Number Fields

  • Daniel A. Marcus

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Daniel A. Marcus
    Pages 1-8
  3. Daniel A. Marcus
    Pages 9-38
  4. Daniel A. Marcus
    Pages 39-67
  5. Daniel A. Marcus
    Pages 69-90
  6. Daniel A. Marcus
    Pages 91-110
  7. Daniel A. Marcus
    Pages 111-127
  8. Back Matter
    Pages 179-203

About this book


Requiring no more than a basic knowledge of abstract algebra, this textbook presents the basics of algebraic number theory in a straightforward, "down-to-earth" manner. It thus avoids local methods, for example, and presents proofs in a way that highlights key arguments. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.

Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.


From the reviews:

“A thoroughly delightful introduction to algebraic number theory” – Ezra Brown in the Mathematical Reviews

“An excellent basis for an introductory graduate course in algebraic number theory” – Harold Edwards in the Bulletin of the American Mathematical Society


number fields number rings prime decomposition in number rings Galois theory applied to prime decomposition ideal class group unit group distribution of ideals Dedekind zeta function and the class number formula distribution of primes class field theory MSC (2010): 12-01, 11Rxx, 11Txx

Authors and affiliations

  • Daniel A. Marcus
    • 1
  1. 1.ColumbusUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-90232-6
  • Online ISBN 978-3-319-90233-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site