Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry - Hardcover

Crass, Scott

Hardcover

ISBN 10: 036756520X ISBN 13: 9780367565206

Verlag: Chapman and Hall/CRC, 2022

Inhaltsangabe

Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry.

Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry

is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems.

Features

Treats the topic—familiar to many—of solving polynomial equations in a way that’s dramatically different from what they saw in school

Accessible to a general audience with limited mathematical background

Abundant diagrams and graphics.

Über diesen Titel

Über die Autorin bzw. den Autor

Scott Crass is a professor of mathematics at California State University, Long Beach, where he created the Long Beach Project in Geometry and Symmetry. The project’s centerpiece is The Geometry Studio, where students explore math in experimental and perceptual ways. Advised by Peter Doyle, his Ph.D. thesis at UCSD was ‘Solving the Sextic by Iteration: A Complex Dynamical Approach’. His research interests involve blending the algebra and geometry induced by finite group actions on complex spaces, in an effort to discover and study symmetrical structures and associated dynamical systems. A prominent feature of his work involves using maps with symmetry in order to construct elegant algorithms that home in on a polynomial’s roots.

Von der hinteren Coverseite

This book is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes.

Details zur Ausgabe

• Verlag: Chapman and Hall/CRC
• Erscheinungsdatum: 2022
• Sprache: Englisch
• ISBN 10: 036756520X
• ISBN 13: 9780367565206
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 169
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland