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The quadratic reciprocity law = a co...

Baumgart, Oswald.

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The quadratic reciprocity law = a collection of classical proofs /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The quadratic reciprocity law/ by Oswald Baumgart ; edited and translated by Franz Lemmermeyer.
Reminder of title:	a collection of classical proofs /
Author:	Baumgart, Oswald.
other author:	Lemmermeyer, Franz,
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xiv, 172 p. :ill., digital ;24 cm.
[NT 15003449]:	Translator's Preface -- Baumgart's Thesis -- Introduction -- First Part: 1. From Fermat to Legendre -- 2. Gauss's Proof by Mathematical Induction -- 3. Proof by Reduction -- 4. Eisenstein's Proof using Complex Analysis -- 5. Proofs using Results from Cyclotomy -- 6. Proofs based on the Theory of Quadratic Forms -- 7. The Supplementary Laws -- 8. Algorithms for Determining the Quadratic Character -- Second Part: 9. Gauss's Proof by Induction -- 10. Proofs by Reduction -- 11. Eisenstein's Proofs using Complex Analysis -- 12. Proofs using Results from Cyclotomy -- 13. Proofs based on the Theory of Quadratic Forms -- Final Comments -- Proofs of the Quadratic Reciprocity Law -- Author Index -- Subject Index.
Contained By:	Springer eBooks
Subject:	Algebraic number theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-16283-6
ISBN:	9783319162836 (electronic bk.)

The quadratic reciprocity law = a collection of classical proofs /
Baumgart, Oswald.

The quadratic reciprocity lawa collection of classical proofs /[electronic resource] :by Oswald Baumgart ; edited and translated by Franz Lemmermeyer. - Cham :Springer International Publishing :2015. - xiv, 172 p. :ill., digital ;24 cm.

Translator's Preface -- Baumgart's Thesis -- Introduction -- First Part: 1. From Fermat to Legendre -- 2. Gauss's Proof by Mathematical Induction -- 3. Proof by Reduction -- 4. Eisenstein's Proof using Complex Analysis -- 5. Proofs using Results from Cyclotomy -- 6. Proofs based on the Theory of Quadratic Forms -- 7. The Supplementary Laws -- 8. Algorithms for Determining the Quadratic Character -- Second Part: 9. Gauss's Proof by Induction -- 10. Proofs by Reduction -- 11. Eisenstein's Proofs using Complex Analysis -- 12. Proofs using Results from Cyclotomy -- 13. Proofs based on the Theory of Quadratic Forms -- Final Comments -- Proofs of the Quadratic Reciprocity Law -- Author Index -- Subject Index.

This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Uber das quadratische Reciprocitatsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

ISBN: 9783319162836 (electronic bk.)

Standard No.: 10.1007/978-3-319-16283-6doiSubjects--Topical Terms:

532574
Algebraic number theory.

LC Class. No.: QA242

Dewey Class. No.: 512.74

The quadratic reciprocity law = a collection of classical proofs /
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245 1 4 $a The quadratic reciprocity law $h [electronic resource] : $b a collection of classical proofs / $c by Oswald Baumgart ; edited and translated by Franz Lemmermeyer.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a xiv, 172 p. : $b ill., digital ; $c 24 cm.
505 0 $a Translator's Preface -- Baumgart's Thesis -- Introduction -- First Part: 1. From Fermat to Legendre -- 2. Gauss's Proof by Mathematical Induction -- 3. Proof by Reduction -- 4. Eisenstein's Proof using Complex Analysis -- 5. Proofs using Results from Cyclotomy -- 6. Proofs based on the Theory of Quadratic Forms -- 7. The Supplementary Laws -- 8. Algorithms for Determining the Quadratic Character -- Second Part: 9. Gauss's Proof by Induction -- 10. Proofs by Reduction -- 11. Eisenstein's Proofs using Complex Analysis -- 12. Proofs using Results from Cyclotomy -- 13. Proofs based on the Theory of Quadratic Forms -- Final Comments -- Proofs of the Quadratic Reciprocity Law -- Author Index -- Subject Index.
520 $a This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Uber das quadratische Reciprocitatsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
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700 1 $a Lemmermeyer, Franz, $3 2153487
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