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© 1984

Topics from the Theory of Numbers

Benefits

  • Motivates the subject with historical background and notes

  • Problems and examples illustrate the ideas of the text

  • Touches upon many of the most famous ideas and proofs in number theory

  • 178 well-chosen problems

Textbook

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Introduction, Historical Background, and Notations

    1. Front Matter
      Pages 1-1
    2. Emil Grosswald
      Pages 3-12
    3. Emil Grosswald
      Pages 13-16
  3. Elementary Number Theory

    1. Front Matter
      Pages 17-17
    2. Emil Grosswald
      Pages 19-33
    3. Emil Grosswald
      Pages 35-65
    4. Emil Grosswald
      Pages 67-80
    5. Emil Grosswald
      Pages 81-107
    6. Emil Grosswald
      Pages 109-140
  4. Topics from Analytic and Algebraic Number Theory

    1. Front Matter
      Pages 141-141
    2. Emil Grosswald
      Pages 169-185
    3. Emil Grosswald
      Pages 187-217
    4. Emil Grosswald
      Pages 219-231
    5. Emil Grosswald
      Pages 233-254
    6. Emil Grosswald
      Pages 255-288
    7. Emil Grosswald
      Pages 289-319
  5. Back Matter
    Pages 321-335

About this book

Introduction

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory.

Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including:

* divisibility

* congruences

* the Riemann zeta function

* Diophantine equations and Fermat’s conjecture

* the theory of partitions

 

Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike.

 

 

"In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald."

Marc Kac

"This book is designed for use in a first course in number theory at the junior or senior level...The author has certainly planned his book well, chosen material that will be stimulating to its intended audience, and carried the project through in such a way that interest seldom flags."

Mathematical Reviews (Review of First Edition)

Keywords

Fermat's equation Riemann zeta function Theory of partitions algebra algebraic number theory arithmetic congruences diophantine equation divisibility ideal theory number theory prime number prime number theorem quadratic residues zeta function

Authors and affiliations

  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

Bibliographic information

  • Book Title Topics from the Theory of Numbers
  • Authors Emil Grosswald
  • Series Title Modern Birkhäuser Classics
  • DOI https://doi.org/10.1007/978-0-8176-4838-1
  • Copyright Information Birkhäuser Boston 1984
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3044-7
  • Softcover ISBN 978-0-8176-4837-4
  • eBook ISBN 978-0-8176-4838-1
  • Series ISSN 2197-1803
  • Series E-ISSN 2197-1811
  • Edition Number 2
  • Number of Pages XV, 335
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Algebra
  • Buy this book on publisher's site
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Reviews

From the reviews:

"When one has the opportunity to teach an undergraduate course on the subject there are plenty of excellent books to choose from. Depending on the approach, one may choose...a classical text that brims with elegance in the choice of topics or proofs that will leave our students avid for more. The book under review falls [into] this category, but also has plenty of well-chosen exercises at the end of every chapter. This is a book written with love for the subject and with the presence of its readers (students) in mind all the time."   MAA Reviews (Review of Second Edition, Softcover Reprint)

“In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald.”   Marc Kac (Review of Second Edition)

“For the second edition the author has made several changes, mainly in the third part of the book concerning analytic and algebraic number theory. There is an entirely new chapter on $L$-functions and primes in arithmetic progressions, another new chapter on the arithmetic of number fields, and a largely rewritten chapter on Diophantine equations...The revisions have undoubtedly increased the value of this textbook, and the reviewer does not hesitate to recommend the volume for anybody interested in number theory. Among the many merits of the book one should mention the author’s lively and stimulating style of writing as well as the carefully chosen exercises at the ends of the chapters.”   —Mathematical Reviews  (Review of Second Edition)

“This book is designed for use in a first course in number theory at the junior or senior level...The author has certainly planned his book well, chosen material that will be stimulating to its intended audience, and carried the project through in such a way that interest seldom flags.”   —Mathematical Reviews (Review of First Edition)