Berkeley Problems in Mathematics (Problem Books in Mathematics)

In 1977 the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the first major requirements toward the Ph.D. degree in Mathematics. Its purpose was to determine whether first-year students in the Ph.D. program had successfully mastered basic mathematics in order to continue in the program with the likelihood of success. Since its inception, the exam has become a major hurdle to overcome in the pursuit of the degree. The purpose of this book is to publicize the material and aid in the preparation for the examination during the undergraduate years. The book is a compilation of over 1,250 problems which have appeared on the preliminary exams in Berkeley over the last twenty-five 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. Tags with the exact exam year provide the opportunity to rehearse complete examinations. The appendix includes instructions on accessing electronic versions of the exams as well as a syllabus and statistics of passing scores.

This new edition has been updated with the most recent exams, including exams given during the Fall 2003 semester. There are numerous new problems and solutions which were not included in previous editions.

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!


What it is   February 14, 2004
 8 out of 16 found this review helpful

The books is a collection of problems of the Preliminary Exam at the Ph.D. Program in Mathematics at Berkeley. Most of them can b solved using undergraduate-level math, but the problems are challenging.

Challenging problems, or just standard textbook stuff.   September 25, 2001
 10 out of 38 found this review helpful

The problem with the contents of this book is that they are mostly standard, or require a simple trick. Many problems also require quite a bit of knowledge in higher mathematics, which may be good if you want to test that.

However, this book is not for problem solving enthusiasts.