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This book, dedicated to the 100th anniversary of the birth of I. M. Vinogradov, contains papers ranging over various areas of mathematics, including number theory, algebra, theory of functions of a real variable and of a complex variable, ordinary differential equations, optimal control, partial differential equations, mathematical physics, mechanics, and probability. ... Read more

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"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.
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Customer Reviews (2)

probably he best first book for number theory
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.

Budding mathematicians only!
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' An Introduction to the Theory of Numbers (Oxford Science Publications).

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! ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 143 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Customer Reviews (1)

a rare book
The book get a very clear view about the trigonometrical sums in number theory and it's not so easy to find a work like this in the specialized literature.By the way it is a work of "first hand" that means that the author is one of the most important theorist in this field and much of the topics are originals.Last but not least the price is very very good. ... Read more

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Chapters: Ivans Klementjevs, Efims Klementjevs, Miķelis Ežmalis, Dagnis Vinogradovs, Kristaps Zalupe, Krists Straume, Dzintra Blūma, Aldis Kļaviņš, Maylon Hanold. Source: Wikipedia. Pages: 25. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Ivan Klementjev (Latvian: , born November 18, 1960 in Riga) is a Soviet-born Latvian politician and former sprint canoer who competed from the mid 1980s to the late 1990s. He won three Olympic medals in C-1 1000 m at the 1988, 1992 and 1996 Summer Olympics. The highlight was the gold medal in 1988, which he won as a competitor for the USSR. He trained at Trudovye Rezervy and later at the Armed Forces sports society in Riga when Latvia was part of the Soviet Union. He also won a total of twelve C-1 medals at the ICF Canoe Sprint World Championships with seven golds (C-1 1000 m: 1985, 1989, 1990, 1991, 1993, 1994; C-1 10000 m: 1989), two silvers (C-1 1000 m: 1986, C-1 10000 m: 1991), and three bronzes (C-1 1000 m: 1987, 1995; C-1 10000 m: 1990). Klementjev's only non C-1 world championship medal was a silver in the C-2 500 m event in 1983. After retiring from canoeing, Klementijevs entered politics and was a Riga city councillor for the TSP in 20012005, then MP (since 2006). ...More: http://booksllc.net/?id=4674685 ... Read more

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Chapters: Ivans Klementjevs, Efims Klementjevs, Miķelis Ežmalis, Dagnis Vinogradovs, Kristaps Zalupe, Krists Straume, Dzintra Blūma, Aldis Kļaviņš. Source: Wikipedia. Pages: 23. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Ivan Klementjev (Latvian: , born November 18, 1960 in Riga) is a Soviet-born Latvian politician and former sprint canoer who competed from the mid 1980s to the late 1990s. He won three Olympic medals in C-1 1000 m at the 1988, 1992 and 1996 Summer Olympics. The highlight was the gold medal in 1988, which he won as a competitor for the USSR. He trained at Trudovye Rezervy and later at the Armed Forces sports society in Riga when Latvia was part of the Soviet Union. He also won a total of twelve C-1 medals at the ICF Canoe Sprint World Championships with seven golds (C-1 1000 m: 1985, 1989, 1990, 1991, 1993, 1994; C-1 10000 m: 1989), two silvers (C-1 1000 m: 1986, C-1 10000 m: 1991), and three bronzes (C-1 1000 m: 1987, 1995; C-1 10000 m: 1990). Klementjev's only non C-1 world championship medal was a silver in the C-2 500 m event in 1983. After retiring from canoeing, Klementijevs entered politics and was a Riga city councillor for the TSP in 20012005, then MP (since 2006). ...More: http://booksllc.net/?id=4674685 ... Read more