Beyond the Quartic Equation

Beyond the Quartic Equation

by R. Bruce King
     
 

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

Editorial Reviews

From the Publisher

From the reviews:

"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)

Product Details

ISBN-13:
9780817648367
Publisher:
Birkhauser Verlag
Publication date:
11/21/2008
Series:
Modern Birkhauser Classics Series
Edition description:
1st ed. 1996. 2nd printing 2008
Pages:
150
Product dimensions:
6.00(w) x 9.10(h) x 0.50(d)

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >