Berkeley Problems in Mathematics

by Paulo N. De Souza; Jorge-Nuno Silva

In 1977 the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the fist 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, multi-variable 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 volume is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.

Genres: Mathematics, Textbooks

443 pages, Paperback

First published January 1, 1901

Reviews

[Viney Kumar · Rating 5 out of 5]

I can't pretend to have solved every single exercise in this book (currently, I've only completed the first two Chapters, with some heavy help from the official solutions). But I'll give this book a 5 star rating due to the unique and frankly amazing collection of problems. The problems are 'non-standard', but they're still designed to test standard techniques. The problems aren't diabolical enough that they require you to develop entirely new approaches, but creative application of standard techniques is called for.

The problems are engaging and challenging to work on. Along with well-written solutions, they make this book a joy to work on.

Rating: 5 stars.

[arash · Rating 4 out of 5]

It is a very nice set of problems in many different subjects such as Analysis,Algebra...
I've solved the Calculus and Analysis and I highly improve my solving problems power.