best author of logic books of all time. He totally knows his stuff, and has an exceptional 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. |
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Age 9 and up "Aha! Gotcha" by Martin Gardner 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" |
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Ages 9 and up "Logic puzzles" by Mark Fowler |
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For kids starting from middle school, and for adults "Walter Wick's Optical Tricks" by Walter Wick You might recognize Walter Wick's spectacular photography from his his photo-work in the "I spy" series |
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For non-beginner chess players "The Chess Mysteries of Sherlock Holmes"
by Raymond M. Smullyan "The Chess Mysteries of the Arabian Knights" by Raymond M. Smullyan |
Here are fun math books for adults.
For people interested in Greek myths
In the book "Mythematics: Solving the Twelve Labors of Hercules The problems in Mythematics are quite advanced. They range in topic from algebra, geometry and probability to differential equations and integral calculus. Plus, as a reward for helping Hercules, Huber gives you variations on Sudoku puzzles. Solving some nice math problems might not be the only reason for people to buy this book. Here are some other reasons:
I like Huber's approach. Future possibilities for more books are endless. Let's write new math problems based on Harry Potter, Batman, the Bible or, maybe, The Joy of Sex |
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For inteview preparation and for fun
I bought the book "Heard on The Street: Quantitative Questions from Wall Street Job Interviews" by Timothy Falcon Crack The book has problems in logic, probability, statistics and finance, as well as a very useful chapter of general interview questions. If you're interested in buying this book, I should mention that some questions require calculus and knowledge of financial terms. I do love the author's taste in problems. |
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For adults
"The Symmetries of Things" by John H. Conway, Heidi Burgiel and Chaim Goodman-Strauss The first chapter is very nicely written and is suitable for high school and undergraduate students. It covers symmetries of finite and infinite 2D objects. The second chapter adds color to the theory. For colorful pictures with symmetry, there are two symmetry groups: the group that preserves the picture while ignoring its coloring and the group that preserves the picture while respecting its coloring. The latter group is a subgroup of a former group. This second chapter discusses all possible ways to symmetrically color a symmetric 2D picture. The chapter then continues with a discussion of group theory. This chapter is much more difficult to read than the first chapter, as it uses a lot of notations. The pictures are still beautiful, though. The third chapter is even more difficult to read and the notations become even heavier. This chapter discusses hyperbolic groups and symmetries of objects in the hyperbolic space. Then the chapter moves into 3D and 4D. I guess that some parts of the second and the third chapters are not meant for light reading; they should be considered more as reference materials. |
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For adults If you love mathematics and the show "Numb3rs", this book is for you. "The Numbers Behind NUMB3RS: Solving Crime with Mathematics" by Keith Devlin and Gary Lorden |
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For adults "PopCo" by Scarlett Thomas 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. |
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For adults I always wanted to find mathematical papers which applied mathematical ideas to sex, love and marriage. "Mathematics and Sex" by Clio Cresswell 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. |
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For adults "The Music of the Primes" by Marcus du Sautoy |
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For high school kids preparing for competitions, and for adult math puzzle lovers In "Mathematical Puzzles" Peter Winkler "Mathematical Mind-Benders" |
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For people preparing for interviews and adult math puzzle lovers "How Would You Move Mount Fuji? Microsoft's Cult of the Puzzle - How the World's Smartest Company Selects the Most Creative Thinkers" by William Poundstone |
I was on the Soviet IMO team twice and now my younger son is preparing for USAMOs. Here is my list of useful literature.
In "Mathematical Puzzles" Peter Winkler "Mathematical Mind-Benders" |
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The book "International Mathematical Olympiad 1959-1999" by Istvan Reiman |
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I like how "The Art and Craft of Problem Solving" by Paul Zeitz There are no solutions — only hints about selected problems. For those of us who are impatient and might succumb to the urge to check the solution, there's a real advantage to working with at least one book with a lot of problems and no solutions. |
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"The USSR Olympiad Problem Book" This book restricts itself to only arithmetic and algebra problems. It has 320 mostly classical problems and it covers all the arithmetic and algebra Olympiad ideas. |
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"Mathematical Olympiad Challenges" by Titu Andreescu The downside of this volume is that the writing reflects the fact that the author is not a native English speaker. |
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The standard geometry course in the US is insufficient preparation 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" by Victor Gutenmacher and N.B. Vasilyev |
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"Geometry Revisited" by H. S. M. Coxeter and Samuel L. Greitzer |
Last revised February 2009