Problems and Solutions in Mathematics

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World Scientific, 2011 - 793 pagina's
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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. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference.
 

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Inhoudsopgave

Part 2 Topology
119
Part 3 Differential Geometry
215
Part 4 Real Analysis
347
Part 5 Complex Analysis
503
Part 6 Partial Differential Equations
675
Abbreviations of Universities in this Book
793
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