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Making Mathematics Come to Life: A Guide for Teachers and Students
 
O. A. Ivanov St. Petersburg State University, St. Petersburg, Russia
Making Mathematics Come to Life
Hardcover ISBN:  978-0-8218-4808-1
Product Code:  MBK/61
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-1205-0
Product Code:  MBK/61.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Hardcover ISBN:  978-0-8218-4808-1
eBook: ISBN:  978-1-4704-1205-0
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
Making Mathematics Come to Life
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Making Mathematics Come to Life: A Guide for Teachers and Students
O. A. Ivanov St. Petersburg State University, St. Petersburg, Russia
Hardcover ISBN:  978-0-8218-4808-1
Product Code:  MBK/61
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-1205-0
Product Code:  MBK/61.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Hardcover ISBN:  978-0-8218-4808-1
eBook ISBN:  978-1-4704-1205-0
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 Details
     
     
    2009; 337 pp
    MSC: 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.

    Readership

    High 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2009; 337 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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