**Mathematical World**

Volume: 7;
1996;
272 pp;
Softcover

MSC: Primary 00;

**Print ISBN: 978-0-8218-0430-8
Product Code: MAWRLD/7**

List Price: $45.00

AMS Member Price: $36.00

MAA Member Price: $40.50

**Electronic ISBN: 978-1-4704-2473-2
Product Code: MAWRLD/7.E**

List Price: $42.00

AMS Member Price: $33.60

MAA Member Price: $37.80

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# Mathematical Circles

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*Dmitri Fomin; Sergey Genkin; Ilia V. Itenberg*

“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.

#### Readership

Graduate students and high school and college mathematics teachers.

#### Reviews & Endorsements

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

# Table of Contents

## Mathematical Circles

- Cover Cover11 free
- Title iii4 free
- Contents v6 free
- Foreword vii8 free
- Preface to the Russian Edition ix10 free
- Part I. The First Year of Education 114 free
- Part II. The Second Year of Education 7790
- Chapter 9. Induction 7790
- Chapter 10. Divisibility–2: Congruence and Diophantine Equations 95108
- Chapter 11. Combinatorics–2 107120
- Chapter 12. Invariants 123136
- Chapter 13. Graphs–2 135148
- Chapter 14. Geometry 153166
- Chapter 15. Number Bases 167180
- Chapter 16. Inequalities 175188
- Chapter 17. Problems for the Second Year 187200

- Appendix A. Mathematical Contests 201214
- Appendix B. Answers, Hints, Solutions 211224
- Appendix C. References 269282
- Back Cover Back Cover1286