Problems and Solutions in Mathematics

by Chen, Ji-Xiu; Guo-Ying, Jiang; Yang-Lian, Pan; Tie-Hu, Qin; Yu-Sun, Tong; Quan-Shui, Wu; Shen-Zhi, Xu; Li, Ta-Chien

• ISBN13: 9789810234805
• ISBN10: 9810234805
• Format: Paperback
• Copyright: 1999-06-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Covers 6 aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis & Partial Differential Equations. Contains a selection of more than 500 problems & solutions based on the Ph.D. qualifying test papers of a decade of influential universities in North America. Paper. DLC: Mathematics - Problems, exercises, etc.

Table of Contents

Preface
Algebra	p. 1
Linear Algebra	p. 3
Group Theory	p. 26
Ring Theory	p. 44
Field and Galois Theory	p. 59
Topology	p. 81
Point Set Topology	p. 83
Homotopy Theory	p. 99
Homology Theory	p. 118
Differential Geometry	p. 151
Differential Geometry of Curves	p. 153
Differential Geometry of Surfaces	p. 171
Differential Geometry of Manifold	p. 194
Real Analysis	p. 229
Measurablity and Measure	p. 231
Integral	p. 256
Space of Integrable Functions	p. 283
Differential	p. 302
Miscellaneous Problems	p. 322
Complex Analysis	p. 333
Analytic and Harmonic Functions	p. 335
Geometry of Analytic Functions	p. 360
Complex Integration	p. 377
The Maximum Modulus and Argument Principles	p. 413
Series and Normal Families	p. 433
Partial Differential Equations	p. 455
General Theory	p. 457
Elliptic Equations	p. 472
Parabolic Equations	p. 496
Hyperbolic Equations	p. 513
Abbreviations of Universities in This Book	p. 539
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