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Algebraic Theory of Quadratic Numbers

  • Mak Trifković

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Mak Trifković
    Pages 1-25
  3. Mak Trifković
    Pages 27-44
  4. Mak Trifković
    Pages 45-59
  5. Mak Trifković
    Pages 61-86
  6. Mak Trifković
    Pages 107-130
  7. Mak Trifković
    Pages 131-184
  8. Back Matter
    Pages 185-197

About this book

Introduction

By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group.  The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms.  The treatment of quadratic forms is somewhat more advanced  than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes.

The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields.  The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders.  Prerequisites include elementary number theory and a basic familiarity with ring theory.

Keywords

ideal class group number theory quadratic forms ring theory

Authors and affiliations

  • Mak Trifković
    • 1
  1. 1.Department of Math and StatisticsUniversity of VictoriaVictoriaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7717-4
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7716-7
  • Online ISBN 978-1-4614-7717-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site