Beyond the Quartic Equation / Edition 1

Beyond the Quartic Equation / Edition 1

by R. Bruce King
     
 

ISBN-10: 0817637761

ISBN-13: 9780817637767

Pub. Date: 07/30/1996

Publisher: Birkhauser Verlag

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

Overview

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

Product Details

ISBN-13:
9780817637767
Publisher:
Birkhauser Verlag
Publication date:
07/30/1996
Edition description:
1996
Pages:
150
Product dimensions:
9.21(w) x 6.14(h) x 0.50(d)

Table of Contents

Preface.- Introduction.- 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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