Items related to Abstract Algebra and Famous Impossibilities: Squaring...
Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations (Undergraduate Texts in Mathematics) - Softcover
- PublisherSpringer
- Publication date2023
- ISBN 10 3031057007
- ISBN 13 9783031057007
- BindingPaperback
- Edition number2
- Number of pages240
Buy New
Learn more about this copy
US$ 71.62
Shipping:
US$ 24.91
From Germany to U.S.A.
Top Search Results from the AbeBooks Marketplace
Seller Image
Abstract Algebra and Famous Impossibilities
Published by
Berlin Springer International Publishing Springer
(2023)
ISBN 10: 3031057007
ISBN 13: 9783031057007
New
Taschenbuch
Quantity: 2
Seller:
Rating
Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel's original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus. 218 pp. Englisch. Seller Inventory # 9783031057007
Buy New
US$ 71.62
Convert currency
Seller Image
Abstract Algebra and Famous Impossibilities : Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations
Published by
Springer International Publishing
(2023)
ISBN 10: 3031057007
ISBN 13: 9783031057007
New
Taschenbuch
Quantity: 1
Seller:
Rating
Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel's original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus. Seller Inventory # 9783031057007
Buy New
US$ 71.62
Convert currency
Seller Image
Abstract Algebra and Famous Impossibilities
Published by
Springer International Publishing
(2023)
ISBN 10: 3031057007
ISBN 13: 9783031057007
New
Softcover
Quantity: > 20
Seller:
Rating
Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Motivates the development of algebraic concepts through tantalizing geometric questions from historyIllustrates the power of algebraic abstraction for tackling concrete questionsEngages the reader with abundant examples, commentary, and exe. Seller Inventory # 1228908930
Buy New
US$ 62.23
Convert currency