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Number Theory: An Introduction to Mathematics: Universitext

Autor W. a. Coppel
en Limba Engleză Paperback – 12 aug 2009
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
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Specificații

ISBN-13: 9780387894850
ISBN-10: 0387894853
Pagini: 610
Ilustrații: XIV, 610 p. 17 illus.
Dimensiuni: 156 x 234 x 32 mm
Greutate: 0.86 kg
Ediția:2nd ed. 2009
Editura: Springer
Colecția Springer
Seria Universitext

Locul publicării:New York, NY, United States

Public țintă

Lower undergraduate

Cuprins

The Expanding Universe of Numbers.- Divisibility.- More on Divisibility.- Continued Fractions and Their Uses.- Hadamard#x2019;s Determinant Problem.- Hensel#x2019;s -adic Numbers.- The Arithmetic of Quadratic Forms.- The Geometry of Numbers.- The Number of Prime Numbers.- A Character Study.- Uniform Distribution and Ergodic Theory.- Elliptic Functions.- Connections with Number Theory.

Textul de pe ultima copertă

"Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
 
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse–Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions.
 
The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
 
From the reviews:
"This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics."
—Canadian Mathematical Society
"As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work."
—Mathematical Association of America

Caracteristici

A modern introduction to number theory, emphasizing its connections with other branches of mathematics, including algebra, analysis, and discrete math Suitable for first-year undergraduates through more advanced math students; prerequisites are elements of linear algebra only A self-contained text, useful for self-study: includes references at the end of each chapter Includes supplementary material: sn.pub/extras

Recenzii

Aus den Rezensionen:“... Die Grundidee besteht darin, ein Gefühl der Einheit und der Vielfalt der Mathematik beizubringen. Dazu eignet sich Zahlentheorie besonders gut ... In diesem Sinne ist das Buch eine Einführung in die Mathematik durch die Zahlentheorie ... Zunächst wird die Theorie pädagogisch entwickelt, mit Beispielen oder einfachen Ergebnissen beginnend. In einem weiteren Abschnitt werden Verallgemeinerungen, Anwendungen, Verfeinerungen ohne Beweis erwähnt, historische und fachliche Anmerkungen hinzugefügt, und eine ausführliche Literaturliste angegeben. ... ein schöner Text über klassische Zahlentheorie.“ (G. Barat, in: Internationale Mathematische Nachrichten, December/2009, Issue 12, S. 48 f.)