58,45 €*
Versandkostenfrei per Post / DHL
Lieferzeit 2-3 Wochen
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.
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.
Sidney A. Morris is Emeritus Professor at the Federation University, Australia (formerly University of Ballarat) and Adjunct Professor at La Trobe University, Australia. His primary research is in topological groups, topology, and transcendental number theory, with broader interests including early detection of muscle wasting diseases, health informatics, and predicting the Australian stock exchange. He is the author of several books.
Arthur Jones [1934-2006] and Kenneth R. Pearson [1943-2015] were Professors in Mathematics at La Trobe University, Australia. Each had a great passion for teaching and for mathematics.
Motivates the development of algebraic concepts through tantalizing geometric questions from history
Illustrates the power of algebraic abstraction for tackling concrete questions
Engages the reader with abundant examples, commentary, and exercises
Erscheinungsjahr: | 2022 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
xxii
218 S. 29 s/w Illustr. 218 p. 29 illus. |
ISBN-13: | 9783031056970 |
ISBN-10: | 3031056973 |
Sprache: | Englisch |
Einband: | Gebunden |
Autor: |
Morris, Sidney A.
Pearson, Kenneth R. Jones, Arthur |
Auflage: | 2nd edition 2022 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 18 mm |
Von/Mit: | Sidney A. Morris (u. a.) |
Erscheinungsdatum: | 28.11.2022 |
Gewicht: | 0,573 kg |
Sidney A. Morris is Emeritus Professor at the Federation University, Australia (formerly University of Ballarat) and Adjunct Professor at La Trobe University, Australia. His primary research is in topological groups, topology, and transcendental number theory, with broader interests including early detection of muscle wasting diseases, health informatics, and predicting the Australian stock exchange. He is the author of several books.
Arthur Jones [1934-2006] and Kenneth R. Pearson [1943-2015] were Professors in Mathematics at La Trobe University, Australia. Each had a great passion for teaching and for mathematics.
Motivates the development of algebraic concepts through tantalizing geometric questions from history
Illustrates the power of algebraic abstraction for tackling concrete questions
Engages the reader with abundant examples, commentary, and exercises
Erscheinungsjahr: | 2022 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
xxii
218 S. 29 s/w Illustr. 218 p. 29 illus. |
ISBN-13: | 9783031056970 |
ISBN-10: | 3031056973 |
Sprache: | Englisch |
Einband: | Gebunden |
Autor: |
Morris, Sidney A.
Pearson, Kenneth R. Jones, Arthur |
Auflage: | 2nd edition 2022 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 18 mm |
Von/Mit: | Sidney A. Morris (u. a.) |
Erscheinungsdatum: | 28.11.2022 |
Gewicht: | 0,573 kg |