Problems and solutions in mathematics
Ji-Xiu Chen (Editor), Guo-Ying Jiang (Editor), Yang-Lian Pan (Editor), Tie-Hu Qin (Editor), Yu-Sun Tong (Editor), Quan-Shui Wu (Editor), Sheng-Zhi Xu (Editor), Daqian Li (Editor of compilation)
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
Problems, exercises, etc
x, 791 s. : ill. ; 23 cm.
9789814304955, 9789814304962, 9814304956, 9814304964
1023156581
PART 1: Algebra
Linear Algebra
Group Theory
Ring Theory
Field and Galois Theory
PART 2: Topology
Point Set Topology
Homotopy Theory
Homology Theory
PART 3: Differential Geometry
Differential Geometry of Curves
Differential Geometry of Surfaces
Differential Geometry of Manifolds
PART 4: Real Analysis
Measurability and Measure
Integral
Space of Integrable Functions
Differential
Miscellaneous Problems
PART 5: Complex Analysis
Analytic and Harmonic Functions
Geometry of Analytic Functions
Complex Integration
The Maximum Modulus and Argument Principles
Series and Normal Families
PART 6: Partial Differential Equations
General Theory
Elliptic Equations
Parabolic Equations
Hyperbolic Equations