IMC Resources

A Decade of the Berkeley Math Circle: The American Experience, Volume I
Publisher: AMS and the Mathematical Sciences Research Institute
Editor: Zvezdelina Stankova, Tom Rike
Book Description:

Many mathematicians have been drawn to mathematics through their experience with math circles: extracurricular programs exposing teenage students to advanced mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics. 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. The treatments of these subjects encompass every significant method of proof and emphasize ways of thinking and reasoning via 100 problem solving techniques. Also featured are 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions.


A Decade of the Berkeley Math Circle: The American Experience, Volume II
Publisher: AMS and the Mathematical Sciences Research Institute (MSRI)
Editor: Zvezdelina Stankova and Tom Rike
Book Description:

Based on a dozen of math circle 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. The treatments of these subjects encompass every significant method of proof and emphasize ways of thinking and reasoning via 100 problem solving techniques. Also featured are 300 problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions. The book presents possible paths to studying mathematics and inevitably falling in love with it, via teaching two important skills: thinking creatively while still "obeying the rules," and making connections between problems, ideas, and theories.

The book encourages you to apply the newly acquired knowledge to problems and guides you along the way, but rarely gives you ready answers. "Learning from our own mistakes" often occurs through discussions of non-proofs and common problem solving pitfalls. The reader has to commit to mastering the new theories and techniques by "getting your hands dirty" with the problems, going back and reviewing necessary problem solving techniques and theory, and persistently moving forward in the book. The mathematical world is huge: you'll never know everything, but you'll learn where to find things, how to connect and use them. The rewards will be substantial.


Kiselev's Geometry: Book 1, Planimetry
Publisher: Sumizdat
Author: Kiselev
Book Description:

This is a wonderful, easy-going introduction to plane geometry, which was used for decades as a regular textbook in Russian middle schools. It has been translated from its original Russian to English by one of UC Berkeley's very own math instructors, Professor Alexander Givental.


Kiselev's Geometry: Book 2, Stereometry
Publisher: Sumizdat
Author: Kiselev
Book Description:

This is the second volume of the famous Kiselev's work. A marvelous self-contained exposition on stereometry that proved to be a favorite for generations of students and mathematicians in Russia. Thanks to our UC Berkeley Professor Alexander Givental this book is now available in English.


Math Circle by the Bay Topics for Grades 1-5 (MSRI Mathematical Circles Library)
Publisher: American Mathematical Society (AMS)
Author: Laura Givental, Maria Nemirovskaya, Ilya Zakharevich
Book Description:

This book is based on selected topics that the authors taught in math circles for elementary school students at the University of California, Berkeley; Stanford University; Dominican University (Marin County, CA); and the University of Oregon (Eugene). It is intended for people who are already running a math circle or who are thinking about organizing one. It can be used by parents to help their motivated, math-loving kids or by elementary school teachers. We also hope that bright fourth or fifth graders will be able to read this book on their own. The main features of this book are the logical sequence of the problems, the description of class reactions, and the hints given to kids when they get stuck. This book tries to keep the balance between two goals: inspire readers to invent their own original approaches while being detailed enough to work as a fallback in case the teacher needs to prepare a lesson on short notice. It introduces kids to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context. These topics are just as engaging and entertaining to children as typical recreational math problems, but they can be developed deeper and to more advanced levels.

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