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Problems and solutions in mathematics (PhD qualifying questions)

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Author(s): Li Ta-Tsien (ed.)
Series: Major American Universities Ph.d. Qualifying Questions And Solutions - Mathematics
Edition: 2nd ed
Publisher: World Scientific Publishing Company
Year: 2011

Language: English
Commentary: PhD qualifying questions
Pages: 804
City: Singapore

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.