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Gyorgy Polya
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The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics) 1/20/09 Edition

by G. Polya (Author), J. Kilpatrick (Author)
4.5 4.5 out of 5 stars 299 ratings
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This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.
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  1. ISBN-10
    9780486469249
  2. ISBN-13
    978-0486469249
  3. Edition
    1/20/09
  4. Publisher
    Dover Publications
  5. Publication date
    February 19, 2009
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    5.5 x 0.25 x 8.25 inches
  9. Print length
    80 pages
  10. See all details
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Editorial Reviews

About the Author

George Pólya (1887–1985) was a professor of mathematics at Stanford University who made lasting contributions to combinatorics, number theory, numerical analysis, and probability theory. He was also very well-known for his work in mathematics education. In his later days, Dr. Pólya spent considerable effort to document the methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote four books on the subject.

Product details

  • ASIN ‏ : ‎ 0486469247
  • Publisher ‏ : ‎ Dover Publications; 1/20/09 edition (February 19, 2009)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 80 pages
  • ISBN-10 ‏ : ‎ 9780486469249
  • ISBN-13 ‏ : ‎ 978-0486469249
  • Item Weight ‏ : ‎ 3.81 ounces
  • Dimensions ‏ : ‎ 5.5 x 0.25 x 8.25 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 299 ratings

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Gyorgy Polya

Gyorgy Polya

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4.5 out of 5 stars
4.5 out of 5
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299 global ratings

Top reviews from the United States

Sasha Alyson
5.0 out of 5 stars Challenging, top-notch, and original
Reviewed in the United States on June 2, 2015
Verified Purchase
You would expect a book with this pedigree to be good, and it is.

From 1946 to 1965, Stanford University gave high school students a chance to win a scholarship by taking a difficult math test, with just four questions. This book collects those questions, and their answers. The subject matter varies, including algebra, geometry, and trigonometry.

Most notably, the questions try to measure not achievement, but aptitude. They require a sound foundation of learning, but also original thinking or a flash of insight. The first question in each set is easiest; a sharp high school student would probably have a reasonable shot at answering it. Then the questions get more difficult. I found it to be a fascinating and enjoyable collection, even when that flash of insight eluded me. Months after I bought it, I still open it occasionally and try a new problem.
17 people found this helpful
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Betholwen
5.0 out of 5 stars Great book of problems
Reviewed in the United States on November 27, 2012
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My 17 year-old son loves this book so much, that when his bookbag was stolen from his locker during gym he asked me to replace this book! He's on a math team, and they work on problems like this all the time. It must be good!
12 people found this helpful
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Aristarchus
4.0 out of 5 stars Good Problem Collection, but NO Process for HOW to solve problems
Reviewed in the United States on August 5, 2016
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The difficulty with rating a book like this is deciding what criteria should be used to rate the book. I rated the book as "4 stars" because of my reverence for George Polya. Polya was a great teacher and I have read all of his books. Unfortunately, this book does not teach the art of problem solving. It is simply a collection of interesting and challenging mathematics problems, along with solutions. The problems are very good. The difficulty of the problems depends on your level of experience and knowledge. I have a Ph.D. in mathematics, so I find the problems to be interesting and mildly challenging. A novice, or someone who is struggling to learn mathematics, may find the problems to be impossibly difficult. And when you read the solutions, you might feel stupid, because there is little chance that you would have the genius required to invent the solution. The book omits the human exploratory process of how to actually solve a mathematics problem. Most problem books and research papers omit all the pain, suffering, and hard work that goes between the problem statement and the seemingly miraculous solution. This book is a really great collection of problems, but it will NOT teach you how to create, invent, or solve these kinds of problems. If you want to learn that, I suggest that you read Polya's "How to Solve It, " or Polya's "Mathematics and Plausible Reasoning." To solve mathematics problems, you need knowledge, experience, intuition, passion, hard work, good luck, and a PROCESS that works. This book has none of those things. Read the other two books of Polya's.
64 people found this helpful
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Kindle Customer
5.0 out of 5 stars Very cool problems inside!
Reviewed in the United States on August 30, 2019
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I recommend it. There's some cool problems in here! I'd give it a whirl.
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Ke Wang
5.0 out of 5 stars the delivery is so fast
Reviewed in the United States on April 27, 2013
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I get the book so fast ,thanks. I like it, especially your service attitude.
very good!
this book is a good resource for problem solving in Mathematics. It is very useful .
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Stephen G. Margolis
5.0 out of 5 stars Excellent
Reviewed in the United States on May 11, 2013
Verified Purchase
This book is exactly what I was looking for. This book will be used in coaching very advanced 5th grade students for the "5th Grade Math Challenge" of Minneapolis Public Schools.
2 people found this helpful
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Kindle Customer2
3.0 out of 5 stars Not so hot on the Kindle
Reviewed in the United States on December 31, 2015
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Fine on computer but the problems on the Kindle Paperwhite are too small to read. Increasing the font size works for the general text but not for the actual problems. So almost unusable on the Kindle.
14 people found this helpful
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Abhi
5.0 out of 5 stars Great!
Reviewed in the United States on March 26, 2013
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The service was great and the book reached me on time. The author is a great author and this can be a very useful book to young kids.
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Jose Lourenço Claudio Junior
5.0 out of 5 stars There are 20 sets of problems and solutions based on the Stanford University exam in mathematics.
Reviewed in Brazil on February 5, 2023
Verified Purchase
Excellent workbook with logic and probability problems.
Originality and insight require development of competence in theorizing and verifying mathematical facts:
I) Examine the results of the general declarations;
II) Discover how conjectures can be incorrect;
III) Solving sequences of subproblems to reveal theory construction;
IV) Recognize "red herrings", in which the obvious relationships between the data prove irrelevant to the solutions.
V) Tips for each problem presenting the appropriate procedures.
A source of captivating challenges.
One person found this helpful
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Client Kindle
5.0 out of 5 stars Excellent livre
Reviewed in France on July 18, 2023
Verified Purchase
C'est un très bon livre de problèmes accessible pour n'importe qui ayant fait des maths au lycée.
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Luke Dunn
5.0 out of 5 stars Excellent well rounded set of problems
Reviewed in the United Kingdom on September 17, 2021
Verified Purchase
This is a really good little book. The problems all draw insight from the reader and build mathematical confidence without requiring very in depth knowledge. Basic arithmetic skills, a tadge of algebra and geometry... and of course a logical systematic approach. Even relatively little calculus in what I've seen so far. This is because I think the authors want to encourage talent in the essence of mathematical reasoning, without necessitating a large background of knowledge. Every problem is interesting but *within reach* for someone entering university.
3 people found this helpful
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Richardclk
5.0 out of 5 stars FAST SERVICE
Reviewed in Canada on August 21, 2019
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Really very fast delivery I am totally impressed. Arrived as stated "New"
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Cliente Amazon
5.0 out of 5 stars libro interessante come da aspettative
Reviewed in Italy on September 25, 2020
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mi e' piaciuto pressocche' tutto del libro che conoscevo e che amplia e sistema le mie conoscenze della materia
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