Elements of Number Theory (Dover Books on Mathematics) by I. M. Vinogradov (PDF)

Description

“A very welcome addition to books on number theory.”—Bulletin, American Mathematical SocietyClear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems and full solutions appear in the text, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. Translation of 1949 Russian edition.

User’s Reviews

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

⭐If you are already familiar with number theory and are just interested in how this famous (and infamous — see below) Russian mathematician presents the material, then this is a good Kindle book. However, if you actually want to learn number theory, you will find this edition very aggravating because the Kindle links are hopelessly screwed up. Whoever set up links obviously had no comprehension of the actual meaning of the text. When you click on a link to a previously elucidated theorem it almost always goes to the wrong place. Thus what would be the most useful feature of reading a math text on a Kindle is lost.In case it maters to you, the author, I. M. Vinogradov, was an antisemite who tried to purge Jewish influence from Soviet mathematics.

⭐Entrega rápida. El libro en condiciones óptimas.

⭐

⭐This book has two parts: a very elementary introduction to number theory concentrating on congruences presented in a number of chapters. Each chapter ends with a set of straightforward numerical exercises. The second part consists of a set of problems presented at the end of each chapter but having no relation to the content of the chapter. Each problem is provided with a solution or outline of a solution. It is this set of problems that makes the book really interesting. The problems are challenging, in fact many of them appear as theorems in Hardy and Wrights’

⭐.I bought this book some thirty years ago when I studied mathematics at the university. Working through these problems greatly improved my problem solving abilities. To be able to work through the problems the only prerequisites are arithmetic and some elementary calculus. But be sure to have the right mind set, only for budding mathematicians!

⭐The best way to get a feeling for the subject is by doing problems, and this back has great ones, which emphasize elementary methods, but very quickly get you to the research frontier (one of the many charms of the subject is that some very simple and natural questions are still wide open). After working through this book, you will really understand the subject. The only negative is that the areas covered are a little narrow (since they follow Vinogradov’s personal interests), so essentially no algebraic number theory is introduced, for example.

⭐It’s a classical book in number theory.

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