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Theory and Application of Infinite Series (Dover Books on Mathematics) Paperback – March 1, 1990

4.1 out of 5 stars 14 customer reviews

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Language Notes

Text: English
Original Language: German
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 592 pages
  • Publisher: Dover Publications (March 1, 1990)
  • Language: English
  • ISBN-10: 0486661652
  • ISBN-13: 978-0486661650
  • Product Dimensions: 5.4 x 1.2 x 8.4 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #246,235 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
The last chapter on the Euler-MacLauren summation formula, and attendant interrelations among the Zeta function, Bernoulli Numbers and Bernoulli Polynomials is alone worth three times the price of this gem. Chock full of recipes and explanations of many of those little annoying points you don't understand fully. Do you REALLY understand what 'asymptotically equal to (~)' means? Heartily recommended!
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Format: Paperback Verified Purchase
Anything to do with "infinity" is fascinating. Much of the history of mathematics has been a duel between those who see "infinity" as a delusion and impediment to progress, and those who see it as the greatest tool in the mathematician's toolbox. Infinite series, which may be loosely defined as sums of an infinite number of terms (numbers), take on some of this fascination. Although this book will appeal mainly to the professional mathematician, there is enough historical and elementary material to profit many college students- and possibly even some high school students.
Professional mathematician will find this book useful for filling in gaps left by topics not covered in traditional courses. An example is the detailed discussion of Euler's summation formula, which goes far beyond the simplified form usually encountered in textbooks. Another fascinating topic covered is divergent series, and methods by which meaningful sums can be assigned to these. There is something counterintuitive -- and, frankly, mind-boggling -- about many of these results.

Mathematicians can be put into several categories: 1) applied-mathematicians/computer-scientists/engineers concerned with solving practical problems, 2) those concerned with pedagogy and the history of mathematics, 3) epistemology and rigorous proofs, and 4) formalists. The fourth category, formalists, is difficult to define, but may be described as those that emphasize obtaining new results through formal (technical) manipulations, without undue concern regarding the meaning of the intermediate steps. The greatest exponents of this art were Euler and Ramanujan, though Fourier, Dirac and Heaviside are also solid members of this camp.
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Format: Paperback
Excellent book for consulting with lots of examples and problems. Very well written but with the problem of very old notation. Everything you need to know about series is in this book. Very good to use in problems seminars
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Format: Kindle Edition Verified Purchase
This is a classic book written by Knopp who shows a complete mastery of the subject. The construction of real numbers is unique and he uses nests to define them. If ever you wanted information on series then this book is a bible on that topic. Any student of mathematics must have this in his collection. The translator has done an excellent job.
Dr. Knopp also has a series of books on the theory of complex functions and are highly recommended.
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Format: Paperback Verified Purchase
This is a very fantastic book on infinite series. The coverage of subjects in the book is very comprehensive and goes way beyond a simple introduction to infinite series. Reading this book though, I would recommend teaching yourself Real/Complex Analysis along with this as it will give you greater insights. Overall though I am pleased with this book, and the price cannot be beat.
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Format: Kindle Edition Verified Purchase
The Kindle edition is a flawed copy of the paper edition. I only have two examples, but being a math text where every symbol counts, that's enough for me to abandon the electronic version in favor of the paper version.

Example 1: Page 6 in the print book compares sets named M and N, but on the Kindle these are both referred to as M.
Example 2: Reference numbers set aside in the margin of the paper edition get interspersed throughout the Kindle edition. This is confusing as they sometimes come in the middle of an ordered list.

I encountered both problems very early, so there may be many more problems. The text is already a challenge for me, so I don't need additional, unnecessary problems to sort out. I do not recommend the Kindle version.
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Format: Paperback
I read this book in graduate school, though it was not required or assigned, I heard about it and read it carefully cover-to-cover. Twenty years later I am now in the process of reading it again, carefully, cover-to-cover. I found this book to be indispensable reading for studying higher level math. It's really a beautiful book and a classic. But I don't think it would be good to read as a first introduction to the subject.

The real problem with this book is its 1920's style. It desperately needs to beu pdated to modern exposition. There is WAY too much flowery exposition in his construction of the real numbers. I think it could be cut down by 2/3 without losing any content and be far more readable by a modern student. Maybe I'll do that if I get a chance, since I doubt there are still copyrights on a book this old.

There are several ways to construct the real numbers. Knopp chose to use "nets". He also discusses Dedekind cuts and the approach of using Cauchy sequences. If I were to update this book I would still use nets, because it would be too big of a modification. But if I were writing the subject from scratch I would use Cauchy sequences because that is the method that generalizes best to arbitrary metric spaces.

But once you get past these painful introductions, and get used to his style, the rest of the book is really very pleasant to read. If you take the time to study this well, you will be a better mathematician all around.
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