Customer Reviews

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

5 star:		(6)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

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.

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.

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.

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.

Elementary Number Theory: Second Edition is a relatively short mathematics book that deals a lot with prime number theory. The topics covered in this book are senior college level topics, making the name "Elementary" in the title somewhat deceptive. While topics they talk about in an intro to proofs class focus on the basics, this book focuses on the applied basics. The book is short and has many examples for the student to work out, but it is limited in that there are few examples that the author worked out. Because of the level of this book, many steps are also removed, however, even for a math student, some of the steps skipped left me stumped, and many topics are still out of grasp through independent study. There is a nice section of the book that has some induction problems, which is geared towards those who have already done proofs and now are working on number theory. This book is solid for the $10 it cost, but there is a reason other math texts run from $100-200, and that's because of the extensive amount of problems worked out in those texts. (You get what you pay for)