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The Quadratic Reciprocity Law: A Collection of Classical Proofs
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. 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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The Quadratic Reciprocity Law: A Collection of Classical Proofs
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. 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.

119.99 In Stock
The Quadratic Reciprocity Law: A Collection of Classical Proofs

The Quadratic Reciprocity Law: A Collection of Classical Proofs

The Quadratic Reciprocity Law: A Collection of Classical Proofs

The Quadratic Reciprocity Law: A Collection of Classical Proofs

Overview

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. 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.

Product Details

ISBN-13: 9783319162829
Publisher: Springer International Publishing
Publication date: 05/28/2015
Edition description: 2015
Pages: 172
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

About the Author

Franz Lemmermeyer received his Ph.D. from Heidelberg University and has worked at Universities in California and Turkey. He is now teaching mathematics at the Gymnasium St. Gertrudis in Ellwangen, Germany.

Table of Contents

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.
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