Elementary Introduction to Number Theory by Calvin T. Long | (PDF) Free Download

Description

This accessible, highly regarded volume teaches the theory of numbers. It incorporates especially complete and detailed arguments, illustrating definitions, theorems, and subtleties of proof with explicit numerical examples whenever possible. The author has organized the results and constructed the arguments in such a way as to reveal the essential structure of the subject and to impart an understanding of the various methods of proof as methods rather than tricks. Hundreds of exercises, including computer-oriented problems, are included.

User’s Reviews

Editorial Reviews: From the Publisher Titles of related interest from Waveland Press: Strayer, Elementary Number Theory (ISBN 9781577662242) and Vanden Eynden, Elementary Number Theory, Second Edition (ISBN 9781577664451).

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an excellent book. The selection of topics is interesting, and the proofs illustrate proof technique well. I disagree with the previous reviewer that this would make a good text to learn proof techniques from. Also, while the level of this book may be below the level of an average introductory number theory course, I wouldn’t recommend this to a lay audience. The book is in so called “Satz-Beweise” style. It’s a progression of theorems and proofs with relatively little commentary. The proofs are illuminating, but at some points I would’ve appreciated some helpful intuitions with the theorems and proofs, instead of slogging through a proof only to discover that the underlying mathematical “idea” is really very simple.Maybe a bit of a nit-picky point, sometimes the proofs can be confusing. The author occasionally does things like use the same variable to refer to two distinct mathematical objects in a proof. This is annoying and will occasionally waste a few hours of your time.Otherwise, this book really is excellent. If you like this sort of thing, it’s quite a bit of fun. Also, as the previous reviewer mentioned, lots of problems (but not many solutions.)Edit, Another annoyance (2/19/2012):Sometimes the author really fails to show the connection between theorems. The most glaring example is in Chapter 2.7. The author shows two different expressions of Legendre’s formula and only mentions in passing that “The resemblance is more than superficial.” IT’S THE SAME FORMULA!!!! Occasionally, I can’t help feel but the book is artificially vague. Still, five stars.Edit (4/29/2012):I am, at this point, almost done with the book. Overall, it’s been pretty good. I’d like to stress to anyone that is thinking about picking this up that they should already know how to read proofs. Also, the chapters are strangely structured. Bits of intuition are strewn about in the proofs, so you don’t typically begin the chapter with a whole lot of intuition concerning the topic. My advice would be to skim each chapter to try to get the “big idea” before really digging in. It will save you lots of frustration.

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