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Principles of Real Analysis

Santosh Man Maskey
Publisher: 
Ratna Pustak Bhandar
Publication Date: 
2007
Number of Pages: 
574
Format: 
Paperback
Edition: 
2
Price: 
0.00
ISBN: 
9789993306863
Category: 
Textbook
[Reviewed by
Luiz Henrique de Figueiredo
, on
12/29/2008
]

The title of this book reminded me of Rudin's classic, Principles of Mathematical Analysis. Like my ("international") copy of Rudin, it seems to be an inexpensive edition targeted at students. However, the two books are quite different: Maskey's book is explicitly addressed at undergraduates and covers only a fraction of what Rudin does. Maskey does just the basics: real numbers, topology of the real line, sequences and series, limits and continuity, differentiation, and the Riemann integral.

To help beginners, Maskey starts each chapter with an "executive summary" and a few historical facts. He also provides a review and a self-test (with answers) at the end of each chapter. The review lists the key terms discussed in the chapter, but not the results, which I think reduces its value. The self-test is of the objective sort, which is unusual in mathematics books, especially those on analysis. There also traditional exercises after each section.

The presentation of the material is traditional: definitions, examples, theorems, corollaries, and remarks (called notes). Less traditionally, there are worked-out exercises. The contents is also traditional and unsurprising, both the theorems and the exercises. There are several misprints, which are distracting but do not compromise the mathematics.


 

 

Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.

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