"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."--BOOK JACKET. "This book is a compilation of more than 1,000 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. 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."--BOOK JACKET.