Articoli correlati a Beyond the Quartic Equation
The objective of this book is to present for the first time the complete algorithm for roots of the general quintic equation with enough background information to make the key ideas accessible to non-specialists and even to mathematically oriented readers who are not professional mathematicians. The book includes an initial introductory chapter on group theory and symmetry, Galois theory and Tschirnhausen transformations, and some elementary properties of elliptic function in order to make some of the key ideas more accessible to less sophisticated readers. The book also includes a discussion of the much simpler algorithms for roots of the general quadratic, cubic, and quartic equations before discussing the algorithm for the roots of the general quintic equation. A brief discussion of algorithms for roots of general equations of degrees higher than five is also included.
"If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations."
--New Scientist
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"If you want something truly unusual, try [this book] by R. Bruce King, which revives some fascinating, long-lost ideas relating elliptic functions to polynomial equations." --New Scientist
This book presents for the first time a complete algorithm for finding the zeros of any quintic equation based on the ideas of Kiepert. For the sake of completeness, there are chapters on group theory and symmetry, the theory of Galois and elliptic functions. The book ends with considerations on higher degree polynomial equations. --Numerical Algorithms Journal
“The idea of the book at hand is the development of a practicable algorithm to solve quintic equations by means of elliptic and theta functions. ... the book can be recommended to anyone interested in the solution of quintic equations.” (Helmut Koch, Zentralblatt MATH, Vol. 1177, 2010)
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.
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- EditoreBirkhauser
- Data di pubblicazione2008
- ISBN 10 0817648364
- ISBN 13 9780817648367
- RilegaturaCopertina flessibile
- Numero di pagine149
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Beyond the Quartic Equation (Modern Birkhà ¤user Classics) by King, R. Bruce [Paperback ]
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Beyond the Quartic Equation
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ISBN 13: 9780817648367
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Descrizione libro Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 160 pp. Englisch. Codice articolo 9780817648367
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Descrizione libro Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. An affordable softcover edition of a classic textComplete algorithm for roots of the general quintic equationKey ideas accessible to non-specialistsIndroductory chapter covers group theory and symmetry, Galois theory, Tschirnhausen t. Codice articolo 5975908
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Beyond the Quartic Equation
Editore:
Birkhäuser Boston
(2008)
ISBN 10: 0817648364
ISBN 13: 9780817648367
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Taschenbuch
Quantità: 1
Da:
Valutazione libreria
Descrizione libro Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9780817648367
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