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Number Theory and Its History (Dover Books on Mathematics) Paperback – April 1, 1988

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 400 pages
  • Publisher: Dover Publications (April 1, 1988)
  • Language: English
  • ISBN-10: 0486656209
  • ISBN-13: 978-0486656205
  • Product Dimensions: 8.5 x 5.4 x 0.8 inches
  • Shipping Weight: 14.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #808,546 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

28 of 28 people found the following review helpful By David S. Mazel on April 1, 2004
Format: Paperback
Ore's book is an excellent introduction to the fascinating topic of number theory. He takes his time explaining the history of numbers and goes into Euclid's algorithm so smoothly you hardly realize what you've learned. He discusses prime numbers and I was particularly delighted to see diophantine equations explained with lots of examples and an easy to follow method. The book is filled with interesting concepts, lots of examples, and good problems to do on your own.
At the end, for example, Ore talks of how number theory relates to geometry and I wish there were more of that in it.
I took this book on a very long trip, worked through many of the problems and simply found it a wonderful companion. If you get it, enjoy. One caution: if you already know some number theory you may find this book too simplistic. Still, it's worth having.
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16 of 20 people found the following review helpful By A Customer on July 22, 1998
Format: Paperback
This book goes into detail on number theory, but it is often hard to follow with the history mingled with the theory. More advanced material is referenced without proofs. Two readers will especially like this book: those who want an introduction to number theory and those who want a good introduction to the history of number theory.
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4 of 4 people found the following review helpful By Rakesh Kumar on February 5, 2011
Format: Paperback
I had bought this book for my son in high school based on some recommendation. Yesterday I opened the book and without realizing I had finished first 5 chapters and there was no strain of reading mathematics. Ore is able to introduce the topics and theorems very smoothly and sprinkles those with anecdotes providing a nice backdrop for such serious topic. He has really worked hard to covered the basics of the Number Theory in a manner that is easily digestible by a high school level math student.

I would recommend this book as the first book on Number Theory.
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6 of 7 people found the following review helpful By David S. Mazel on April 1, 2004
Format: Paperback
Ore's book is an excellent introduction to the fascinating topic of number theory. He takes his time explaining the history of numbers and goes into Euclid's algorithm so smoothly you hardly realize what you've learned. He discusses prime numbers and I was particularly delighted to see diophantine equations explained with lots of examples and an easy to follow method. The book is filled with interesting concepts, lots of examples, and good problems to do on your own.
At the end, for example, Ore talks of how number theory relates to geometry and I wish there were more of that in it.
I took this book on a very long trip, worked through many of the problems and simply found it a wonderful companion. If you get it, enjoy. One caution: if you already know some number theory you may find this book too simplistic. Still, it's worth having.
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3 of 3 people found the following review helpful By flashgordon on April 5, 2013
Format: Paperback
A agree with somebody that the history didn't provide much in teaching number theory. John Stillwell's "Elements of Number theory" is more succesfull.

Oystein's book partly tries to show the historical development; but, he's always introducing concepts that only make sense or are proved in more advanced settings like the 'trivial factors'(both the minus and positive versions of the same divisor). 4K+1 theorem is introduced. He mostly tries to only get into pre-Gaussian number theory, but ends up talking a lot about congruence number theory. In fact, compared to John Stillwell, I like this book for Oystein's much more thourough introduction to congruence integers. Also compared to John Stillwell, Oystein goes through Fermat's infinit descent method a lot better. And yet, Oystein mentions things like Leonard Euler's zeta function and some other post-gaussian number theory. It's a weird book like that.

I also like Oystein's treatment of Euclid's algorith and the general solution of linear number theory equations over John Stillwell's. All in all, it's a good valuable book, but hardly historically accurate; or he mixes modern mathematics up with old to make the old easier to handle(as does John Stillwell). Oystein's book is better for pre-gaussian number theory imo over John Stillwells. John Stillwell's book is better for an easy introduction to post-gaussian number theory. For a better introduction to the issues of ancient number theory see Van Der Waerden's almost anything, but generally "Science Awakening", and Thomas Heath's "A History of Greek Mathematics" volume 1 and 2 really for the Diophantine analyses. I havn't read Andre Weil's book which is probably the best overal technical history of number theory.
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13 of 17 people found the following review helpful By D. Taylor on December 26, 2000
Format: Paperback
A noted conjecture of the author's on the harmonic mean of the divisors is tucked unobtrusively in this pleasant reader: "Every harmonic number is even." See problem B2 in Richard K. Guy's Unsolved Problem's in Number Theory.
A good book (but not a great book). Very basic. For the more advanced historical approach, Andre Weil's Number Theory: An approach through history" is to be recommended. Or even Guy's book mentioned above.
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Number Theory and Its History (Dover Books on Mathematics)
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