Problems and solutions in mathematics (PhD qualifying questions)

✍ Scribed by Li Ta-Tsien (ed.)

• Publisher: World Scientific Publishing Company
• Year: 2011
• Tongue: English
• Leaves: 804
• Series: Major American Universities Ph.d. Qualifying Questions And Solutions - Mathematics
• Edition: 2nd ed
• Category: Library

✦ Table of Contents

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.