Elementary Real and Complex Analysis (Dover Books on Mathematics) [Paperback]

Georgi E. Shilov (Author)

Book Description

ISBN-10: 0486689220 | ISBN-13: 978-0486689227 | Publication Date: February 7, 1996 | Edition: Revised

Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, series, the derivative, higher derivatives, the integral and more. Each chapter contains a problem set (hints and answers at the end), while a wealth of examples and applications are found throughout the text. Over 340 theorems fully proved. 1973 edition.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Russian

Product Details

• Paperback: 528 pages
• Publisher: Dover Publications; Revised edition (February 7, 1996)
• Language: English
• ISBN-10: 0486689220
• ISBN-13: 978-0486689227
• Product Dimensions: 8.5 x 5.4 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #170,971 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

80 of 84 people found the following review helpful:

5.0 out of 5 stars Getting started in math analysis, January 8, 2005

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
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This review is from: Elementary Real and Complex Analysis (Dover Books on Mathematics) (Paperback)

This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

28 of 28 people found the following review helpful:

5.0 out of 5 stars A wonderful text -- Highly recommended!, January 11, 2004

By A Customer

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This review is from: Elementary Real and Complex Analysis (Dover Books on Mathematics) (Paperback)

I purchased this book as a reference book for my first analysis course. It is very well written, and easy to follow. Dr. Shilov has a very nice way of organizing this text: He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions. It makes for a very quick reference. His presentation of the included proofs is also very nice. There were several occasions I found myself thumbing through it for a second perspecitve.

As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology. He does keep in mind this is intended for undergrads and first year grads though.

Oh, another nice feature is the price! I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course.

72 of 83 people found the following review helpful:

5.0 out of 5 stars Dr. Shilov could teach complex analysis to a chimpanzee., July 5, 1998

By 

Andy McManus [e-mail] (Hanover, Pennsylvania) - See all my reviews

This review is from: Elementary Real and Complex Analysis (Dover Books on Mathematics) (Paperback)

The book is one of the finest mathematics texts that I have ever read. That does'nt mean much because I'm 16 years old, and have only been studying advanced math for a little over a year. The treatment was basic enough for someone like me to understand. I strongly recommend it to college students and young people who are interested in mathematics.

After introducing concepts from set theory, the foundations of analysis, and the notion of a "mathematical structure," he gives a detailed presentation of limits and series. He also introduces elementary functions in terms of their functional equations. Then he covers differentiation and integration, first of real, and then of complex functions. He uses Taylor series to introduce ideas about complex functions.

In short, it is a good book for those who hope to become mathematicians, physicists, or engineers, and have had a few college math courses already.