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.

Includes supplementary material: sn.pub/extras

Zusammenfassung
The appendix includes instructions on accessing electronic versions of the exams as well as a syllabus and statistics of passing scores.This new edition has been updated with the most recent exams, including exams given during the Fall 2003 semester.

Inhalt
1 Real Analysis.- 2 Multivariable Calculus.- 3 Differential Equations.- 4 Metric Spaces.- 5 Complex Analysis.- 6 Algebra.- 7 Linear Algebra.- 1 Real Analysis.- 2 Multivariable Calculus.- 3 Differential Equations.- 4 Metric Spaces.- 5 Complex Analysis.- 6 Algebra.- 7 Linear Algebra.- III Appendices.- A How to Get the Exams.- A.1 On-line.- A.2 Off-line, the Last Resort.- B Passing Scores.- C The Syllabus.- References.