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Real and Complex Analysis, Two Volumes

Rajnikant Sinha
Publisher: 
Springer
Publication Date: 
2018
Number of Pages: 
637
Format: 
Hardcover
Price: 
99.99
ISBN: 
9789811309373
Category: 
Textbook
[Reviewed by
Charles Traina
, on
09/8/2019
]
The two volumes of “Real and Complex Analysis” by Rajnikant Sinha are an introduction to real and complex analysis that will be useful to undergraduate students in mathematics and engineering.  To quote the author in his introduction:
 
It is designed to equip the reader with tools that will help them understand the concepts of real analysis and complex analysis. In addition, it contains the essential topics of analysis that are needed for the study of functional analysis. Its guiding principles help develop the necessary concepts rigorously with enough detail and with the minimum prerequisites. Further, I have developed the necessary tools to enhance the readability. This book contains complete solutions to almost all problems discussed within.
Volume 1 is a detailed introduction to the theory of Lebesgue measure. It begins with a detailed exposition of the exponential function, and from there develops in detail Lebesgue measure.  All definitions are clearly labeled, and detailed examples follow.  All theorems are clearly stated and proved in detail.   There are many detailed examples with complete explanations provided.  Volume 2 is a very detailed introduction to Complex Analysis.  As in Volume I, all definitions and theorems are clearly stated and illustrated. As in the first volume, the theorems are proved in detail.  The approach to these two volumes is like Walter Rudin's classic text Real and Complex Analysis.  In fact, the author received suggestions from Walter Rudin and Paul Halmos.
 
The author has succeeded in what he states in his introduction.  As a textbook for a course, it may be difficult to cover all the material. Also, the majority of the problems within the text have solutions included. The two volumes would certainly serve as an excellent reference for both student and instructor.  These two volumes were written by a mathematician who understands the subject matter and is enthusiastic about the material and who wishes to convey this to the reader.  The author has done so with this work.
Charles Traina is a professor of mathematics at St. John's University in Jamaica, NY.  His research interest is in Group Theory and Measure Theory.

See the table of contents in the publisher's webpage.

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