北美考博数学习题精选及解答Problems And Solutions In Mathematics_1998
作者：Ji-Xiu Chen, Li Ta-Tsien, Ji-Xiu Chen, Li Ta-Tsien, Jiang Guo-Ying, Pan Yang-Lian, Qin Tie-Hu, Tong Yu-Sun, Wu Quan-Shui, Xu Shen
1998年，549 页，PDF，12.7 MB。
Language: English
简介：
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 problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. The depth of knowledge involved is not beyond the contents of the textbooks for graduate students, while solution of the problems requires deep understanding of the mathematical principles and skilled techniques. For students this book is a valuable complement to textbooks; for lecturers teaching graduate school mathematics, a helpful reference.


CONTENTS
Preface ................................................................ (v)
Part I. Algebra ......................................................... (1)
1. Linear Algebra ................................................... (3)
2. Group Theory ................................................... (26)
3. Ring Theory (44)
4. Field and Galois Theory (59)
Part 11. Topology (81)
1. Point Set Topology .............................................. (83)
2. Homotopy Theory ............................................... (99)
3. Homology Theory .............................................. (118)
Part 111. Differential Geometry ........................................ (151)
1. Differential Geometry of Curves ................................ (153)
2. Differential Geometry of Surfaces (171)
3. Differential Geometry of Manifold (194)
Part IV. Real Analysis ................................................ (229)
1. Measurablity and Measure (231)
2. Integral ........................................................ (256)
3. Space of Integrable Functions (283)
4. Differential ..................................................... (302)
5. Miscellaneous Problems ......................................... (322)
Part V. Complex Analysis ............................................ (333)
1. Analytic and Harmonic Functions (335)
2. Geometry of Analytic Functions ................................ (360)
3. Complex Integration ............................................ (377)
4. The Maximum Modulus and Argument Principles ............... (413)
5. Series and Normal Families ..................................... (433)
Part VI. Partial Differential Equations ................................ (455)
1. General Theory ................................................ (457)
2. Elliptic Equations .............................................. (472)
3. Parabolic Equations ............................................ (496)
4. Hyperbolic Equations ........................................... (513)
Abbreviations of Universities in This Book ............................ (539)

精选试题题500多道。