A chance for students to apply a wide range of mathematics to an engaging problem
This book helps students at the advanced undergraduate and beginning graduate levels to develop connections between the algebra, geometry, and analysis that they know, and to better appreciate the totality of what they have learned.
The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem--solving the quintic. The problem is approached from two directions: the first is Felix Klein's nineteenth-century approach, using the icosahedron. The second approach presents recent works of Peter Doyle and Curt McMullen, which update Klein's use of transcendental functions to a solution through pure iteration.
Filling a pedagogical gap in the literature and providing a solid platform from which to address more advanced material, this meticulously written book:
* Develops the Riemann sphere and its field of functions, classifies the finite groups of its automorphisms, computes for each such group a generator of the group-invariant functions, and discusses algebraic aspects of inverting this generator
* Gives, in the case of the icosahedral group, an elegant presentation of the relevant icosahedral geometry and its relation to the Brioschi quintic
* Reduces the general quintic to Brioschi form by radicals
* Proves Kronecker's theorem that an "auxiliary" square root is necessary for any such reduction
* Expounds Doyle and McMullen's development of an iterative solution to the quintic
* Provides a wealth of exercises and illustrations to clarify the geometry of the quintic
"Sinopsis" puede pertenecer a otra edición de este libro.
A consolidation of mature mathematical subjects like geometry, linear algebra, group theory, complex analysis and Galois theory into one source, this simple, easy-to-follow text develops deep connections between seemingly unrelated areas in mathematics. It updates Felix Klein's "Lectures on the Icosahedron and Equations of the Fifth Degree", and Peter Doyle's and Curt McMullen's "Solving the quintic by iteration." It provides an active approach to learning, and presents familiar subjects in a nonredundant, forward looking fashion.About the Author:
JERRY SHURMAN received his PhD in mathematics from Princeton University in 1988 and is an Associate Professor of Mathematics at Reed College, Portland, Oregon.
"Sobre este título" puede pertenecer a otra edición de este libro.
Descripción Wiley-Interscience, 1997. Paperback. Estado de conservación: New. Nº de ref. de la librería P110471130176
Descripción Wiley-Interscience, 1997. Paperback. Estado de conservación: New. 1. Nº de ref. de la librería DADAX0471130176
Descripción Wiley-Interscience, 1997. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 471130176
Descripción Wiley-Interscience, 1997. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0471130176