Quadratics

Richard A. Mollin

• Publisher: CRC Press
• Year: 2018
• Print ISBN:
  9780367401528
  9780367837976
• Edition: 1
• eBook ISBN:
  9781351420761
• Topic: Mathematics
• Subtopic: Cyber Security
• Index: Mathematics

The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarily a reference book and graduate student text with more than 200 exercises and a great deal of hints! The motivation for the text is best given by a quote from the Preface of Quadratics: "There can be no stronger motivation in mathematical inquiry than the search for truth and beauty. It is this author's long-standing conviction that number theory has the best of both of these worlds. In particular, algebraic and computational number theory have reached a stage where the current state of affairs richly deserves a proper elucidation. It is this author's goal to attempt to shine the best possible light on the subject."

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• List of Symbols
• Preface
• Introduction
• 1 Background from Algebraic Number Theory.
• 2 Continued Fractions Applied to Quadratic Fields.
• 3 Diophantine Equations and Class Numbers.
• 4 Prime-Producing Polynomials.
• 5 Class Numbers: Criteria and Bounds.
• 6 Ambiguous Ideals.
• 7 Influence of the Infrastructure.
• 8 Algorithms.
• APPENDIX A: Tables.
• APPENDIX B: Fundamental Units of Real Quadratic Fields.
• APPENDIX C: Class Numbers of Real Quadratic Fields.
• APPENDIX D: Class Numbers of Complex Quadratic Fields (and their class group structure).
• APPENDIX E: A Gazetteer of Forms
• APPENDIX F: Analytic Considerations
• BIBLIOGRAPHY.
• INDEX.