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  1. Bog
  2. Matematik
  3. Algebra

A History of Abstract Algebra

- From Algebraic Equations to Modern Algebra
Af: Jeremy Gray Engelsk Paperback

A History of Abstract Algebra

- From Algebraic Equations to Modern Algebra
Af: Jeremy Gray Engelsk Paperback
Tjek vores konkurrenters priser

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.

Beginning with Gauss''s theory of numbers and Galois''s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat''s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois''s approach to the solution of equations. The book also describes the relationship between Kummer''s ideal numbers and Dedekind''s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer''s.

Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

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Tjek vores konkurrenters priser

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.

Beginning with Gauss''s theory of numbers and Galois''s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat''s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois''s approach to the solution of equations. The book also describes the relationship between Kummer''s ideal numbers and Dedekind''s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer''s.

Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

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Produktdetaljer
Sprog: Engelsk
Sider: 415
ISBN-13: 9783319947723
Indbinding: Paperback
Udgave:
ISBN-10: 3319947729
Kategori: Algebra
Udg. Dato: 16 aug 2018
Længde: 25mm
Bredde: 152mm
Højde: 217mm
Forlag: Springer International Publishing AG
Oplagsdato: 16 aug 2018
Forfatter(e): Jeremy Gray
Forfatter(e) Jeremy Gray

Kategori Algebra

ISBN-13 9783319947723

Sprog Engelsk

Indbinding Paperback

Sider 415

Udgave

Længde 25mm

Bredde 152mm

Højde 217mm

Udg. Dato 16 aug 2018

Oplagsdato 16 aug 2018

Forlag Springer International Publishing AG

Kategori sammenhænge