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© 1996

Beyond the Quartic Equation

  • Authors
  • 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

Book

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages 1-9
  2. R. Bruce King
    Pages 1-5
  3. R. Bruce King
    Pages 1-28
  4. R. Bruce King
    Pages 1-26
  5. R. Bruce King
    Pages 1-13
  6. R. Bruce King
    Pages 1-11
  7. Back Matter
    Pages 1-1

About this book

Introduction

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

Keywords

Algebra Galois theory Mathematics Quartic Equation Tschirnhausen transformations elliptic function equation function general quintic equation group theory symmetry

Bibliographic information

  • Book Title Beyond the Quartic Equation
  • Authors R. Bruce King
  • Series Title Modern Birkhäuser Classics
  • DOI https://doi.org/10.1007/978-0-8176-4849-7
  • Copyright Information Birkhäuser Boston 1996
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3776-7
  • Softcover ISBN 978-0-8176-4836-7
  • eBook ISBN 978-0-8176-4849-7
  • Edition Number 1
  • Number of Pages VIII, 150
  • Number of Illustrations 16 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as a monograph
  • Topics Algebra
  • Buy this book on publisher's site

Reviews

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)