2009;
337 pp;
Hardcover

MSC: Primary 00;

**Print ISBN: 978-0-8218-4808-1
Product Code: MBK/61**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

**Electronic ISBN: 978-1-4704-1205-0
Product Code: MBK/61.E**

List Price: $73.00

AMS Member Price: $58.40

MAA Member Price: $65.70

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#### Supplemental Materials

# Making Mathematics Come to Life: A Guide for Teachers and Students

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*O. A. Ivanov*

“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.

#### Readership

High school teachers, undergraduate and graduate students interested in learning and teaching mathematics.

#### Table of Contents

# Table of Contents

## Making Mathematics Come to Life: A Guide for Teachers and Students

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Foreword ix10 free
- Introduction 112 free
- Induction 718 free
- Combinatorics 2738
- The whole numbers 5970
- Geometric transformations 89100
- Inequalities 117128
- Graphs 151162
- The pigeonhole principle 185196
- Complex numbers and polynomials 205216
- Rational approximations 233244
- Mathematics and the computer 265276
- Instead of a conclusion: teaching how to look for solutions of problems, or fantasy in the manner of Pólya 287298
- Solutions of the supplementary problems 295306
- Bibliography 329340
- Index 331342 free
- Back Cover Back Cover1349