Berkeley Problems in Mathematics

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.