This book is a compilation of approximately nine hundred problems, that have appeared in the pre-award surveys in Berkeley in the last twenty years. It is a valuable source of problems and solutions for each student of mathematics that the plans to introduce a doctorate it programs. The students who work through this book are going to develop abilities to solve problems in areas such as the real analysis, the multi-variate calculation, metric differential equations, spaces, complex analysis, algebra and linear algebra. The problems are organized by subjects and are ordered in an increasing level of difficulty.

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