# Number Theory: An Introduction to Mathematics

Springer Science & Business Media, Aug 12, 2009 - Mathematics - 610 pages

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."

"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