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Mathematical Circles
Dmitri Fomin, St. Petersburg State University, Russia, Sergey Genkin, Microsoft Corporation, and Ilia V. Itenberg, Institut de Recherche Mathématique de Rennes, France

Mathematical World
1996; 272 pp; softcover
Volume: 7
ISBN-10: 0-8218-0430-8
ISBN-13: 978-0-8218-0430-8
List Price: US$40
Member Price: US$32
Order Code: MAWRLD/7
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"This is a sample of rich Russian mathematical culture written by professional mathematicians with great experience in working with high school students ... Problems are on very simple levels, but building to more complex and advanced work ... [contains] solutions to almost all problems; methodological notes for the teacher ... developed for a peculiarly Russian institution (the mathematical circle), but easily adapted to American teachers' needs, both inside and outside the classroom."

--from the Translator's notes

What kind of book is this? It is a book produced by a remarkable cultural circumstance in the former Soviet Union which fostered the creation of groups of students, teachers, and mathematicians called "mathematical circles". The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport--without necessarily being competitive.

This book is intended for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. It is also a book of mathematical recreations and, at the same time, a book containing vast theoretical and problem material in main areas of what authors consider to be "extracurricular mathematics". The book is based on a unique experience gained by several generations of Russian educators and scholars.


Graduate students and high school and college mathematics teachers.


"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

"A valuable resource, primarily for middle school, but also for high school extra-curricular activities and class work ... well written, and well translated."

-- Zentralblatt MATH

"A rich collection of good problems ... useful notes for teachers ... will be especially interesting for those who are dealing with all forms of cooperative learning ... may be very useful wherever there are classes devoted to solving non-standard problems."

-- American Mathematical Monthly

Table of Contents

  • Chapter zero (Chapter 0)
  • Parity (Chapter 1)
  • Combinatorics-1 (Chapter 2)
  • Divisibility and remainders (Chapter 3)
  • The pigeon hole principle (Chapter 4)
  • Graphs-1 (Chapter 5)
  • The triangle inequality (Chapter 6)
  • Games (Chapter 7)
  • Problems for the first year (Chapter 8)
  • Induction (Chapter 9)
  • Divisibility-2: Congruence and Diophantine equations (Chapter 10)
  • Combinatorics-2 (Chapter 11)
  • Invariants (Chapter 12)
  • Graphs-2 (Chapter 13)
  • Geometry (Chapter 14)
  • Number bases (Chapter 15)
  • Inequalities (Chapter 16)
  • Problems for the second year (Chapter 17)
  • Mathematical contests (Chapter 18)
  • Answers, hints, solutions (Chapter 19)
  • References
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