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An Adventurer's Guide to Number Theory (Dover Books on Mathematics) Reprint Edition

4.3 out of 5 stars 10 customer reviews
ISBN-13: 978-0486281339
ISBN-10: 0486281337
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 240 pages
  • Publisher: Dover Publications; Reprint edition (January 9, 1995)
  • Language: English
  • ISBN-10: 0486281337
  • ISBN-13: 978-0486281339
  • Product Dimensions: 5.4 x 0.5 x 8.4 inches
  • Shipping Weight: 7.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #820,009 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Jeffrey L. Cooper on September 4, 2002
Format: Paperback Verified Purchase
I think this book is a masterpiece in mathematical exposition. All you need to know is how to add, subtract, multiply, and divide and maybe a vague memory of algebra. Mr. Friedberg will walk you through a lot of number theory after which (or maybe even during which) you may find a number theory textbook more approachable. If you read carefully you will really internalize what a proof by contradiction is and what an infinite descent is. You'll get a real appreciation for the logic of a proof and you'll see some ingenius tricks used by some great mathematicians ... and you'll understand them!
This book is approachable and doable by anyone with a motivation for what can be understood about numbers. And I can't stress how carefully, thoughtfully, and articulately it is written.
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Format: Paperback
The author's enthusiasm shines through as he explains primes, perfect numbers, quadratic forms, and more. The explanations are clear: not too easy, but not too hard; Mr. Friedberg does a remarkable job of gauging the reader's level (at least MY level!).
I didn't realize number theory was so much fun until I started reading this book.
Note: I noticed a small typo on p.95: the equation to generate Pythagorean triplets is missing a 'square' on the left hand side.
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Format: Paperback Verified Purchase
Friedberg's text, which is written in an inviting conversational tone, is an idiosyncratic introduction to number theory which stresses the subject's historical development. The material is introduced through problems that motivate the results that Friedberg discusses. These results include Euclid's theorem that there are infinitely many prime numbers, the use of the sieve of Eratosthenes to find prime numbers less than the square root of a positive integer n, Gauss' Fundamental Theorem of Arithmetic, perfect and amicable numbers, Pythagorean triples, modular arithmetic, factoring numbers of the form x^2 + ny^2, and the Law of Quadratic Reciprocity. Friedberg ably links these topics together and places them in historical perspective. However, there are better introductions to number theory. This text has no formal exercises, so you do not have an opportunity to reinforce what you are learning. It is also a poor reference because definitions, theorems, and proofs are stated within paragraphs, the whimsical chapter titles do not convey what topics are covered, and there is no subject index to help you find the definitions and theorems that are buried within the paragraphs. Also, the scope of coverage is less than that of other introductions to number theory.

In his introduction, Friedberg, a physicist, distinguishes between the common and scientific meanings of the word theory. He also discusses the difference between a scientific theory and a mathematical theorem.

Friedberg uses sequences to introduce proofs by mathematical induction. Friedberg shows how proofs of mathematical induction work and discusses why they are valid.
Read more ›
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Format: Paperback
I felt like I suited up for space travel and got grounded by equipment malfunction. Perhaps I took the title too literally. Since there are so many books on number theory, surely one with such a title should cover the outer reaches. This is nothing but a basic introduction. More is covered in Albert Beiler's "Recreations in the Theory of Numbers" and it's much more adventurous. Still worth 3 stars, and worth owning - but not worth keeping under your pillow.
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Format: Paperback
...but the dropdown allows you to pick either four or five; I felt generous.
This book is great in that I managed to become "number-theory literate" in a matter of days. Historical tidbits not only make the book flow smoothly, but make it fun to read. The actual mathematical content that is covered nails down the fundamental concepts of number theory pretty well. For clarity, the author is generous with examples.
My only complaint is that the writing, while clear and conversational, is almost too conversational. In the first part of the book, you have to question the author's mathematical background when he makes an embarassing claim and corrects himself in a footnote. Granted, we're all human, but this is a book for goodness sake, you can take your words back! Also, the examples occasionally skip steps, forcing you to stare at the problem longer if it's not clear to you what happened. This isn't always a bad thing, I suppose, but it can be distracting. Still, the book serves it's purpose well and is a good primer for anyone who at least understands high school algebra.
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