Berkeley Problems in Mathematics

by Jorge-Nuno Silva, Paulo Ney de Souza, Jorge-Nuno O. Silva

Book Overview

The 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.

• Format: Paperback
• Language: English
• ISBN: 0387008926
• ISBN13: 9780387008929
• Release Date: January 2004
• Publisher: Springer
• Length: 591 Pages
• Weight: 1.92 lbs.
• Dimensions: 1.1" x 6.1" x 9.2"

Customer Reviews

Excellent Problem Book

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.

Excellent Problems!

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.

A real pearl!

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 beautifullywritten, 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!

TEST YOUR PREPAREDNESS!

A GOOD COLLECTION OF PROBLEMS THAT HAVE BEEN THE BENCH MARK OF SELECTION TO THE PhD PROGRAMME AT UNIVERSITY OF CALIFORNIA AT BERKLEY IN MATHEMATICS. THERE IS A WIDE RANGE OF PROBLEMS THAT COMPRISE SOME SIMPLE AND SOME HARDER NUTS TO CRACK.THE PROBLEMS HAVE BEEN PUT IN THE ORDER IN WHICH THEY HAVE APPEARED IN THE EXAMS. NOT ALL QUESTIONS FIND SOLUTIONS IN THE BOOK HENCE THIS KEEPS UP THE SPIRIT OF THE EXAMINATION BUT THE SOLVED ONES SHALL HELP TO VENT FRUSTARTION OR OVER COME FALIURE AT TIMES. THIS BOOK IS A MUST READ FOR STUDENTS WHO ARE PLANNING TO TAKE UP A PhD IN MATHEMATICS TO GUAGE THEIR AREAS OF STRENGTH AND WEAKNESS.A VERY WELL COMPILED SET THAT COMES YET AGAIN WITH THE GUIDENCE OF P.R.HALMOS.