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Elementary Number Theory: Second Edition (Dover Books on Mathematics) Second Edition Edition

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Underwood Dudley (Author)
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Underwood Dudley (Author)
4.4 out of 5 stars 22 customer reviews
ISBN-13: 978-0486469317
ISBN-10: 048646931X
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 272 pages
  • Publisher: Dover Publications; Second Edition edition (September 25, 2008)
  • Language: English
  • ISBN-10: 048646931X
  • ISBN-13: 978-0486469317
  • Product Dimensions: 0.8 x 5.5 x 8.5 inches
  • Shipping Weight: 10.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (22 customer reviews)
  • Amazon Best Sellers Rank: #137,354 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

41 of 41 people found the following review helpful
It is a book that has aged very well
By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on August 10, 2005
Format: Hardcover
Published in 1978, this book suffers very little from the illness of being dated. Of course, Fermat's last theorem has been proven and computers have grown much more powerful. However, those advances have little affect on the value of the book. Done well, basic number theory is timeless, and Dudley does it very well. The explanations of the fundamentals are sound and solved exercises are scattered throughout. Solutions to most of the odd numbered problems at the end of the chapters are also included.

The coverage is fairly typical, so the book can still be used as the text for a course in beginning number theory. Chapter 23 contains a set of 267 additional problems, a set for each of the other chapters in the book. Solutions to most of the odd problems in this set are also included. I commend Dudley for including so many solutions; I have little time for authors of books who do not provide solutions to at least some of the exercises. If I ever teach a course in basic number theory, this is the book that I would use.
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37 of 39 people found the following review helpful
A lot of examples and proofs! Perfect book for a beginner.
By Yuan J. Son on February 13, 2003
Format: Hardcover
This is the excellent book if you want to study the
number theory but don't know where to start.
The explanations are sound and CLEAR. A lot of problems
are actually solved by an author and many answers to
the exercises are given at the end of book.
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22 of 23 people found the following review helpful
great problems
By another reader on April 11, 2004
Format: Hardcover
Some of the problems in this book are unlike any I've seen before, like Dudley gives a bunch of equations, you're supposed to see the pattern & he writes "guess & prove a theorem". Dudley's writing style is very informal & I thought it was a nice change from other books. Like the other person said, the book is clearly written and there are lots of examples. I had this book for a 3rd-year course, but I think a 1st or 2nd-year student could handle this book.
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20 of 21 people found the following review helpful
Undergrad math and phys major review
By Bill Nye on June 4, 2010
Format: Hardcover Verified Purchase
I picked up this book after taking a course in set theory/math logic. It was my first experience with proof based math and I found it very challenging and rewarding. I decided over the summer I would teach myself number theory as well. So far I am about 3 or 4 weeks into the summer and I've chopped down sections 1-6. Keep in mind I am also doing undergrad physics research and a directed study astrophysics course as well, you could easily progress further. I really have enjoyed this book thus far. I often get so caught up in it that I am up until morning toying with problems. The author did a fantastic job of finding the fine line between too difficult and elementary. It seems just short of a graduate text but a little above a common undergraduate text. Thanks to this text I am becoming much more confident in my ability to set up and execute proofs. I don't want to spoil the methods- but it seems MOSTLY up until this point all proofs are found in the same manner. I have not been able to execute a variety of proof methods (e.g. deduction, mathematical induction, contrapositive, and contradiction.) I would have liked to be able to switch it up some. However, I am no expert and this may be my own doing.
If that is the best "CON" I can come up with for this book, that says a lot. I HIGHLY recommend ANY student who enjoys thinking to pick up this book and complete it in it's entirety. I feel deprived that I wasn't given this opportunity sooner.

I am a 3rd year math+physics major. This book changed me from physics and chemistry to math and physics student and possibly from a physics grad student to a math grad.
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15 of 15 people found the following review helpful
Good overview to basic number theory
By J. A. Bradley on August 20, 2009
Format: Paperback
This is a great book for the mathematically-interested layman, non-math-major undergraduate, and people in other fields (such as computer science) who want a fairly quick read on the basics of this fascinating field. It would also serve well as a a precursor/warmup for more advanced treatments of the subject.
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9 of 9 people found the following review helpful
Excellent on Elementary Number Theory
By Indikos on December 6, 2009
Format: Paperback
Excellent text on number theory. Topic coverage is extensive: quadratic reciprocity, linear diophantine equations, Lagranges's 4-square theorem, Pell's equation and more. Proofs are very good and plenty of exercises.
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9 of 10 people found the following review helpful
Might be good, but early errors cause concern ...
By David Eisner on May 14, 2012
Format: Paperback
I've only just begun to work my way through this text, but a few errors early on are a cause of concern. For example, on page 6: "From 69 = 3*21 + 7 we get (69,21) = (21,7)..." As it turns out, 3*21 + 7 is equal to 70, not 69. Or consider the first sentence on the same page, "Although the theorem [the division algorithm] was stated only for positive integers a and b, because it is most often applied for positive integers, nowhere in the proof did we need a to be positive." Yet the second sentence of the proof (on page 5) reads: "It contains a subset of nonnegative integers which is nonempty (because a is positive) ..."

These mistakes are easy enough to catch, but it makes me wonder about the quality of what follows.
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5 of 5 people found the following review helpful
Enlightening Elementary Exposition
By G. A. Schoenagel on June 11, 2013
Format: Paperback Verified Purchase
Spend a fruitful afternoon perusing this slim text and most assuredly the reader's outlook on elementary number theory
will be enhanced. The book can be tackled in a brief sojourn, with many exercises reinforcing the reader's confidence
and building mathematical acuity. An acquaintance with Algebra is presumed, but all else is clearly enunciated within the
confines of the exposition.The clarity of writing and breadth of topics treated (at a truly introductory level) provides the
student of Number Theory a wonderful opportunity to learn something of this most demanding of mathematical disciplines.
As the author remarks, Number Theory arms the student with a mathematical style of thinking: "Problem,Deduction,Solution."
A worthwhile addition to the literature of elementary expositions on the subject and time well spent.
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Most Recent Customer Reviews

The Book is written in clear and concise language so ...

The Book is written in clear and concise language so that anyone who is interested in the theory of numbers or Primes will benefit from the book

Published 2 months ago by Alf
Four Stars

OK

Published 7 months ago by Wilfred J Cruz Sr
A very clear and smart introduction to number theory

A very clear and smart introduction to number theory.
I have a BA in Theoretical Mathematics and this book is
perfect for understanding much of the foundations of... Read more

Published 8 months ago by Ron Barry
need to reformat

Five stars for content but three for this particular format. There are no set page numbers, so when my teacher tells the class to flip to page 47, I have no idea where to look. Read more

Published 14 months ago by Victoria Forest
Five Stars

thanks

Published 17 months ago by michel reed
an excellent book a lousy display

This is not the first instance of a technical book which has been greatly maimed by a poor choice of visual display. Read more

Published 18 months ago by Ana Maria Veronica G
An explicit book on number theory

Each chapter is focused on one concept of number theory. Gives good excercises to help the reader understand these concepts. Read more

Published 19 months ago by Steven Baer
Stodgy, Old and not as easy as Quoted

Not quite so easy as it makes out. And written many years ago so it is a bit stodgy to read. Its a small book so despite the "you don't need any difficult math" the... Read more

Published 19 months ago by Robert J.
Simple and easy to understand.

The headline says it all. This book was simple and easy to get through. Made complex concepts manageable. Highly recommend.

Published 22 months ago by BeachyKeen
K.I.S.S. - keep it simple sweetie

I bought it, I like or it works for me or the recipient of the item or it makes the college students in the family happy. Read more

Published on November 30, 2013 by Amazon Customer

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