Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.

  • Apple
  • Android
  • Windows Phone
  • Android

To get the free app, enter your mobile phone number.

FREE Shipping on orders with at least $25 of books.
Only 10 left in stock (more on the way).
Ships from and sold by Amazon.com. Gift-wrap available.
A Mathematical Mosaic: Pa... has been added to your Cart
+ $3.99 shipping
Used: Good | Details
Sold by HPB Inc.
Condition: Used: Good
Comment: Connecting readers with great books since 1972. Used books may not include companion materials, some shelf wear, may contain highlighting/notes, may not include cdrom or access codes. Customer service is our top priority!
Have one to sell? Sell on Amazon
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See this image

A Mathematical Mosaic: Patterns & Problem Solving (Revised Edition) Perfect Paperback – September 28, 2007

5.0 out of 5 stars 3 customer reviews

See all formats and editions Hide other formats and editions
New from Used from
Perfect Paperback, September 28, 2007
"Please retry"
$15.95 $6.46

The Amazon Book Review
The Amazon Book Review
Author interviews, book reviews, editors picks, and more. Read it now
$19.95 FREE Shipping on orders with at least $25 of books. Only 10 left in stock (more on the way). Ships from and sold by Amazon.com. Gift-wrap available.
click to open popover

Frequently Bought Together

  • A Mathematical Mosaic: Patterns & Problem Solving (Revised Edition)
  • +
  • My Best Mathematical and Logic Puzzles (Dover Recreational Math)
  • +
  • The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)
Total price: $28.10
Buy the selected items together

Editorial Reviews


There are different books on my shelf. Some are large like dinosaurs: these are textbooks. Others are much smaller, but their educational value may be greater. For example, Kordemsky's book [3] contributed a lot to Russian childrens' interest in mathematics although its English edition fits in a hand. The book I am going to discuss fits in a coat pocket, but it speaks in an interesting and understandable way about number theory, combinatorics, game theory, geometry, and calculus, to say nothing about magic tricks, puzzles and other digressions. What is most important is that whenever Vakil starts to discuss something, he never leaves the reader without a piece of exact, rigorous knowledge. This is a book about mathematics, not about its fuzzy placebo. Ravi Vakil… tries to encourage curiosity, a sense of beauty, and the love of knowledge. This is a book I would like to have read as a boy. Why? Because it addresses the normal curiosity of children. It contains many good problems, facts, and stories. It is a mixture of just those ingredients which are most useful for children. Vakil enjoys ideas that seem simple if you already know them, but may seem paradoxical if you don't. One of them is presented as a card trick (p. 44): I ask you to shuffle a deck of cards thoroughly. Then I ask for them back (face down). Carefully examining the backs of the cards, I separate them into two piles. I then claim that, through the power of magic, I've made sure that the number of black cards in the first pile is the number of red cards in the second pile! Although Vakil's book is intended to be recreative and facultative, it contains many facts that are indispenable for mathematical literacy, including: Criteria for divisibility. Those for 2, 3 and 7 are proved; other proofs are left for the reader (pp. 23, 29). Let g(x) denote any polynomial in x. Then the remainder when g(x) is divided by x a is g(a). 2 is irrational (p. 121). There are infinitely many primes (p. 124). Heron's formula for the area of a triangle (p. 160) The harmonic series diverges (p. 180). This book contains several personal profiles of gifted youngsters with whom Vakil became acquainted at olympiads. Vakil writes several lines about how they found their way into mathematics. More than once Vakil stresses that mathematics is beautiful. In his preface he writes: Math is a uniquely aesthetic discipline; mathematicians use words like beauty, depth, elegance, and power to describe excellent ideas --American Mathematical Monthly-André Toom

Ravi Vakil has put together a collection of wonderful topics from number theory through combinatorics to game theory in a fashion that seventh- and eighth-grade students can handle yet high school students will find challenging. His book is divided into two parts. Part 1 introduces to the young reader a number of mathematics topics that will be very useful in part 2. For example, in the first section, Number Theory, such topics as calculating tricks, divisibility rules with proofs of why they work, and magic squares are investigated fully and clearly. In part 2, many of the earlier topics are revisited, but the level of difficulty is increased. In 'Number Theory Revisited,' an in-depth study of rational and irrational numbers, a fascinating painted-school-lockers problem, and other topics challenge students in an entertaining manner. Perhaps the best features of the book, however, are the historical digressions on great mathematicians and short personal profiles of contemporaries of the author. These glimpses into the lives of young male and female mathematicians make this book very much worth its price. Without a doubt, this book is a must for any library, teacher's reference, or student's amusement.- --The Mathematics Teacher, Vol 89, #7- John Cocharo

About the Author

Ravi Vakil s resume reads like a dictionary of superlatives. During his high school years he won every major mathematics competition. These include first place standing in the Canadian Mathematical Olympiad for two successive years, first place standing in North America on the USA Mathematical Olympiad, and two gold medals and one silver medal in the International Mathematical Olympiad (including a perfect score). He also won first prize in the Canadian Association of Physicists Competition and led his high school computer team to three provincial championships. During his undergraduate years at the University of Toronto, Ravi raised his brilliant achievements to new heights. In all four years he placed among the top five competitors in the prestigious North American William Lowell Putnam Mathematical Competition, earning him the top award of Putnam Fellow in each year. He graduated in 1992 with B. Sc. and M. Sc. degrees; for his B. Sc., he was awarded the Governor General s Medal for the highest graduating marks at the University of Toronto. Ravi s extraordinary achievements have not prevented him from pursuing his many other interests. These include squash, debating, student government, journalism, and Amnesty International. For this breadth of involvement he has received numerous scholarships including the John H. Moss Scholarship for the best all-round graduating student at the University of Toronto. Ravi Vakil is a compassionate person with an eager willingness to help others. He has coached the Canadian Team at the International Mathematical Olympiad from 1989 through 1996. He was also cofounder of Mathematical Mayhem, a mathematical problem-solving journal for high school and undergraduate students the only student-run journal of its kind in the English-speaking world. This book was written while Ravi was a graduate student. Since the first edition was completed, Ravi received his Ph.D. in pure mathematics at Harvard in 1997, and subsequently taught at Princeton and M.I.T. before moving to Stanford in 2001. He is an algebraic geometer, and his work touches on many other parts of mathematics, including topology, string theory, applied mathematics, combinatorics, number theory, and more. His awards include the Alfred P. Sloan Research Fellowship, the National Science Foundation CAREER Award, the American Mathematical Society Centennial Fellowship, and the Dean s Award for Distinguished Teaching. In 2004, he traveled to the White House to receive the Presidential Early Career Award for Scientists and Engineers. He continues to work extensively with talented younger mathematicians at all levels, from high school (through math circles, camps, and olympiads) through recent Ph.D. s.

The latest book club pick from Oprah
"The Underground Railroad" by Colson Whitehead is a magnificent novel chronicling a young slave's adventures as she makes a desperate bid for freedom in the antebellum South. See more

Product Details

  • Perfect Paperback: 288 pages
  • Publisher: Brendan Kelly Publishing Inc.; 2nd edition (September 28, 2007)
  • Language: English
  • ISBN-10: 1895997283
  • ISBN-13: 978-1895997286
  • Product Dimensions: 8.9 x 5.9 x 0.8 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,052,570 in Books (See Top 100 in Books)

Customer Reviews

5 star
4 star
3 star
2 star
1 star
See all 3 customer reviews
Share your thoughts with other customers

Top Customer Reviews

I picked up the first edition of this book in 1997 and spent countless hours flipping back and forth over the pages in High School. Ravi's presentation is amazing and his book shows remarkably how math was meant to be taught.
Comment One person found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Excellent, most wonderful book which makes mathematical exploration of the universe a pure joy! ... If you used to know all this stuff and just need a quick refresher ... or if you've never known this stuff and just want a quick intro ... this book is for you ... Illustrations coupled with text are fantastic!
Comment 4 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Verified Purchase
great book, very well written and a pleasure to read.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse

Set up an Amazon Giveaway

A Mathematical Mosaic: Patterns & Problem Solving (Revised Edition)
Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway
This item: A Mathematical Mosaic: Patterns & Problem Solving (Revised Edition)