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Mathematical Circles: Russian Experience (Mathematical World, Vol. 7) Paperback – July 22, 1996

ISBN-13: 978-0821804308 ISBN-10: 0821804308

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Mathematical Circles: Russian Experience (Mathematical World, Vol. 7) + A Decade of the Berkeley Math Circle: The American Experience (MSRI Mathematical Circles Library) (v. 1) + A Moscow Math Circle: Week-by-Week Problem Sets (MSRI Mathematical Circles Library)
Price for all three: $76.40

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Product Details

  • Paperback: 272 pages
  • Publisher: American Mathematical Society (July 22, 1996)
  • Language: English
  • ISBN-10: 0821804308
  • ISBN-13: 978-0821804308
  • Product Dimensions: 6.9 x 9.8 inches
  • Shipping Weight: 1.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #672,649 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Fomin's Mathematical Circles is a strikingly elegant, practical tool for enabling American high-school teachers and math coaches to replicate the Russian mathematical circle here." ---- Dianne Butkus, Saint Ignatius Loyola School

"There is much to find, learn, and enjoy in this work for both students and teachers ... well-prepared mathematical amateurs will also be delighted ... throughout, the presentation and tone are charmingly appealing and appropriately "light", even when more difficult topics are under discussion ... a very worthwhile book; it most definitely belongs in every school and personal library." ----Mathematical Reviews

"Could be considered among many other recreational mathematics books as one source of interesting problems to supplement instruction and encourage an appreciation for the beauty of mathematics." ---- Mathematics Teaching in the Middle School

Language Notes

Text: English (translation)
Original Language: Russian

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Customer Reviews

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Most Helpful Customer Reviews

46 of 47 people found the following review helpful By A Customer on July 25, 2002
Format: Paperback
In sharp contrast to standard US math education, which
is generally a death march from algebra to calculus, this
book suggests a wonderful new way to organize the ideas
of elementary mathematics. The organizational principle
here is around fundamental ideas that underlie
every mathematical proof ever conceived: parity, the
pigeonhole principle, induction, counting (combinatorics),
etc. Each section starts off with easy problems that anyone
can get, and leads you through to more and more challenging
illustrations of that section's principle; the last problems
of each section are often quite sophisticated and rewarding.
Do the problems in this book, and you can't help but just
be smarter for it.
When I was a kid, I was mystified by puzzle problems that I
had no idea how to tackle, and intimidated by kids who could
solve those types of problems. Had this book been available
back then, it would have de-mystified those problems for me,
and I would have acquired the kinds of skills and insights
that make a real mathematician. Whatever your age, if you
are interested in developing your core competencies in math,
I can't think of a better endeavor than to do all the problems
in this book. If I were the US Secretary of Education, I would
make solving all the problems in this book a mandatory
requirement for all math teachers, and all graduating high
school students. Even a partial implementation of such a
policy would make this country mathematically literate in a
way that we can't even conceive of today. It would de-mistify
mathematical "genius" on a global scale.
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20 of 21 people found the following review helpful By P. H. on April 26, 2007
Format: Paperback
Russia perennially places among the top three performers in the International Mathematical Olympiad, the world's most prestigious mathematical competition for high-school students. The "mathematical circle" is undoubtedly one element of the mathematical culture that has contributed to Russia's success in that competition.

A Russian mathematical circle is not a geometrical shape, but rather a group of mathematically motivated students guided by a university-level mathematician who helps the students enlighten themselves about simple, yet beautiful and powerful, mathematical concepts. Fomin's Mathematical Circles is a strikingly elegant, practical tool for enabling American high-school teachers and math coaches to replicate the Russian mathematical circle here.

Mathematical Circles has two parts, each intended to be taught over one year. The first part has sections covering parity, combinatorics, divisibility and remainders, the pigeon-hole principle, graphs, the triangle inequality, and games. The second part has sections covering more advanced topics in divisibility, combinatorics, and graphs, as well as sections on invariants, number bases, geometry, and inequalities.

Each section begins with a short introduction addressed to the teacher and then proceeds to a series of problems periodically interspersed with concise explanations about new concepts being introduced through the problems and pedagogical advice related to those concepts. In any given section, the first problem is generally extraordinarily simple. The first problem in the parity section is:

Problem 1. Eleven gears are placed on a plane, arranged in a chain as shown [in a diagram with eleven gears interlocking in a circular arrangement]. Can all the gears rotate simultaneously?
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20 of 23 people found the following review helpful By Sebastien Gilmour on September 30, 2003
Format: Paperback
I bought this book to help me learn how to solve problems. However, when it arrived, I realised it was destined as a book for 12 to 14 year old students. Still, I gave it a try ( I am 19 years old). The problems are well stated, easy to do, and methodologicaly sound. I found the problems too easy, but my little brother ( 9 years old ) had trouble. It's great for some young students who would like to learn the basics of problem solving.
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3 of 4 people found the following review helpful By CC on August 5, 2013
Format: Paperback Verified Purchase
While covering much of the same ground as A Moscow Math Circle: Week-by-Week Problem Sets, this book pales in comparison, both due to poorer organization and more work to implement by a prospective math circle instructor. The material jumps around a lot (great if you have a mixed group of students, poor if you have a homogeneous group of students). The highlight of this book is the SMALL discussion of the culture and education of mathematics students in Russia, but even that is not as good as the aforementioned title. Overall, its a fine collection of problems at the secondary level for U.S. students, but better alternatives (using U.S. materials like Contest Problem Books I-IX that feature AMC problems) exist.
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