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Problems in Algebraic Number Theory

  • Textbook
  • © 2005

Overview

Authors:
  1. M. Ram Murty

    1. Department of Mathematics and Statistics, Queen's University, Kingston, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Jody Esmonde

    1. Graduate School of Education, University of California at Berkeley, Berkeley, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Problems

    1. Elementary Number Theory

      Pages 3-11

    2. Euclidean Rings

      Pages 13-26

    3. Algebraic Numbers and Integers

      Pages 27-39

    4. Integral Bases

      Pages 41-52

    5. Dedekind Domains

      Pages 53-68

    6. The Ideal Class Group

      Pages 69-79

    7. Quadratic Reciprocity

      Pages 81-97

    8. The Structure of Units

      Pages 99-116

    9. Higher Reciprocity Laws

      Pages 117-125

    10. Analytic Methods

      Pages 127-138

    11. Density Theorems

      Pages 139-155

  3. Solutions

    1. Elementary Number Theory

      Pages 159-178

    2. Euclidean Rings

      Pages 179-196

    3. Algebraic Numbers and Integers

      Pages 197-206

    4. Integral Bases

      Pages 207-225

    5. Dedekind Domains

      Pages 227-244

    6. The Ideal Class Group

      Pages 245-262

    7. Quadratic Reciprocity

      Pages 263-278

    8. The Structure of Units

      Pages 279-298
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Keywords

About this book

Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially asking "well-posed" questions. The approach taken by the authors in Problems in Algebraic Number Theory is based on the principle that questions focus and orient the mind. The book is a collection of about 500 problems in algebraic number theory, systematically arranged to reveal ideas and concepts in the evolution of the subject. While some problems are easy and straightforward, others are more difficult. For this new edition the authors added a chapter and revised several sections. The text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition facilitates independent study, and students having taken a basic course in calculus, linear algebra, and abstract algebra will find these problems interesting and challenging. For the same reasons, it is ideal for non-specialists in acquiring a quick introduction to the subject.

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)

Authors and Affiliations

  • Department of Mathematics and Statistics, Queen's University, Kingston, Canada

    M. Ram Murty

  • Graduate School of Education, University of California at Berkeley, Berkeley, USA

    Jody Esmonde

Bibliographic Information

  • Book Title: Problems in Algebraic Number Theory

  • Authors: M. Ram Murty, Jody Esmonde

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/b138452

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2005

  • Hardcover ISBN: 978-0-387-22182-3Published: 25 October 2004

  • Softcover ISBN: 978-1-4419-1967-0Published: 19 November 2010

  • eBook ISBN: 978-0-387-26998-6Published: 28 September 2005

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XVI, 352

  • Topics: Number Theory

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