# Number Fields

Textbook

Part of the Universitext book series (UTX)

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. Daniel A. Marcus
Pages 129-158
9. Daniel A. Marcus
Pages 159-177
10. Back Matter
Pages 179-203

### Introduction

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

### Keywords

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

1. 1.ColumbusUSA

Daniel A. Marcus received his PhD from Harvard University in 1972. He was a J. Willard Gibbs Instructor at Yale University from 1972 to 1974 and Professor of Mathematics at California State Polytechnic University, Pomona, from 1979 to 2004. He published research papers in the areas of graph theory, number theory and combinatorics. The present book grew out of a lecture course given by the author at Yale University.

### Bibliographic information

• Book Title Number Fields
• Authors Daniel A. Marcus
• Series Title Universitext
• Series Abbreviated Title Universitext
• DOI https://doi.org/10.1007/978-3-319-90233-3
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Softcover ISBN 978-3-319-90232-6
• eBook ISBN 978-3-319-90233-3
• Series ISSN 0172-5939
• Series E-ISSN 2191-6675
• Edition Number 2
• Number of Pages XVIII, 203
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour