Overview
- Contains over 300 exercises
- Assumes only basic abstract algebra
- Covers topics leading up to class field theory
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
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
Reviews
“This volume has stood the test of time. It is both demanding of and rewarding for anyone willing to work through it.” (C. Baxa, Monatshefte für Mathematik, Vol. 201 (2), 2023)
“It is well structured and gives the reader lots of motivation to learn more about the subject. It is one of the rare books which can help students to learn new stuff by themselves by solving the numerous exercises which cover very deep and important results … . The prerequisites for the reader are kept to a minimum making this book accessible to students at a much earlier stage than usual textbooks on algebraic number theory.”
“A book unabashedly devoted to number fields is a fabulous idea. … it goes without saying that the exercises in the book — and there are many — are of great importance and the reader should certainly do a lot of them; they are very good and add to the fabulous experience of learning this material. … it’s a wonderful book.” (Michael Berg, MAA Reviews, October 22, 2018)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Number Fields
Authors: Daniel A. Marcus
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-90233-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-90232-6Published: 23 July 2018
eBook ISBN: 978-3-319-90233-3Published: 05 July 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XVIII, 203
Additional Information: Originally published by Springer-Verlag New York, 1977
Topics: Number Theory, Algebra