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Review
There are a handful of really wonderful books that can introduce a young high-school student to the beauty of mathematics. This is definitely one of them. Besides, this book is probably going to be known as the first book written by one of the best mathematicians of the twenty-first century. (Mihaela Poplicher, MAA Reviews )
Product Description
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
17 of 17 people found the following review helpful
Format:Paperback
First, the bad news.
The front cover of this book gives its author as "Terence Tao, Fields Medal winner 2006". Well ... yes, and no. The thing is, this book was written when Tao was 15 years old. It reflects the precocious skill and insight of an outstandingly gifted 15-year-old, who had won a gold medal at the International Mathematical Olympiad at age 13 (most participants are 17-ish), but not really those of the outstandingly gifted 31-year-old who won the Fields.
It's only about 100 pages long; the problems it discusses are mostly relatively easy (meaning, say, national high-school mathematics competition level or thereabouts, rather than IMO, so not *that* easy). It doesn't give away any very deep secrets (if there are any) about how to solve such problems. Write down what you know, look for symmetries, simplify step by step, etc.; the real rocket science, as it were, is hidden away in the bits of Tao's brain that instinctively know what symmetries to look for, what steps are likely to lead in the right direction, and so on.
The good news: You wouldn't know it was written by a 15-year-old if the preface didn't tell you. It *is* a book about mathematics written by someone with a Fields-medal-quality brain, and a book about Olympiad-style problems written by one of the greatest-ever exponents of that art. It contains some nice problems, with solutions by (I repeat myself) one of the finest minds in the business. It's also quite cheap.
If you're interested in this, you should also look at Paul Zeitz's "The art and craft of problem-solving"; it has more pages and more substance to it, but it's twice the price and wasn't written by a Fields medalist.
The front cover of this book gives its author as "Terence Tao, Fields Medal winner 2006". Well ... yes, and no. The thing is, this book was written when Tao was 15 years old. It reflects the precocious skill and insight of an outstandingly gifted 15-year-old, who had won a gold medal at the International Mathematical Olympiad at age 13 (most participants are 17-ish), but not really those of the outstandingly gifted 31-year-old who won the Fields.
It's only about 100 pages long; the problems it discusses are mostly relatively easy (meaning, say, national high-school mathematics competition level or thereabouts, rather than IMO, so not *that* easy). It doesn't give away any very deep secrets (if there are any) about how to solve such problems. Write down what you know, look for symmetries, simplify step by step, etc.; the real rocket science, as it were, is hidden away in the bits of Tao's brain that instinctively know what symmetries to look for, what steps are likely to lead in the right direction, and so on.
The good news: You wouldn't know it was written by a 15-year-old if the preface didn't tell you. It *is* a book about mathematics written by someone with a Fields-medal-quality brain, and a book about Olympiad-style problems written by one of the greatest-ever exponents of that art. It contains some nice problems, with solutions by (I repeat myself) one of the finest minds in the business. It's also quite cheap.
If you're interested in this, you should also look at Paul Zeitz's "The art and craft of problem-solving"; it has more pages and more substance to it, but it's twice the price and wasn't written by a Fields medalist.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
4 reviews
17 of 19 people found the following review helpful
15 year old math tips
20 May 2007
Format:Paperback
This charming book explains why math olympiad puzzles are fun, and gives 15 year old insights ( in two senses --- most of the text was written by the 15 year old Terence Tao, but revised with some additional good exercises 15 years later by 30 year old Fields medalist Terence Tao.) The style is chatty, and the advice and worked examples are very good and do not require any math beyond pre-calculus. The level of difficulty is just right for would be high school math competitors, and adults with some math who enjoy a mild challenge.
20 of 30 people found the following review helpful
Six easy steps to becoming a Fields medalist
30 Jan 2007
Format:Paperback|Amazon Verified Purchase
I came across this book after reading about Terence Tao, a recent Fields medalist. It's interesting to see a book like this by such an accomplished mathematician. The book gives practical approaches to solving the types of math problems encountered in math olympiad competitions. I am not, nor have I ever been, a math olympian, but I found the book to be entertaining and useful for intellectual fortification purposes.
4 of 6 people found the following review helpful
Good reference from a beautiful mind
21 Mar 2009
Format:Paperback|Amazon Verified Purchase
I really liked this book. It is written by one of the most brilliant mathematicians of our generation. It presents some of the problem solving techniques math contestants should master in a mature though approachable manner. I wouldn't suggest it as the only book to consult when designing a training curriculum for high level math contestants, but it is definitelly a good reference, and nicely written.
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