A comprehensive compilation of approximately 900 problems which have appeared on the preliminary exams in Berkeley, and as such is designed to be a source of problems and solutions for mathematics students embarking on PhD programmes. The work is designed to develop problem-solving skills in areas such as real analysis, multi-variable calculus, differential equations, metric spaces, complex analysis, algebra and linear algebra. The problems are organized by subject and ordered by increasing level of difficulty, while tags with the exact examination year provide the opportunity to rehearse complete mock exams. The text also includes statistics on passing scores.
The problems in this book are excellent, they are both entertaining and instructive. I thought I knew calculus, linear algebra, and all of the other typical undergraduate subjects very well, until I purchased this book. After working several problems, mostly without success, I realized that there is a big difference between knowing theorems and knowing how to use them. Since then I have worked these problems daily to improve my "working knowledge," and it has made me a much better mathematician. Learning the definitions and theorems is just the first stage of mathematical knowledge.
In this form your knowledge is simply something stored in memory. In the second stage, you must turn it into something more like "software," something that is an active part of your thinking. The only way to do this is by solving problems, and for undergraduate mathematics, this is probably the best book of problems you will find. Highly recommended.
Berkeley Problems Mathematics Problem Books Product Features:
* Hardcover: 443 pages
* Publisher: Springer-Verlag (September 1998)
* Language: English
* ISBN-10: 0387949348
* ISBN-13: 978-0387949345
* Product Dimensions: 9.6 x 6.4 x 1.2 inches
Most Helpful Berkeley Problems Mathematics Problem Books Customer Reviews:
23 of 24 people found the following review helpful:
5.0 out of 5 stars - A real pearl!, February 14, 2004 By Jim Heuser (New York, NY)
This book is a rare peak inside one of the best Ph.D. programs in Mathematics in the world. It allows you to try out and test yourself on the same problems that the best young and aspiring mathematicians are testing themselves.
The problems are neatly arranged by subject and in increasing level of difficulty, and the solutions, are not only beautifully
written, but somewhat surprising and unexpected for a seasoned student... Read more
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