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Lectures and Problems - A Gift to Young Mathematicians (Paperback)
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Lectures and Problems - A Gift to Young Mathematicians (Paperback)
Series: MSRI Mathematical Circles Library
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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.
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