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

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.

As a mathematician I love this book because you can do the proofs pretty easily and you can also explain this math easily to non mathematicians and have them interested in mathematics.

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)

Simply excellent. For someone such as myself who is mathematically-inclined but never had exposure to a number theory course, this book offers a perfect balance of accessibility and depth. The organization of the material has clearly been carefully thought-out so as to inflict minimal pain on newcomers like me. The practice problems are numerous, varied, interesting, and span a fairly broad range of difficulty, meaning you can push yourself to *really* absorb the material if you like. Perhaps, above all else, what this book offers -- or at least what I have found myself experiencing as each chapter unfolds -- is a glimpse at the beauty of number theory. The book has turned something that I once thought to be an abstract, toy-problem-ish area of mathematics into a genuine joy as I come to understand more and more this strange, oft-baffling, occasionally outright-magical branch of math. It is, dare I say, quite a fun read :)

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 Mathematics without requiring higher math. It has many great exercises and the second edition corrects mistakes made in the first. Perfect !

I got this book for the class Theory of Numbers. It has all of the theorems and lemmas needed to theoretically learn all of the subject matter, and all of the problems are very good practice. But to get a really good grasp of the material and its practical applications this book needs to be supplemented in some way (lectures, another book, examples from the internet, etc.).

I'm using this to teach advanced highschool students. I find the topic choice and length of each section perfect to keep students interested. The exercises at the end of each section are rather simple, but the additional problems at the end of the book offer a wealth of much more challenging problems.

I took a course on number theory decades ago in college. I've been looking for something to refresh my memory (math major 😊). This is the right book.

Great introductory number theory textbook. Quite student friendly

C'est une façon très douce d'aborder la théorie des nombres qui est très formatrice d'un esprit de mathématicien. C'est une autre manière de voir les nombres, on n'étudie pas 3 kilos de pommes mais on recherche les propriétés du nombre 3; c'est du lourd.

Empfehlenswertes Buch... ich habe es auch Interesse und zum Selbststudium gekauft... Themen werden gut erläutert...

Disparado, um dos melhores livros de matemática que já li. Mesmo sendo enxuto, possui uma curva de dificuldade muito boa, te levando a concluir por conta própria a teoria e instigando a curiosidade para aprender mais. Recomendo muito!

Good value as a paperback. Very easy style of writing. Dark bold print allows for smaller than desired typeface being reader friendly for us oldies. Covers a good (but not extensive) selection of NT topics. Overall very good value as a book. I am sure his other books are worth checkng out.