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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. 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 edition has been updated with the most recent exams, including exams given during the Fall 2003 semester. The edition contains numerous problems and solutions.
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