Product Description

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 since a) students are already deeply involved with the material and b) they will be prepared to take the exam within the first month of the graduate program rather than in the middle or end of the first year. 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. 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, statistics of passing scores, and a Bibliography used throughout the solutions. 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.

Product Details

• Amazon Sales Rank: #276197 in Books
• Published on: 2004-01-20
• Original language: English
• Number of items: 1
• Binding: Paperback
• 616 pages

Features

• ISBN13: 9780387008929
• Condition: NEW
• Notes: Brand New from Publisher. No Remainder Mark.
• Click here to view our Condition Guide and Shipping Prices

Review

From the reviews of the third edition:

"This new edition has been updated with the most recent exams … . There are numerous new problems and solutions which were not included in previous editions. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph. D program. … 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. … Tags with the exact exam year provide the opportunity to rehearse complete examinations. … This new edition has been updated with the most recent exams … ." (Zentralblatt für Didaktik der Mathematik, November 2004)

"The Mathematics department of the University of California, Berkeley, has set a written preliminary examination to determine whether first year Ph.D. students have mastered enough basic mathematics to succeed in the doctoral program. Berkeley Problems in Mathematics is a compilation of all the … questions, together with worked solutions … . All the solutions I looked at are complete … . Some of the solutions are very elegant. … This is an impressive piece of work and a welcome addition to any mathematician’s bookshelf." (Chris Good, The Mathematical Gazette, 90:518, 2006)

"During the last twenty-five years problems from written preliminary examinations that are required for the Ph.D. degree at the Mathematics Department of the University of California, Berkeley, have been assembled. … The book is suited for students in mathematics, physics or engineering. Solutions are well explained, making the book valuable for self-study. The problems have a satisfactory high level, so the book is a rich resource of examples for lecturers as well, who need exercises … . This book certainly is to be recommended." (Paula Bruggen, Bulletin of the Belgian Mathematical Society, 12:4, 2005)

Customer Reviews

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 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!

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.

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.