Number Theory: An Introduction to Mathematics

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"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

Author(s): W.A. Coppel (auth.)
Series: Universitext
Edition: 2
Publisher: Springer-Verlag New York
Year: 2009

Language: English
Pages: 610
Tags: Number Theory; Mathematics, general

Front Matter....Pages 1-11
The Expanding Universe of Numbers....Pages 1-82
Divisibility....Pages 83-127
More on Divisibility....Pages 129-178
Continued Fractions and Their Uses....Pages 179-222
Hadamard’s Determinant Problem....Pages 223-259
Hensel’s p -adic Numbers....Pages 261-290
The Arithmetic of Quadratic Forms....Pages 291-326
The Geometry of Numbers....Pages 327-362
The Number of Prime Numbers....Pages 363-398
A Character Study....Pages 399-446
Uniform Distribution and Ergodic Theory....Pages 447-492
Elliptic Functions....Pages 493-540
Connections with Number Theory....Pages 541-586
Back Matter....Pages 1-24