Berkeley Math Circle

With the help of the Mathematical Sciences Research Institute (MSRI), the Berkeley Math Circle will be selling these recommended books to circle participants, teachers, and instructors at a discounted price. Below you will find information, descriptions, and BMC prices for these books. These books are available for purchase at each of our Tuesday circle sessions. Please e-mail David Wertheimer, the 2006-2007 BMC Administrative Assistant, if you have any questions regarding these books.

1. Mathematical Adventures For Students and Amateurs

Edited by: David F. Hayes and Tatiana Shubin

Published by: Mathematical Association of America (this book contains many lectures given by our own Berkeley Math Circle Instructors at a monthly lecture series in San Jose/Santa Clara State Universities).

Excerpt of book description on Amazon.com:
"How should you encode a message to an extraterrestrial? What do frogs and powers of 2 have in common? How many faces does the Stella Octangula have? Is a plane figure of constant diameter a circle, and what does this have to do with NASA? Is there any such thing as a truly correct map? What patterns are possible in juggling? What do all of these questions have in common? They--and many others--are answered in this book." "This is a partial record of the Bay Area Mathematical Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area of California. These lectures are aimed primarily at bright high school students, the emphasis on 'bright', and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are serious mathematical issues addressed here."

Price: $15

2. Mathematical Circles: Russian Experience

Authors: Dmitri Fomin, Sergey Genkin, and Ilia V. Itenberg

Published by: American Mathematical Society

Excerpt of book description on Amazon.com:
"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."

Price: $20

3. Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition

Author: Steve Olson

Excerpt from the official book description from the publisher (available at Amazon.com):
"Each summer six math whizzes selected from nearly a half-million American teens compete against the world's best problem solvers at the International Mathematical Olympiad. Steve Olson followed the six 2001 contestants from the intense tryouts to the Olympiad's nail-biting final rounds to discover not only what drives these extraordinary kids but what makes them both unique and typical… Beyond the Olympiad, Olson Sheds light on many questions, from why Americans feel so queasy about math, to why so few girls compete in the subject, to whether or not talent is innate."

Price: $8!

4. Proofs that Really Count: The Art of Combinatorial Proof

Authors: Arthur T. Benjammin and Jennifer J. Quinn

Published by: Mathematical Association of America

Excerpt of book description on Amazon.com:
"Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguements. The arguements primarily take one of two forms:

A counting question is posed and answered in two different ways. Since both answers solve the same question, they must be equal.

Two different sets are described, counted, and a correspondence found between them. One-to-one correspondences guanrantee sets of the same size. Almost one-to-one correspondences take error terms into account. Even many-to-one correspondences are utilized.

The book explores more than 200 identities throughout the text and exercises, frequently emphasizing numbers not often thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels from high school math students to professional mathematicians."

Price: $23

5. Kiselev's Geometry: Book 1, Planimetry

Translated from Russian by Alexander Givental

Published by: Sumizdat

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

Price: $20

6. Mathematical Omnibus: Thirty Lectures on Classical Mathematics

Authors: Dmitry Fuchs and Serge Tabachnikov

Published by: American Mathematical Society

Dmitry Fuchs, a longtime lecturer at the Berkeley Math Circle, has compiled his notes from BMC Sessions into this wonderful book published by AMS. The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Price: $40