Problems and solutions in mathematics (PhD qualifying questions)

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.