Number Theory: An Introduction to Mathematics

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Springer Science & Business Media, Aug 11, 2009 - Mathematics - 610 pages
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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

  

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Contents

The Expanding Universe of Numbers
1
Divisibility
83
More on Divisibility
128
Continued Fractions and Their Uses
179
Hadamards Determinant Problem
223
Hensels padic Numbers
261
The Arithmetic of Quadratic Forms
291
The Geometry of Numbers
327
A Character Study
399
Uniform Distribution and Ergodic Theory
447
Elliptic Functions
493
Connections with Number Theory
541
Notations
587
Axioms
591
Index
592
Copyright

The Number of Prime Numbers
363

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About the author (2009)

Coppel-Australian National University

Bibliographic information