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

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Written for readers with an understanding of arithmetic and beginning algebra, this book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.

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
Moreover, the author has included a number of unusual features to challenge and stimulate students:
  • 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.
 

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Richard Friedberg
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Customer reviews

4.5 out of 5 stars
31 global ratings

Top 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, 2018
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    A 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 helpful
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  • 4 out of 5 stars
    Not what I expected
    Reviewed in the United States on August 12, 2023
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    I 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

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  • 5 out of 5 stars
    What a carefully written exploration!
    Reviewed in the United States on September 4, 2002
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    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.

    19 people found this helpful
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  • 5 out of 5 stars
    Getting infinity makes everything else easier
    Reviewed in the United States on January 12, 2020
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    There 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.

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  • 4 out of 5 stars
    Be carefull
    Reviewed in the United States on August 24, 2001
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    You must have a medium understanding of mathematics and algebra.

    One person found this helpful
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  • 5 out of 5 stars
    Correct item arrived quickly in good condition.
    Reviewed in the United States on December 22, 2023
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    Correct item arrived quickly in good condition.

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  • 3 out of 5 stars
    Not that adventurous
    Reviewed in the United States on December 26, 2000
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    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.

    16 people found this helpful
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  • 5 out of 5 stars
    Great approach
    Reviewed in the United States on October 26, 2013
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    This 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

  • 4 out of 5 stars
    Four Stars
    Reviewed in India on December 5, 2015
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    the book is quite good. it's a dover classic and is hugely enjoyable.

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