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Variations On A Theme Of Euler
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Variations On A Theme Of Euler - neues Buch

ISBN: 9780306447891

ID: 5895019

The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers. The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e, the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, Variations On A Theme Of Euler~~Book~~9780306447891~~Takashi Ono, , , , , , , , , ,, [PU: Consultants Bureau, and Kluwer Academic (NY)]

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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps - Takashi Ono
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Takashi Ono:

Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps - gebrauchtes Buch

ISBN: 9780306447891

ID: 9780306447891

In this first-of-its-kind book, Professor Ono postulates that one aspect of classical and modern number theory, including quadratic forms and space elliptic curves as intersections of quadratic surfaces, can be considered as the number theory of Hopf maps. The text, a translation of Dr. Ono's earlier work, provides a solution to this problem by employing three areas of mathematics: linear algebra, algebraic geometry, and simple algebras. This English language edition presents a new chapter on In this first-of-its-kind book, Professor Ono postulates that one aspect of classical and modern number theory, including quadratic forms and space elliptic curves as intersections of quadratic surfaces, can be considered as the number theory of Hopf maps. The text, a translation of Dr. Ono's earlier work, provides a solution to this problem by employing three areas of mathematics: linear algebra, algebraic geometry, and simple algebras. This English language edition presents a new chapter on arithmetic of quadratic maps, along with an appendix featuring a short survey of subsequent research on congruent numbers by Masanari Kida. The original appendix containing historical and scientific comments on Euler's Elements of Algebra is also included. Variations on a Theme of Euler is an important reference for researchers and an excellent text for a graduate-level course on number theory. Textbooks New, Books~~Mathematics~~Number Theory, Variations-on-a-Theme-of-Euler~~Takashi-Ono, 999999999, Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps, Takashi Ono, 0306447894, Springer US, , , , , Springer US

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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps (Hardback) - Takashi Ono
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Takashi Ono:
Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps (Hardback) - gebunden oder broschiert

1994

ISBN: 0306447894

ID: 11221191713

[EAN: 9780306447891], Neubuch, [PU: Kluwer Academic Publishers Group, Netherlands], Language: English Brand New Book ***** Print on Demand *****. The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps (Hardback) - Takashi Ono
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Takashi Ono:
Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves, and Hopf Maps (Hardback) - gebunden oder broschiert

1994, ISBN: 0306447894

ID: 3119707693

[EAN: 9780306447891], Neubuch, [PU: Kluwer Academic Publishers Group, Netherlands], Language: English Brand New Book ***** Print on Demand *****.The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

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Variations on a Theme of Euler - Takashi Ono
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Takashi Ono:
Variations on a Theme of Euler - gebunden oder broschiert

1994, ISBN: 9780306447891

ID: 2289258

Hardcover, Buch, [PU: Kluwer Academic / Plenum Publishers]

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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves and Hopf Maps
Autor:

Ono, Takashi

Titel:

Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves and Hopf Maps

ISBN-Nummer:

0306447894

From a review of the Japanese-language edition: A beautifully written book...The statement of the problem is very clear-that is, [the author] claims that one aspect of classical and modern number theory can be considered as the number theory of Hopf maps-and then he solves this problem....skillfully and perspectively organized...This book will be a good introductory textbook...There has never been a textbook similar to this....I highly recommend this book.' Michio Kuga, Professor, late of State University of New York at Stony Brook

Detailangaben zum Buch - Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves and Hopf Maps


EAN (ISBN-13): 9780306447891
ISBN (ISBN-10): 0306447894
Gebundene Ausgabe
Erscheinungsjahr: 1994
Herausgeber: Springer-Verlag GmbH
364 Seiten
Gewicht: 0,665 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 05.06.2007 23:44:14
Buch zuletzt gefunden am 29.10.2015 14:39:34
ISBN/EAN: 0306447894

ISBN - alternative Schreibweisen:
0-306-44789-4, 978-0-306-44789-1

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