This 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. The problems are organized by subject
and ordered in an increasing level of difficulty. This new edition
contains approximately 120 new problems and 200 new solutions. It
is an ideal means for students to strengthen their foundation in
basic mathematics and to prepare for graduate studies.
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