Hardcover ISBN:  9781470446949 
Product Code:  CHEL/384.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470448448 
Product Code:  CHEL/384.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Hardcover ISBN:  9781470446949 
eBook: ISBN:  9781470448448 
Product Code:  CHEL/384.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 
Hardcover ISBN:  9781470446949 
Product Code:  CHEL/384.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470448448 
Product Code:  CHEL/384.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Hardcover ISBN:  9781470446949 
eBook ISBN:  9781470448448 
Product Code:  CHEL/384.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsAMS Chelsea PublishingVolume: 384; 2018; 212 ppMSC: Primary 11
Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honorslevel 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 selfstudy 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.
ReadershipUndergraduate and graduate students and researchers interested in the history of number theory.

Table of Contents

Chapters

Chapter 1. Prime Numbers and Unique Factorization

Chapter 2. Sums of Two Squares

Chapter 3. Quadratic Reciprocity

Chapter 4. Indefinite Forms

Chapter 5. The Class Group and Genera

Appendix A. $\Delta = b^{2}  4ac^{*}$

Appendix B. Tables


Additional Material

Reviews

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


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Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honorslevel 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 selfstudy 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.
Undergraduate and graduate students and researchers interested in the history of number theory.

Chapters

Chapter 1. Prime Numbers and Unique Factorization

Chapter 2. Sums of Two Squares

Chapter 3. Quadratic Reciprocity

Chapter 4. Indefinite Forms

Chapter 5. The Class Group and Genera

Appendix A. $\Delta = b^{2}  4ac^{*}$

Appendix B. Tables

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