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19 Reviews
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33 of 33 people found the following review helpful
5.0 out of 5 stars It is a book that has aged very well
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...
Published on August 10, 2005 by Charles Ashbacher

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8 of 9 people found the following review helpful
3.0 out of 5 stars Might be good, but early errors cause concern ...
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,...
Published on May 14, 2012 by David Eisner


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33 of 33 people found the following review helpful
5.0 out of 5 stars It is a book that has aged very well, August 10, 2005
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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32 of 34 people found the following review helpful
5.0 out of 5 stars A lot of examples and proofs! Perfect book for a beginner., February 13, 2003
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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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20 of 21 people found the following review helpful
5.0 out of 5 stars great problems, April 11, 2004
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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15 of 16 people found the following review helpful
5.0 out of 5 stars Undergrad math and phys major review, June 4, 2010
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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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12 of 12 people found the following review helpful
5.0 out of 5 stars Good overview to basic number theory, August 20, 2009
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This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (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
5.0 out of 5 stars Excellent on Elementary Number Theory, December 6, 2009
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Indikos (Fairfax, Va) - See all my reviews
This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (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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8 of 9 people found the following review helpful
3.0 out of 5 stars Might be good, but early errors cause concern ..., May 14, 2012
This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (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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3 of 3 people found the following review helpful
5.0 out of 5 stars Enlightening Elementary Exposition, June 11, 2013
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This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (Paperback)
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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2 of 2 people found the following review helpful
4.0 out of 5 stars Very good, June 8, 2011
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This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (Paperback)
I like this book. It has some minor editing errors and the examples are not that great. The notation can be a bit confusing at time. Overall, however, it is a very good book for someone new to number theory or with limited understanding of it. It is also a good refresher course.
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3 of 4 people found the following review helpful
2.0 out of 5 stars Stodgy, Old and not as easy as Quoted, April 19, 2014
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This review is from: Elementary Number Theory: Second Edition (Dover Books on Mathematics) (Paperback)
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 material (which is new to the reader) is presented very concisely with few explanations. Most of the book seems to be taken up with lots of difficult questions only a small percentage of which have any answers. Most of all I disliked the authors patronizing and elitist demeanor. A favorite tactic is to supposedly quote another mathematician saying "If you don't implicitly understand the current question - you shouldn't consider studying number theory"" Wooah!!
You have to go over this stuff again and again and even then I had to seek online help to fill in the gaps. Really not the user friendly bedtime reading for even a math buff I was hoping for. I donated mine to the local library.
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Elementary Number Theory: Second Edition (Dover Books on Mathematics)
Elementary Number Theory: Second Edition (Dover Books on Mathematics) by Underwood Dudley (Paperback - September 25, 2008)
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