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| by: Paulo Ney De Souza, Jorge-Nuno Silva, Paulo Ney De Souza |
Berkeley Problems in Mathematics (Problem Books in Mathematics)
By Paulo Ney De Souza, Jorge-Nuno Silva, Paulo Ney De Souza
* Publisher: Springer-Verlag
* Number Of Pages: 443
* Publication Date: 1998-09
* ISBN-10 / ASIN: 0387949348
* ISBN-13 / EAN: 9780387949345
* Binding: Hardcover
Product Description:
This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.
Summary: Excellent Problem Book
Rating: 5
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.
Summary: Excellent Problems!
Rating: 4
These are great problems for those who would like to review undergraduate mathematics or those who would like to try some challenging problems. They are not as difficult as the problems on the Putnam competitions or those in the Math Monthly , but many require a bit of thought and some ingenuity. Some of the problems are routine, and if you don't want to review the basics, you can skip those and just try the more difficult ones. Even experienced problem solvers will have fun with some of these! Anyone who teaches undergraduate mathematics should have this collection. Highly recommended.
Summary: A real pearl!
Rating: 5
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. I pull mine out of the shelf on the rainy days and try a few more, and when I get one, I really savour it!
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