國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

The quadratic reciprocity lawa colle...

Baumgart, Oswald.

The quadratic reciprocity lawa collection of classical proofs /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The quadratic reciprocity lawby Oswald Baumgart ; edited and translated by Franz Lemmermeyer.
其他題名:	a collection of classical proofs /
作者:	Baumgart, Oswald.
其他作者:	Lemmermeyer, Franz,
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xiv, 172 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Algebraic number theory.
電子資源:	http://dx.doi.org/10.1007/978-3-319-16283-6
ISBN:	9783319162836 (electronic bk.)

The quadratic reciprocity lawa 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:

190879
Algebraic number theory.

LC Class. No.: QA242

Dewey Class. No.: 512.74

The quadratic reciprocity lawa collection of classical proofs /
LDR:02538nmm a2200325 a 4500 001 469185
003 DE-He213
005 20160105134903.0
006 m d
007 cr nn 008maaau
008 160118s2015 gw s 0 eng d
020 $a 9783319162836 (electronic bk.)
020 $a 9783319162829 (paper)
024 7 $a 10.1007/978-3-319-16283-6 $2 doi
035 $a 978-3-319-16283-6
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA242
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 512.74 $2 23
090 $a QA242 $b .B348 2015
100 1 $a Baumgart, Oswald. $3 725086
240 1 0 $a Uber das quadratische Reciprocitatsgesetz. $l English
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.
650 0 $a Algebraic number theory. $3 190879
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Number Theory. $3 274059
700 1 $a Lemmermeyer, Franz, $3 725087
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-16283-6
950 $a Mathematics and Statistics (Springer-11649)