Items related to Geometry of the Quintic
Synopsis
This book offers a stimulating exposition of Felix Klein's proof of Kronecker's Theorem and his classical development of icosahedral geometry to solve the quintic equation. It also synthesizes Klein's ideas with dynamics to solve the quintic by iteration in text form.
"synopsis" may belong to another edition of this title.
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.
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 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
"About this title" may belong to another edition of this title.
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Geometry of the Quintic
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Geometry of the Quintic
Published by
Wiley-Interscience / John Wiley & Sons, Inc., 1997
ISBN 10: 0471130176
ISBN 13: 9780471130178
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Geometry of the Quintic
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Geometry of the Quintic
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GEOMETRY OF THE QUINTIC
Published by
Wiley-Interscience Publication, New York, 1997
ISBN 10: 0471130176
ISBN 13: 9780471130178
Used
Softcover
First Edition
Seller: Second Story Books, ABAA, Rockville, MD, U.S.A.
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Softcover. First Edition, First Printing. Octavo, xi, 200 pages. In Very Good condition. Spine is black with yellow lettering. Scuffing to covers. Minor bumping to edges of spine and covers. Minor staining to text block. Shelved in Mathematics. 1414818. Shelved Dupont Bookstore. Seller Inventory # 1414818
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Geometry of the quintic.
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Softcover. Condition: Gut. 200 S. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. 9780471130178 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2348833