Hardcover ISBN:  9780821848081 
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eBook ISBN:  9781470412050 
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Hardcover ISBN:  9780821848081 
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Product Code:  MBK/61.B 
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Hardcover ISBN:  9780821848081 
Product Code:  MBK/61 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470412050 
Product Code:  MBK/61.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Hardcover ISBN:  9780821848081 
eBook ISBN:  9781470412050 
Product Code:  MBK/61.B 
List Price:  $164.00 $124.50 
MAA Member Price:  $147.60 $112.05 
AMS Member Price:  $131.20 $99.60 

Book Details2009; 337 ppMSC: Primary 00
“It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a ‘book for reading about mathematics’. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.”
—from the Preface by A. S. Merkurjev
If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book.
An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them.
Unfortunately, what is sometimes studied at school under the name “mathematics” resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun.
ReadershipHigh school teachers, undergraduate and graduate students interested in learning and teaching mathematics.

Table of Contents

Chapters

Introduction

Chapter 1. Induction

Chapter 2. Combinatorics

Chapter 3. The whole numbers

Chapter 4. Geometric transformations

Chapter 5. Inequalities

Chapter 6. Graphs

Chapter 7. The pigeonhole principle

Chapter 8. Complex numbers and polynomials

Chapter 9. Rational approximations

Chapter 10. Mathematics and the computer

Instead of a conclusion: teaching how to look for solutions of problems, or fantasy in the manner of Pólya

Solutions of the supplementary problems


Additional Material

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“It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a ‘book for reading about mathematics’. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.”
—from the Preface by A. S. Merkurjev
If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book.
An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them.
Unfortunately, what is sometimes studied at school under the name “mathematics” resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun.
High school teachers, undergraduate and graduate students interested in learning and teaching mathematics.

Chapters

Introduction

Chapter 1. Induction

Chapter 2. Combinatorics

Chapter 3. The whole numbers

Chapter 4. Geometric transformations

Chapter 5. Inequalities

Chapter 6. Graphs

Chapter 7. The pigeonhole principle

Chapter 8. Complex numbers and polynomials

Chapter 9. Rational approximations

Chapter 10. Mathematics and the computer

Instead of a conclusion: teaching how to look for solutions of problems, or fantasy in the manner of Pólya

Solutions of the supplementary problems