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| Required and Recommended Books |
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The Berkeley Math Circle will be selling some of these required and recommended books
to circle participants, teachers, and instructors at a discounted price. Below you will
find information, descriptions, and prices for these books. The books that we have in
stock are available for purchase at each of our Tuesday circle sessions. Please e-mail
Michael Pejic, the fall 2009
BMC Assistant, if you have any questions regarding these books.
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| Required Books for BMC Beginner and Advanced |
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1. A Decade of the Berkeley Math Circle: The American Experience, Volume I
Edited by: Zvezdelina Stankova and Tom Rike
A co-publication of the AMS and Mathematical Sciences Research Institute
Excerpt of book description by the American Mathematical Society:
"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.
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.
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Readership
High school students, high school teachers, and undergraduates interested in problem solving and introductions
to mathematical methods."
Price: $25
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| Highly Recommended Books for BMC Beginner |
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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: $25
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| Suggested Books for BMC Elementary |
3. Math Olympiad Contest Problems for Elementary and Middle Schools
Author: Dr. G. Lenchner
Published by: Mathematical Olympiads For Elementary and Middle Schools, Inc.
Book description by the publisher:
The Math Olympiad contests presented these 400 challenging problems and ingenious solutions over a period of 16 years.
Aimed at young students, their teachers and parents, the book contains an unusual variety of problems, a section of hints to help the reader get started, and seven unique appendices that inform and enrich,
among other features.
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4. Math Olympiad Contest Problems, Vol. 2
Editor: Richard Kalman
Published by: Mathematical Olympiads For Elementary and Middle Schools, Inc.
Book description by the publisher:
A continuation of our first volume, Math Olympiad Contest Problems for Elementary and Middle Schools, it is full of useful features for PICO[Person In Charge of Olympiads] and mathlete alike, and can be a valuable addition to your library.
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| These two volumes may be purchased directly from the publisher. |
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| | Recommended Books for BMC Beginner |
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5. Proofs that Really Count: The Art of Combinatorial Proof
Authors: Arthur T. Benjamin 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
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6. 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: $25
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7. Kiselev's Geometry: Book 2, Stereometry
Translated from Russian by Alexander Givental
Published by: Sumizdat
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.
Price: $15
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8. 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."
Note: three members of the Berkeley Math Circle were on this team as well as 2009 BMC instructor Ian Le.
Price: $8! |
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| Recommended Books for BMC Advanced |
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9. 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
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10.
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 |
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