Description:
The book is a compilation of more than 1,800 problems that have appeared on Berkeley's preliminary exams since 1977. It is an invaluable resource 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. This new edition has been updated with the most recent exams, including those given during the Fall 2025 semester.
Review Quotes:
From the reviews of the third edition:
"Problems that appeared in the preliminary exams ... are treated in this very interesting book. It is extremely helpful that the problems appear by subject ... . It is also convenient for the solver that in each chapter the problems are ordered in an increasing level of difficulty. A very clever idea is included in the appendix: the method to access the electronic versions of the exams and some relevant statistics." (Panayiotis Vlamos, Zentralblatt MATH, Vol. 1041 (16), 2004)
"Over 1250 problems that appeared in the preliminary exams of the Mathematics Department at the University of California, Berkeley, over the last 25 years are treated in this very interesting book. It is extremely helpful that the problems appear by subject ... . It is also convenient for the solver that in each chapter the problems are ordered in an increasing level of difficulty. A very clever idea is included in the appendix: the method to access ... ." (Panayiotis Vlamos, Zentralblatt MATH, Vol. 1041 (16))