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Lectures on Number Theory
P. G. L. Dirichlet (with supplements by R. Dedekind)
A co-publication of the AMS and the London Mathematical Society.
cover
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History of Mathematics
1999; 275 pp; softcover
Volume: 16
ISBN-10: 0-8218-2017-6
ISBN-13: 978-0-8218-2017-9
List Price: US$57
Member Price: US$45.60
Order Code: HMATH/16
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See also:

Sources of Hyperbolic Geometry - John Stillwell

This volume is a translation of Dirichlet's Vorlesungen über Zahlentheorie which includes nine supplements by Dedekind and an introduction by John Stillwell, who translated the volume.

Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.

The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory. The legendary story is told how Dirichlet kept a copy of Gauss's Disquisitiones Arithmeticae with him at all times and how Dirichlet strove to clarify and simplify Gauss's results. Dedekind's footnotes document what material Dirichlet took from Gauss, allowing insight into how Dirichlet transformed the ideas into essentially modern form.

Also shown is how Gauss built on a long tradition in number theory--going back to Diophantus--and how it set the agenda for Dirichlet's work. This important book combines historical perspective with transcendent mathematical insight. The material is still fresh and presented in a very readable fashion.

This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, "Sources", are classical mathematical works that served as cornerstones for modern mathematical thought. (For another historical translation by Professor Stillwell, see Sources of Hyperbolic Geometry, Volume 10 in the History of Mathematics series.)

Readership

Graduate students and research mathematicians interested in number theory; mathematical historians.

Reviews

"A new edition of Dirichlet's Lectures on Number Theory would be big news any day, but it's particularly gratifying to see the book appear as "the first of an informal sequence" which is to include "classical mathematical works that served as cornerstones for modern mathematical thought." So all power to the American Mathematical Society and the London Mathematical Society in their joint-venture History of Mathematics series: may the "Sources" subseries live long and prosper. [T]his is quite accessible, and could almost be used as a textbook still today. For those who like to heed Abel's admonition to "read the masters, not their students," here's a great opportunity to learn more about Number Theory."

-- MAA Online

"This is a nice English edition of Dirichlet's famous Vorlesungen über Zahlentheorie, including the nine Supplements by Dedekind, translated by John Stillwell. As one of the most important number-theoretical books of the 19th century this book needs no further description, and can be recommended to those who have problems with the German language, or to those who cannot find the German original in the library. This book should certainly have a permanent place on every mathematical bookshelf."

-- European Mathematical Society Newsletter

Table of Contents

  • On the divisibility of numbers
  • On the congruence of numbers
  • On quadratic residues
  • On quadratic forms
  • Determination of the class number of binary quadratic forms
  • Some theorems from Gauss's theory of circle division
  • On the limiting value of an infinite series
  • A geometric theorem
  • Genera of quadratic forms
  • Power residues for composite moduli
  • Primes in arithmetic progressions
  • Some theorems from the theory of circle division
  • On the Pell equation
  • Convergence and continuity of some infinite series
  • Index
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