R. Bruce King: Beyond the Quartic Equation

Cover: 9780817648367 | Beyond the Quartic Equation | R. Bruce King | Taschenbuch | Paperback

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Beschreibung

One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general al- braic equations of degrees higher than four. This proof by the French mathema- cian Evariste Galois in the early nineteenth century used the then novel concept of the permutation symmetry of the roots of algebraic equations and led to the invention of group theory, an area of mathematics now nearly two centuries old that has had extensive applications in the physical sciences in recent decades. The radical-based algorithms for solutions of general algebraic equations of degrees 2 (quadratic equations), 3 (cubic equations), and 4 (quartic equations) have been well-known for a number of centuries. The quadratic equation algorithm uses a single square root, the cubic equation algorithm uses a square root inside a cube root, and the quartic equation algorithm combines the cubic and quadratic equation algorithms with no new features. The details of the formulas for these equations of degree d(d = 2,3,4) relate to the properties of the corresponding symmetric groups Sd which are isomorphic to the symmetries of the equilateral triangle for d = 3 and the regular tetrahedron for d ¿ 4.

Zusammenfassung

An affordable softcover edition of a classic text

Complete algorithm for roots of the general quintic equation

Key ideas accessible to non-specialists

Indroductory chapter covers group theory and symmetry, Galois theory, Tschirnhausen transformations, and some elementary properties of an elliptic function

Discussion of algorithms for roots of general equation of degrees higher than five

Includes supplementary material: [...]

Inhaltsverzeichnis

Group Theory and Symmetry.- The Symmetry of Equations: Galois Theory and Tschirnhausen Transformations.- Elliptic Functions.- Algebraic Equations Soluble by Radicals.- The Kiepert Algorithm for Roots of the General Quintic Equation.- The Methods of Hermite and Gordan for Solving the General Quintic Equation.- Beyond the Quintic Equation.

Details

Erscheinungsjahr:	2008
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Modern Birkhäuser Classics
Inhalt:	viii 150 S. 16 s/w Illustr. 150 p. 16 illus.
ISBN-13:	9780817648367
ISBN-10:	0817648364
Sprache:	Englisch
Herstellernummer:	12532490
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	King, R. Bruce
Auflage:	1st ed. 1996. 2nd printing 2008
Hersteller:	Birkhuser Boston Birkhäuser Boston Modern Birkhäuser Classics
Maße:	235 x 155 x 9 mm
Von/Mit:	R. Bruce King
Erscheinungsdatum:	13.11.2008
Gewicht:	0,254 kg

Artikel-ID: 101744675