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© 2005

Problems in Algebraic Number Theory

  • Theory is quickly translated into experience with the problem-solving approach. The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject. Includes various levels of problems - some are easy and straightforward, while others are more challenging. All problems are elegantly solved

  • An ideal book for self-study

Textbook
  • 96k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 190)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Problems

    1. Pages 13-26
    2. Pages 41-52
    3. Pages 53-68
    4. Pages 69-79
    5. Pages 81-97
    6. Pages 99-116
    7. Pages 117-125
    8. Pages 127-138
    9. Pages 139-155
  3. Solutions

    1. Pages 159-178
    2. Pages 179-196
    3. Pages 207-225
    4. Pages 227-244
    5. Pages 245-262
    6. Pages 263-278
    7. Pages 279-298

About this book

Introduction

From Reviews of the First Edition:

This book provides a problem-oriented first course in algebraic number theory. ... The authors have done a fine job in collecting and arranging the problems. Working through them, with or without help from a teacher, will surely be a most efficient way of learning the theory. Many of the problems are fairly standard, but there are also problems of a more original type. This makes the book a useful supplementary text for anyone studying or teaching the subject. ... This book deserves many readers and users.

- T. Metsänkylä , Mathematical Reviews

The book covers topics ranging from elementary number theory (such as the unique factorization of integers or Fermat's little theorem) to Dirichlet's theorem about primes in arithmetic progressions and his class number formula for quadratic fields, and it treats standard material such as Dedekind domains, integral bases, the decomposition of primes not dividing the index, the class group, the Minkowski bound and Dirichlet's unit theorem ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory.

- Franz Lemmermeyer, Zentralblatt

This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and $L$-functions highlighting some of the analytic aspects of algebraic number theory.

Keywords

algebra algebraic number theory calculus linear algebra number theory

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsQueen's UniversityKingstonCanada
  2. 2.Graduate School of EducationUniversity of California at BerkeleyBerkeleyUSA

Bibliographic information

  • Book Title Problems in Algebraic Number Theory
  • Authors M. Ram Murty
    Jody (Indigo) Esmonde
  • Series Title Graduate Texts in Mathematics
  • DOI https://doi.org/10.1007/b138452
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-22182-3
  • Softcover ISBN 978-1-4419-1967-0
  • eBook ISBN 978-0-387-26998-6
  • Series ISSN 0072-5285
  • Edition Number 2
  • Number of Pages XVI, 352
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
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Reviews

From the reviews of the second edition:

"Problems in Algebraic Number Theory is intended to be used by the students for independent study of the subject. It provides the reader with a large collection of problems (about 500) … . The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move from topic to topic … . the book is an excellent resource for the instructor and the student as a companion to any algebraic number theory course." (Álvaro Lozano-Robledo, MathDL, May, 2005)

"This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and L-Functions highlighting some of the analytic aspects of algebraic number theory. … the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory." (Zentralblatt für Didaktik der Mathematik, August, 2005)

"This is the second edition of Problems in algebraic number theory. ... errors have been corrected … . The decision to expand the book by including a chapter on density theorems is most welcome." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1055)

"This is the second edition of an unusual introduction to algebraic number theory. … each chapter is written in straightforward textbook style. All chapters contain a very large number of problems. … it presents a good way of acquiring a working knowledge of basic algebraic number theory by using it for independent study or as supplementary reading." (Ch. Baxa, Monatshefte für Mathematik, Vol. 149 (4), 2006)