AMS/MSRI Math Circle Library

The book series Math Circles Library is co-published by the Mathematical Sciences Research Institute and the American Mathematical Society, with the generous support of the John Templeton Foundation. The Mathematical Circles Library includes books of several types: collections of solved problems, pedagogically sound expositions, discussions of experiences in math teaching, and practical books for organizers of mathematical circles.

Some of the books are translations from Russian—there has long been a thriving tradition of math circles in Eastern Europe—while others were written in English by mathematicians who lead circles or are otherwise experienced in mathematics education.

Most books are suitable for both students and leaders in math circles. Parents of participants will also find the books useful.

For an updated list of the books (including forthcoming volumes), more details, and to purchase any items please visit the AMS website.

The MSRI Mathematical Circles Library Series

Mathematical Circles
Dmitri Fomin, Sergey Genkin, Ilia V. Itenberg, 1996.
“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.”
Volume 1. A Decade of the Berkeley Math Circle: The American Experience, Volume I
edited by Zvezdelina Stankova and Tom Rike, 2008.
Founded in 1998, the Berkeley Math Circle (BMC) is a pioneering model of a U.S. math circle, aspiring to prepare our best young minds for their future roles as mathematics leaders. Over the last decade, 50 instructors—from university professors to high school teachers to business tycoons—have shared their passion for mathematics by delivering more than 320 BMC sessions full of mathematical challenges and wonders. Based on a dozen of these sessions, this book encompasses a wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik’s cube and abstract algebra; from number theory to mass point theory; from complex numbers to game theory via invariants and monovariants.
Volume 2. Circle in a Box
Sam Vandervelde, 2009.
Math circles provide a setting in which mathematicians work with secondary school students who are interested in mathematics. This form of outreach, which has existed for decades in Russia, Bulgaria, and other countries, is now rapidly spreading across the United States as well. The first part of this book offers helpful advice on all aspects of math circle operations, culled from conversations with over a dozen directors of successful math circles. Topics include creative means for getting the word out to students, sound principles for selecting effective speakers, guidelines for securing financial support, and tips for designing an exciting math circle session. The purpose of this discussion is to enable math circle coordinators to establish a thriving group in which students can experience the delight of mathematical investigation. The second part of the book outlines ten independent math circle sessions, covering a variety of topics and difficulty levels. Each chapter contains detailed presentation notes along with a useful collection of problems and solutions. This book will be an indispensable resource for any individual involved with a math circle or anyone who would like to see one begin in his or her community.
Volume 3. Geometry: A Guide for Teachers
Judith D. Sally and Paul J. Sally, Jr., 2011.
This geometry book is written foremost for future and current middle school teachers, but is also designed for elementary and high school teachers. The book consists of ten seminars covering in a rigorous way the fundamental topics in school geometry, including all of the significant topics in high school geometry.
Volume 4.Moscow Mathematical Olympiads, 1993-1999
edited by Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, and Ivan Yashchenko, 2011.
The Moscow Mathematical Olympiad has been challenging high school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation.
Volume 5. Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers
Alexander Zvonkin, 2011.
This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work?
Volume 6. Introduction to Functional Equations: Theory and problem-solving strategies for mathematical competitions and beyond
Costas Efthimiou, 2011.
Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level.
Volume 7. Moscow Mathematical Olympiads, 2000-2005
edited by Roman Fedorov, Alexei Belov, Alexander Kovaldzhi, and Ivan Yashchenko, 2011.
The Moscow Mathematical Olympiad has been challenging high school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation.
Volume 8. A Moscow Math Circle: Week-by-week Problem Sets
Sergey Dorichenko and Kvant Magazine, 2012.
Moscow has a rich tradition of successful math circles, to the extent that many other circles are modeled on them. This book presents materials used during the course of one year in a math circle organized by mathematics faculty at Moscow State University, and also used at the mathematics magnet school known as Moscow School Number 57.
Volume 9. 
Euclidean Geometry: A Guided Inquiry Approach

David M. Clark, 2012.
Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation.
Volume 10. 
Integers, Fractions and Arithmetic: A Guide for Teachers 

Judith D. Sally and Paul J. Sally, Jr., 2012.
This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K–8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes.
Volume 11. 
Mathematical Circle Diaries, Year 1: Complete Curriculum for Grades 5 to 7 

Anna Burago, Prime Factor Math Circle, 2012.
Early middle school is a great time for children to start their mathematical circle education. This time is a period of curiosity and openness to learning. The thinking habits and study skills acquired by children at this age stay with them for a lifetime.
Volume 12. 
Invitation to a Mathematical Festival

Ivan Yashchenko, Moscow Center for Continuous Mathematical Education, 2013.
Held annually in Moscow since 1990, the Mathematical Festival is a brilliant and fascinating math competition attended by hundreds of middle school students. Participants of the Festival solve interesting mathematical problems and partake in other engaging activities, while cultivating key skills such as intuitive reasoning and quick thinking. This book contains problems presented at the Festival during the years 1990–2011, along with hints and solutions for many of them.
Volume 13. 
Math Circles for Elementary School Students

Natasha Rozhkovskaya, Kansas State University, 2014.
The main part of this book describes the first semester of the existence of a successful and now highly popular program for elementary school students at the Berkeley Math Circle. The topics discussed in the book introduce the participants to the basics of many important areas of modern mathematics, including logic, symmetry, probability theory, knot theory, cryptography, fractals, and number theory.
Volume 14. 
A Decade of the Berkeley Math Circle: The American Experience, Volume II

Zvezdelina Stankova, Mills College, and Tom Rike, Oakland High School, 2014.
The Berkeley Math Circle (BMC) started in 1998 as one of the very first math circles in the U.S. This second volume of the book series is based on a dozen of these sessions, encompassing a variety of enticing and stimulating mathematical topics, some new and some continuing from Volume I:
Volume 15. 
The ARML Power Contest 

Thomas Kilkelly, Wayzata High School, 2014.The ARML (American Regions Math League) Power Contest is truly a unique competition in which a team of students is judged on its ability to discover a pattern, express the pattern in precise mathematical language, and provide a logical proof of its conjectures. This book contains thirty-seven interesting and engaging problem sets from the ARML Power Contests from 1994 to 2013. They are generally extensions of the high school mathematics classroom and often connect two remote areas of mathematics. Additionally, they provide meaningful problem situations for both the novice and the veteran mathlete.
Volume 16. 
Experimental Mathematics 

V. I. Arnold.Translated by Dmitry Fuchs and Mark Saul, 2015.
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. This book, based on the author’s lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved.
Volume 17. 
Lectures and Problems: A Gift to Young Mathematicians

V.I. Arnold. Translated by: Dmitry Fuchs; Mark Saul, 2015.
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.
Volume 18. 
Geometry in Problems

Alexander Shen. 2016.
Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician’s viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving.

Volume 19. 
Algebraic Inequalities: New Vistas

Titu Andreescu and Mark Saul, 2016.
This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student.

Do you have suggestions for books to add to the MCL? Make a Proposal. We are always on the lookout for a good project! If you would like to suggest a book for publication in the MSRI–MCL series, in any language, whether authored by you or someone else, please write the series managing editor, Silvio Levy,, with a brief description of the work.

Projects are judged by an international Editorial Board with a varied membership: authors, Math Circle organizers, leaders in the teaching of mathematics to gifted students, and research mathematicians with an involvement in K–12 education.