# Lectures and Problems: A Gift to Young Mathematicians

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*V. I. Arnold*

Translated by Dmitry Fuchs and Mark Saul

A co-publication of the AMS and the Mathematical Sciences Research Institute

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.