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Elements of Number Theory, Stillwell John


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Автор: Stillwell John
Название:  Elements of Number Theory
ISBN: 9781441930668
Издательство: Springer
Классификация:

ISBN-10: 1441930663
Обложка/Формат: Paperback
Страницы: 268
Вес: 0.38 кг.
Дата издания: 03.12.2010
Серия: Undergraduate texts in mathematics
Язык: English
Издание: Softcover reprint of
Иллюстрации: Black & white illustrations
Размер: 234 x 156 x 14
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized inte- gers, Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them ideal numbers because he did not know exactly what they were, though he knew how they behaved.


Princeton encyclopedia of classical sites

Автор: Stillwell, Richard
Название: Princeton encyclopedia of classical sites
ISBN: 0691617104 ISBN-13(EAN): 9780691617107
Издательство: Wiley
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Цена: 25186.00 р.
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Описание:

Here are over 1,000 pages of authoritative information on the archaeology of Greek and Roman civilization. The sites discussed in the more than 2,800 entries are scattered from Britain to India and from the shores of the Black Sea to the coast of North Africa and up the Nile. They are located on sixteen area maps, keyed to the entries. The entries were written by 375 scholars from sixteen nations, many of whom have worked at the sites they describe. Until now our knowledge of the Classical period has been scattered in hundreds of sources dating from antiquity to our own times. This volume provides essential information on work accomplished, in progress, and still to be undertaken.

Originally published in 1976.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


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