**AMS Chelsea Publishing**

Volume: 384;
2018;
212 pp;
Hardcover

MSC: Primary 11;

**Print ISBN: 978-1-4704-4694-9
Product Code: CHEL/384.H**

List Price: $53.00

AMS Member Price: $42.40

MAA Member Price: $47.70

**Electronic ISBN: 978-1-4704-4844-8
Product Code: CHEL/384.H.E**

List Price: $53.00

AMS Member Price: $42.40

MAA Member Price: $47.70

#### Supplemental Materials

# Introduction to Number Theory

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*Daniel E. Flath*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

Growing out of a course designed to teach
Gauss's Disquisitiones Arithmeticae to honors-level
undergraduates, Flath's Introduction to Number Theory focuses
on Gauss's theory of binary quadratic forms. It is suitable for use as
a textbook in a course or self-study by advanced undergraduates or
graduate students who possess a basic familiarity with abstract
algebra. The text treats a variety of topics from elementary number
theory including the distribution of primes, sums of squares,
continued factions, the Legendre, Jacobi and Kronecker symbols, the
class group and genera. But the focus is on quadratic reciprocity
(several proofs are given including one that highlights the \(p -
q\) symmetry) and binary quadratic forms. The reader will come
away with a good understanding of what Gauss intended in the
Disquisitiones and Dirichlet in his Vorlesungen. The
text also includes a lovely appendix by J. P. Serre titled \(\Delta
= b^2 - 4ac\).

The clarity of the author's vision is
matched by the clarity of his exposition. This is a book that reveals
the discovery of the quadratic core of algebraic number theory. It
should be on the desk of every instructor of introductory number
theory as a source of inspiration, motivation, examples, and
historical insight.

#### Readership

Undergraduate and graduate students and researchers interested in the history of number theory.

#### Reviews & Endorsements

I really like this book...it sits on a nearby shelf every time I teach number theory. I use it as a source for ideas, examples, and problems. And sometimes, when I'm unhappy with the proof in our textbook, I will check to see if Flath has found the 'right' proof. He often has...I have often found that Flath's account of some topic is easier to understand than others. Most of all, Flath has good mathematical taste: the material he covers is beautiful and definitely worth learning.

-- Fernando Q. Gouvêa, MAA Reviews

#### Table of Contents

# Table of Contents

## Introduction to Number Theory

- Cover Cover11
- Title Page Cover44
- Copyright Page Cover55
- Preface Cover88
- Contents Cover1212
- Chapter 1 Cover1414
- Chapter 2 Cover3737
- Chapter 3 Cover7676
- Chapter 4 Cover117117
- Chapter 5 Cover160160
- Appendix A Cover193193
- Appendix B Cover203203
- Bibliography Cover217217
- Subject Index Cover220220
- Notation Index Cover224224
- Errata from previous printing Cover226226
- Back Cover Back Cover1228