The book is a compilation of more than 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.

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.

New edition featuring over 1,800 real exam problems from Berkeley's Ph.D. prelims from 1977 to 2025 Helps students build strong problem-solving skills across core areas of mathematics Covers real analysis, multivariate calculus, differential equations, complex analysis, algebra, linear algebra, and more

Inhalt

Preface.- Problems.- Real Analysis.- Multivariable Calculus.- Differential Equations.- Metric Spaces.- Complex Analysis.- Algebra.- Linear Algebra.- Solutions.- Real Analysis.- Multivariable Calculus.- Differential Equations.- Metric Spaces.- Complex Analysis.- Algebra.- Linear Algebra.- Appendices.- Bibliography.- Index.