دایره‌های ریاضی (تجربهٔ روسی)

''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. Contents......Page 4 Foreword......Page 6 Preface to Russian Edition......Page 8 C0......Page 11 C1 - Parity......Page 15 C2 - Combinatorics-1 ......Page 21 C3 - Divisibility and Remainders......Page 29 C4 - The pigeon hole principle......Page 41 C5 - Graphs-1......Page 49 C6 - The Triangle Inequality......Page 61 C7 - Games\r......Page 67 C8 - Problems for the First Year\r......Page 75 C9 - Induction\r......Page 87 C10 - Divisibility-2\r......Page 105 C11 - Combinatorics-2......Page 117 C12 - Invariants......Page 133 C13 - Graphs-2\r......Page 145 C14 - Geometry\r......Page 163 C15 - Number bases......Page 179 C16 - Inequalities\r......Page 188 C17 - problems for the second Year\r......Page 200 Appendix A - Mathematical Contests\r......Page 214 Appendix B - Solutions\r......Page 224 Appendix C- References\r......Page 282 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 Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.