Geometry of the Quintic 1st Edition by Jerry Shurman (PDF)

Description

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

User’s Reviews

Editorial Reviews: From the Publisher 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. From the Back Cover 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 generatorGives, in the case of the icosahedral group, an elegant presentation of the relevant icosahedral geometry and its relation to the Brioschi quinticReduces the general quintic to Brioschi form by radicalsProves Kronecker’s theorem that an “auxiliary” square root is necessary for any such reductionExpounds Doyle and McMullen’s development of an iterative solution to the quinticProvides a wealth of exercises and illustrations to clarify the geometry of the quintic 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐the author simply has no idea how to relate to his audience –everything crammed together — most of the work left to”exercises” with no solutions of course — lightly editedif at all ………..it’s free now but still overpriced

⭐

Keywords

Free Download Geometry of the Quintic 1st Edition in PDF format
Geometry of the Quintic 1st Edition PDF Free Download
Download Geometry of the Quintic 1st Edition 1997 PDF Free
Geometry of the Quintic 1st Edition 1997 PDF Free Download
Download Geometry of the Quintic 1st Edition PDF
Free Download Ebook Geometry of the Quintic 1st Edition