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An Adventurer's Guide to Number Theory (Dover Books on Mathematics) Reprint Edition
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In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as:
- Primes and divisibility
- Beginning algebra, geometry, and discussions of Euclid's Elements, calculus, and set theory
- Quadratic forms and residue arithmetic and quadratic reciprocity and related theorems
- The original problems in Diophantus' Arithmetica
- Proofs of Fermat's Last Theorem for the exponents 3and 4
- Two proofs of Wilson's Theorem
Also included is a Table of Theorems grouped into categories according to subject, and an Index of Mathematicians. Readers with a mathematical bent will enjoy and benefit from these entertaining and thought-provoking adventures in the fascinating realm of number theory. Mr. Friedberg is a theoretical physicist who has contributed to a wide variety of problems in mathematics and physics, including mathematical logic, number theory, solid state physics, general relativity, particle physics, quantum optics, genome research, and the foundations of quantum physics.
Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.
- ISBN-100486281337
- ISBN-13978-0486281339
- EditionReprint
- PublisherDover Publications
- Publication dateJanuary 9, 1995
- LanguageEnglish
- Dimensions5.42 x 0.49 x 8.45 inches
- Print length240 pages
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Product details
- Publisher : Dover Publications
- Publication date : January 9, 1995
- Edition : Reprint
- Language : English
- Print length : 240 pages
- ISBN-10 : 0486281337
- ISBN-13 : 978-0486281339
- Item Weight : 8.8 ounces
- Dimensions : 5.42 x 0.49 x 8.45 inches
- Part of series : Dover Books on Mathematics
- Best Sellers Rank: #626,194 in Books (See Top 100 in Books)
- #116 in Number Theory (Books)
- #261 in Mathematics History
- #1,418 in Mathematics (Books)
- Customer Reviews:
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Learn more how customers reviews work on AmazonTop reviews from the United States
- 5 out of 5 stars
A very good introduction to Number Theory for the Layman.
Reviewed in the United States on January 29, 2018A lovely book by a lovely mathematician. Yes, 1 is prime in that book, but why not? Yes, some pythagorean drawing of numbers would have helped, but all that are tiny details concerning a book which can only make people attracted to mathematics. The book is deep, though, and lead the reader to key notion, like a proof of the Quadratic Reciprocity Law, to give one example. I asked myself if that was the "Richard Friedberg" of logic (recursion theory), the one who solved a famous problem by Emil Post, independently with Mucnick, a long time ago, and well, I think so, for a small very curious passage on "mind-reading" sequence of numbers, which makes me hoping the author write a popular book on Logic. There is much love in that book, for the numbers, mathematics, and its audience.
4 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 4 out of 5 stars
Not what I expected
Reviewed in the United States on August 12, 2023I come from a coding background. I ventured into number theory while brushing up on my discrete math for coding. I enjoy numbers and thought this would be right up my alley. Boy was I wrong. I find myself skipping through the proofs and useless information(about half the book). I don't care if a cube cant be the sum of two cubes, or if 1311 is a special number because it has 13 and 11 in it.
Most of the information in here is either just thought exercises, or so inapplicable I cant even see scenarios where its useful. The book isn't bad, just not for me. I am glad it only cost me 1 $10 book to learn enough about number theory to know its not my cup of tea
One person found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
What a carefully written exploration!
Reviewed in the United States on September 4, 2002I 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.
19 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Getting infinity makes everything else easier
Reviewed in the United States on January 12, 2020There is a bit of jump in understanding to get number theory fully, for me that was comprehending infinity once I got that the rest made sense to me. Number theory is amazing and this book does an excellent job of highlighting how fun the subject can be.
Sending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 4 out of 5 stars
Be carefull
Reviewed in the United States on August 24, 2001You must have a medium understanding of mathematics and algebra.
One person found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Correct item arrived quickly in good condition.
Reviewed in the United States on December 22, 2023Correct item arrived quickly in good condition.
One person found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 3 out of 5 stars
Not that adventurous
Reviewed in the United States on December 26, 2000I 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.
16 people found this helpfulSending feedback...Sending feedback...HelpfulThank you for your feedback.Sorry, we failed to record your vote. Please try againThanks, we'll investigate in the next few days.Sorry, We failed to report this review. Please try again - 5 out of 5 stars
Great approach
Reviewed in the United States on October 26, 2013This book really helped explain number theory in user friendly language. I've had number theory textbooks and they were terrible. This book was much better.
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Top reviews from other countries
Amazon Customer4 out of 5 starsFour Stars
Reviewed in India on December 5, 2015the book is quite good. it's a dover classic and is hugely enjoyable.
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