Modern Birkhäuser Classics

Beyond the Quartic Equation

Authors: King, R. Bruce

  • Gives the complete algorithm for roots of the general quintic equation
  • Presents key ideas accessible to non-specialists
  • Includes an introductory chapter that covers group theory and summetry, Galois theory, Tschirnhausen transformations, and some elementary properties of an elliptic function
  • Discusses algorithms for roots of general equation of degrees higher than five
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eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4849-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-0-8176-4836-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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

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)


Table of contents (8 chapters)

  • Group Theory and Symmetry

    King, R. Bruce

    Pages 1-28

  • Introduction

    King, R. Bruce

    Pages 1-5

  • Beyond the Quintic Equation

    King, R. Bruce

    Pages 1-11

  • The Methods of Hermite and Gordan for Solving the General Quintic Equation

    King, R. Bruce

    Pages 1-11

  • The Symmetry of Equations: Galois Theory and Tschirnhausen Transformations

    King, R. Bruce

    Pages 1-22

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4849-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-0-8176-4836-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Beyond the Quartic Equation
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4849-7
DOI
10.1007/978-0-8176-4849-7
Softcover ISBN
978-0-8176-4836-7
Series ISSN
2197-1803
Edition Number
1
Number of Pages
VIII, 150
Number of Illustrations and Tables
16 b/w illustrations
Additional Information
Originally published as a monograph
Topics