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Problems & Solutions in Mathematics (For Ph D)(2E) written by Ji-Xiu Chen, Jiang Guo-Ying, Pan Yang-Lian, Qin Tie-Hu, Tong Yu-Sun, Wu Quan-Shui, Xu Shen-Zhi, Ta-Chien Li .
This book covers six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. It contains a selection of more than 500 problems and solutions based on the Ph.D. qualifying test papers of a decade of influential universities in North America. The mathematical problems under discussion are kept within the scope of the textbooks for graduate students.
Finding solutions to these problems, however, involves a deep understanding of mathematical principles as well as an acquisition of skills in analysis and computation. As a supplement to textbooks, this book may prove to be of some help to the students in taking relevant courses. It may also serve as a reference book for the teachers concerned.
It has to be pointed out that this book should not be regarded as an allpurpose troubleshooter. Nor is it advisable to take the book as an exemplary text and commit to memory all the problems and solutions and make an indiscriminate use of them. Instead, the students are expected to make a selective survey of the problems, take a do-it-yourself approach and arrive at their own solutions which they may check against those listed in the book. It would be gratifying to see that the students can work out the problems on their own and come up with better solutions than those provided by the book. If the students fail to do so or their solutions may turn out to be incomplete, it may reveal the inadequacy of their knowledge or approach, thus spurring them to greater efforts to promote their skills. The very purpose of the authors in writing the book is just to help the students to discover the truth by trial and error.
Book Detail :-
Title: Problems & Solutions in Mathematics (For Ph D)
Author(s): Ji-Xiu Chen, Jiang Guo-Ying, Pan Yang-Lian, Qin Tie-Hu, Tong Yu-Sun, Wu Quan-Shui, Xu Shen-Zhi, Ta-Chien Li
Publisher: World Scientific
Series: Major American Universities Qualifying Questions and Solutions.
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About Author :-
The author Ji-Xiu Chen is a Chinese-American mathematician whose research concerns differential geometry and differential equations. A professor at Stony Brook University since 2010, he was elected a Fellow of the American Mathematical Society in 2015 and awarded the Oswald Veblen Prize in Geometry in 2019.
Chen was born in Qingtian County, Zhejiang, China. He entered the Department of Mathematics of the University of Science and Technology of China in 1982, and graduated in 1987. He subsequently studied under Peng Jiagui (彭家贵) at the Graduate School of the Chinese Academy of Sciences, where he earned his master's degree.
Professors Zhang Yin-nan, Hong Jia-Xing and Chen Xiao-man for their painstaking efforts to collect test-oriented data. For selecting problems and providing solutions, We wish to acknowledge the following professors respectively: Wu Quan-shui (Part-I), Pan Yang-lian (Part-II), Jiang Guo-ying (Part-III), Tong Yu-sun, Xu Sheng-zhi (Part-IV), Chen Ji-xiu (Part-V) and &in Tie-hu (Part-VI). We are also indebted to Professor Guo Yu-tao for carefully reading and correcting the manuscript.
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• Download PDF Problems & Solutions in Mathematics by Ji-Xiu Chen, Jiang Guo-Ying
• Download PDF Problems & Solutions in Mathematics (2E) by Ji-Xiu Chen, Jiang Guo-Ying
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Book Contents :-
Problems & Solutions in Mathematics (For Ph D) (2E) written by Ji-Xiu Chen, Jiang Guo-Ying, Pan Yang-Lian, Qin Tie-Hu, Tong Yu-Sun, Wu Quan-Shui, Xu Shen-Zhi, Ta-Chien Li cover the following topics. '
Linear Algebra, Group Theory, Ring Theory, Field and Galois Theory
Point Set Topology, Homotopy Theory, Homology Theory
Part-III Differential Geometry
Differential Geometry of Curves, Differential Geometry of Surfaces, Differential Geometry of Manifold
Part-IV Real Analysis
Measurablity and Measure, Integral, Space of Integrable Functions, Differential, Miscellaneous Problems
Part-V Complex Analysis
Analytic and Harmonic Functions, Geometry of Analytic Functions, Complex Integration, The Maximum Modulus and Argument Principles, Series and Normal Families
Part-VI Partial Differential Equations
General Theory, Elliptic Equations, Parabolic Equations, Hyperbolic Equations
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