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Continued Fractions (Dover Books on Mathematics) Paperback – May 14, 1997

6 customer reviews
ISBN-13: 000-0486696308 ISBN-10: 0486696308

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Continued Fractions (Dover Books on Mathematics) + Three Pearls of Number Theory (Dover Books on Mathematics) + Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2)
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Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Russian
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 112 pages
  • Publisher: Dover Publications (May 14, 1997)
  • Language: English
  • ISBN-10: 0486696308
  • ISBN-13: 978-0486696300
  • Product Dimensions: 8.5 x 5.4 x 0.2 inches
  • Shipping Weight: 4.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #452,388 in Books (See Top 100 in Books)

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80 of 81 people found the following review helpful By A Customer on October 6, 1999
Format: Paperback
This is Khinchin's classic work, translated from Russian in the 1930's. Although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times, the book moves at a truly alarming pace, and the book is not suitable to be used ALONE as an introduction to continued fractions. To supplement this book if this is a first exposure to continued fractions, I would recommend C.D. Old's book, which has many more examples which can be worked through until the reader is comfortable with the topic.
The book is brilliant and necessary for understanding continued fractions, but can't stand alone without supplemental material unless one is a professional mathematician. Khinchin frequently employs contrapositive proof formats, and there are occasional translation errors from Russian. The errors range from minor (awkward usage) to major (in one place, the translation is "negative" when it should be "non-negative", which confused me for half a day).
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32 of 34 people found the following review helpful By anon2001 on February 24, 2001
Format: Paperback
A Y Khinchin was one of the greatest mathematicians of the first half of the twentieth century. His name is is already well-known to students of probability theory along with A N Kolmogorov and others from the host of important theorems, inequalites, constants named after them. He was also famous as a teacher and communicator. Several of the books he wrote are still in print in English translations, published by Dover. Like William Feller and Richard Feynman he combines a complete mastery of his subject with an ability to explain clearly without sacrificing mathematical rigour.
In this short book the first two chapters contain a very clear development of the theory of simple continued fractions, culminating in a proof of Lagrange's theorem on the periodicity of the continued fraction representation of quadratic surds. Chapter three presents Khinchins beautiful and original work on the measure theory of continued fractions. The proofs of the theorems in this chapter are also entirely elementary.
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11 of 11 people found the following review helpful By Giorgio Ciociano on October 4, 2005
Format: Paperback
You won't find many books on such an out-of-fashion theme as continued fractions, will you? Even less on the arithmetic side of the theory. Yes, it's true, many texts on elementary number theory provide a chapter or so about the subject, but if you want to gain a reasonably thorough picture of the field, without dwelling so much on details, you've got to resort to Kinchin's "Continued fractions": readable (no more mathematic needed than basics of analysis), complete (all fundamental conceptual aspects dealt with, included measure theory and implications on irrational numbers), brief (less than a hundred pages with virtually no applications - not even to Pell's equation!) and LIVELY in style.

All in all a very good start for understanding this profound mathematical tool.
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Continued Fractions (Dover Books on Mathematics)
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