Problems and solutions in mathematics (PhD qualifying questions)
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Content: Intro Contents Preface Preface to the Second Edition Part 1 Algebra Section 1 Linear Algebra Section 2 Group Theory Section 3 Ring Theory Section 4 Field and Galois Theory Part 2 Topology Section 1 Point Set Topology Section 2 Homotopy Theory Section 3 Homology Theory Part 3 Differential Geometry Section 1 Differential Geometry of Curves Section 2 Differential Geometry of Surfaces Section 3 Differential Geometry of Manifolds Part 4 Real Analysis Section 1 Measurability and Measure Section 2 Integral Section 3 Space of Integrable Functions Section 4 Differential. Section 5 Miscellaneous ProblemsPart 5 Complex Analysis Section 1 Analytic and Harmonic Functions Section 2 Geometry of Analytic Functions Section 3 Complex Integration Section 4 The Maximum Modulus and Argument Principles Section 5 Series and Normal Families Part 6 Partial Differential Equations Section 1 General Theory Section 2 Elliptic Equations Section 3 Parabolic Equations Section 4 Hyperbolic Equations Abbreviations of Universities in this Book.
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