This book contains a selection of more than 500 mathematical problems and their solutions from the phd qualifying examination papers of more than ten famous american universities the mathematical problems cover six aspects of graduate school mathematics algebra topology differential geometry real analysis complex analysis and partial differential equations. The problems cover six aspects of graduate school mathematics algebra topology differential geometry real analysis complex analysis and partial differential equations the depth of knowledge involved is not beyond the contents of the textbooks for graduate students while solution of the problems requires deep understanding of the . Most of these exams can now be found online so one can easily collect a good selection of interesting mathematics problems supply solutions and you have this book its a good idea and the authors editors have executed it well. This book contains a selection of more than 500 mathematical problems and their solutions from the phd qualifying examination papers of more than ten famous american universities the mathematical problems cover six aspects of graduate school mathematics algebra topology differential geometry real analysis complex analysis and partial differential equations