Abstract Algebra and Famous Impossibilities by Arthur, Morris, Sidney A., Pearson, Kenneth R. Jones - gebrauchtes Buch

EAN (ISBN-13): 9780387976617
ISBN (ISBN-10): 0387976612
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer
204 Seiten
Gewicht: 0,313 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-11-23T21:11:16+01:00 (Berlin)
Detailseite zuletzt geändert am 2024-02-14T15:23:04+01:00 (Berlin)
ISBN/EAN: 0387976612

ISBN - alternative Schreibweisen:
0-387-97661-2, 978-0-387-97661-7
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: kenneth pearson, morris jones, arthur may
Titel des Buches: famous, algebra imp, abstract algebra

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Daten vom Verlag:

Autor/in: Arthur Jones; Sidney A. Morris; Kenneth R. Pearson
Titel: Universitext; Abstract Algebra and Famous Impossibilities
Verlag: Springer; Springer US
189 Seiten
Erscheinungsjahr: 1993-12-14
New York; NY; US
Gewicht: 0,650 kg
Sprache: Englisch
58,84 € (DE)
60,49 € (AT)
65,00 CHF (CH)
Not available, publisher indicates OP
X, 189 p.

BC; Book; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Zahlentheorie; Verstehen; Finite; Irreducibility; PostScript; Vector space; algebra; algorithms; boundary element method; construction; form; integral; integration; polynomial; proof; proving; ring; B; Number Theory; Number Theory; Mathematics and Statistics; EA; BB

0.1 Three Famous Problems.- 0.2 Straightedge and Compass Constructions.- 0.3 Impossibility of the Constructions.- 1 Algebraic Preliminaries.- 1.1 Fields, Rings and Vector Spaces.- 1.2 Polynomials.- 1.3 The Division Algorithm.- 1.4 The Rational Roots Test.- Appendix to Chapter 1.- 2 Algebraic Numbers and Their Polynomials.- 2.1 Algebraic Numbers.- 2.2 Monic Polynomials.- 2.3 Monic Polynomials of Least Degree.- 3 Extending Fields.- 3.1 An Illustration: $$\\mathbb{Q}(\\sqrt 2 )$$.- 3.2 Construction of $$\\mathbb{F}(\\alpha )$$.- 3.3 Iterating the Construction.- 3.4 Towers of Fields.- 4 Irreducible Polynomials.- 4.1 Irreducible Polynomials.- 4.2 Reducible Polynomials and Zeros.- 4.3 Irreducibility and irr$$(\\alpha ,\\mathbb{F})$$.- 4.4 Finite-dimensional Extensions.- 5 Straightedge and Compass Constructions.- 5.1 Standard Straightedge and Compass Constructions.- 5.2 Products, Quotients, Square Roots.- 5.3 Rules for Straightedge and Compass Constructions.- 5.4 Constructible Numbers and Fields.- 6 Proofs of the Impossibilities.- 6.1 Non-Constructible Numbers.- 6.2 The Three Constructions are Impossible.- 6.3 Proving the “All Constructibles Come From Square Roots” Theorem.- 7 Transcendence of e and ?.- 7.1 Preliminaries.- 7.2 e is Transcendental.- 7.3 Preliminaries on Symmetric Polynomials.- 7.4 ? is Transcendental — Part 1.- 7.5 Preliminaries on Complex-valued Integrals.- 7.6 ? is Transcendental — Part 2.- 8 An Algebraic Postscript.- 8.1 The Ring $$\\mathbb{F}\\left[ X \\right]_{p(X)}$$.- 8.2 Division and Reciprocals in $$\\mathbb{F}\\left[ X \\right]_{p(X)}$$.- 8.3 Reciprocals in $$\\mathbb{F}\\left( \\alpha \\right)$$.- 9 Other Impossibilities and Abstract Algebra.- 9.1 Construction of Regular Polygons.- 9.2 Solution of Quintic Equations.- 9.3 Integration in Closed Form.