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Lectures and Problems: A Gift to Young Mathematicians
 

Translated by Dmitry Fuchs and Mark Saul

A co-publication of the AMS and Mathematical Sciences Research Institute
Lectures and Problems: A Gift to Young Mathematicians
Softcover ISBN:  978-1-4704-2259-2
Product Code:  MCL/17
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
eBook ISBN:  978-1-4704-2735-1
Product Code:  MCL/17.E
List Price: $30.00
MAA Member Price: $27.00
AMS Member Price: $24.00
Softcover ISBN:  978-1-4704-2259-2
eBook: ISBN:  978-1-4704-2735-1
Product Code:  MCL/17.B
List Price: $65.00 $50.00
MAA Member Price: $58.50 $45.00
AMS Member Price: $52.00 $40.00
Lectures and Problems: A Gift to Young Mathematicians
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Lectures and Problems: A Gift to Young Mathematicians

Translated by Dmitry Fuchs and Mark Saul

A co-publication of the AMS and Mathematical Sciences Research Institute
Softcover ISBN:  978-1-4704-2259-2
Product Code:  MCL/17
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
eBook ISBN:  978-1-4704-2735-1
Product Code:  MCL/17.E
List Price: $30.00
MAA Member Price: $27.00
AMS Member Price: $24.00
Softcover ISBN:  978-1-4704-2259-2
eBook ISBN:  978-1-4704-2735-1
Product Code:  MCL/17.B
List Price: $65.00 $50.00
MAA Member Price: $58.50 $45.00
AMS Member Price: $52.00 $40.00
  • Book Details
     
     
    MSRI Mathematical Circles Library
    Volume: 172015; 176 pp
    MSC: Primary 00; Secondary 11;

    Vladimir Arnold (1937–2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre.

    “Continued Fractions” takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision.

    “Euler Groups” treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment.

    In “Complex Numbers” the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics.

    “Problems for Children 5 to 15 Years Old” must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions.

    In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground.

    Arnold's style of exposition is unforgiving. The reader—even a professional mathematician—will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent.

    In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

    Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

    Readership

    Undergraduate and graduate students and researchers interested in mathematics.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Copyright page
    • Contents
    • Preface to the English edition
    • Continued fractions
    • Continued fractions
    • Geometry of complex numbers, quaternions, and spins
    • Geometry of complex numbers, quaternions, and spins
    • Euler groups and arithmetics of geometric progressions
    • Euler groups and arithmetics of geometric progressions
    • Problem for children 5 to 15 years old
    • Problems
    • Solutions to selected problems
    • Bibliography
    • Back Cover
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 172015; 176 pp
MSC: Primary 00; Secondary 11;

Vladimir Arnold (1937–2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre.

“Continued Fractions” takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision.

“Euler Groups” treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment.

In “Complex Numbers” the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics.

“Problems for Children 5 to 15 Years Old” must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions.

In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground.

Arnold's style of exposition is unforgiving. The reader—even a professional mathematician—will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent.

In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Readership

Undergraduate and graduate students and researchers interested in mathematics.

  • Cover
  • Title page
  • Copyright page
  • Contents
  • Preface to the English edition
  • Continued fractions
  • Continued fractions
  • Geometry of complex numbers, quaternions, and spins
  • Geometry of complex numbers, quaternions, and spins
  • Euler groups and arithmetics of geometric progressions
  • Euler groups and arithmetics of geometric progressions
  • Problem for children 5 to 15 years old
  • Problems
  • Solutions to selected problems
  • Bibliography
  • Back Cover
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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