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A Decade of the Berkeley Math Circle: The American Experience (MSRI Mathematical Circles Library) (v. 1) (MSRI Mathematical Circles Library, 1)

by Zvezdelina Stankova (Author, Editor), Tom Rike (Editor)
4.5 4.5 out of 5 stars 27 ratings
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Many mathematicians have been drawn to mathematics through their experience with math 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 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 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 youready 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 you'll never know everything but you'll learn where to find things how to connect and use them. The rewards will be substantial. "
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  1. ISBN-10
    0821846833
  2. ISBN-13
    978-0821846834
  3. Publisher
    American Mathematical Society
  4. Publication date
    December 12, 2008
  5. Part of series
    MSRI Mathematical Circles Library
  6. Language
    English
  7. Dimensions
    7 x 0.75 x 10 inches
  8. Print length
    326 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ American Mathematical Society (December 12, 2008)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 326 pages
  • ISBN-10 ‏ : ‎ 0821846833
  • ISBN-13 ‏ : ‎ 978-0821846834
  • Item Weight ‏ : ‎ 1.37 pounds
  • Dimensions ‏ : ‎ 7 x 0.75 x 10 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 27 ratings

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Zvezdelina Stankova

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4.5 out of 5 stars
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27 global ratings

Top reviews from the United States

ScienceThinker
5.0 out of 5 stars Marvelous! A must-have book
Reviewed in the United States on April 23, 2013
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One of my two favorite books of the AMS/MSRI Mathematical Circles Library. (The other is  Introduction to Functional Equations: Theory and Problem-solving Strategies for Mathematical Competitions and Beyond (MSRI Mathematical Circles Library) .)

It contains 12 sessions in the form of chapters (each dealing with a specific topic from mathematics), an introduction, a very interesting epilogue, an appendix explaining the notation used in the book, an appendix summarizing all abbreviations used in the book, a good bibliography, and a good index.

Each session is written by the actual presenter or by one of the editors based on the original presentation given by a presenter to the students of the Berkeley Math Circle. The editors have done great work to edit all sessions to appear uniform in format and style. The final result is an exciting book that everyone interested seriously in mathematics should read. If you curious, the topics of the sessions are: Inversion in the plane; combinatorics; Rubick's cube; number theory; about proofs (part I and part II); mathematical induction; mass point geometry; complex numbers; games with invariants; favorite problems at BMC; monovariants.

Since I have been negative in my reviews for two other books of the same series ( Geometry: A Guide for Teachers (MSRI Mathematical Circles Library)  and  Integers, Fractions and Arithmetic: A Guide for Teachers (MSRI Mathematical Circles Library) ) written also as a collection of sessions (named seminars there), I would like to explain why there is a difference in my evaluation. The other two books claim to be textbooks. All sessions were presented by the authors. Eventually, they were written by the same authors and were assembled into a book format. Yet, the material is not as well written as it should be in order the final product to be called a textbook. More importantly, these books have nothing to do with mathematical circles, mathematical competitions and imaginative and original thinking. They are just dry retellings of material that is found everywhere. This book is not so. First of all, it does not claim to be a textbook for any of the topics presented. If you do not know some math on a particular topic, you cannot read it. But if you do know some math, you will enjoy it greatly! Second, the topics included are not the same retellings you will find in all books. Some of the topics actually are not found everywhere but, even more standard topics, like mathematical induction, include twists that the reader will enjoy. Third, the book is actually truly related to mathematical circles and competitions. You will find a lot of material that will be of help. And, finally it does goes beyond the standard requirements for mathematical originality and imagination.

Overall, this book was a great choice to be the first volume of the Mathematical Circles Library series. It set a high standard that unfortunately some other volumes in the series did not reach. We can only hope to see the second part of this volume published soon.
14 people found this helpful
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Kimjiman
5.0 out of 5 stars Fantastic, Easy to follow ; deep, profound but very easy.
Reviewed in the United States on December 8, 2010
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This book is so fantastic that I can't belive it hands so many math topics but so easy to read. As a problem solving lover, I'm sure that this book is so good for other person who like problem solving and interested in math contest like math olympiad. When I was a high school student, I was eager to study math and particiated some math contest and got some math tropy. But then there were so little material to study. Now I'm a doctor but still like math-problem solving, there are so many good materials to read. Only problem solving, somtimes boring things. If you want to be a good problem solver, there must be something else. I think this book is good choice for recreation and learning problem solving skills.

Some topics are amazing like mass point geometry. Some others are fun introductions of math theory and problem solving skills.

The only thing I feel sorry is there's just Volume 1. I eargely look forward to Volume 2.
11 people found this helpful
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SDS
5.0 out of 5 stars Five Stars
Reviewed in the United States on November 1, 2016
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Required text for the UCLA Math Circle. Challenging.
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Dr Frank Berkshire
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on August 5, 2015
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Excellent!
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