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# ðŸ“™ Geometry of the Quintic by Jerry Shurman â€” free epub

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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 problemâ€”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 book:

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- Author:
**Jerry Shurman** - Year:
**1997** - Language:
**English** - ISBN:
**0471130176,9780471130178**

- DPI:
**400** - File size:
**2 940 132** - Format:
**djvu**

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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, ...

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challeng...

Focuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and...

This volume contains the proceedings of the NSF-CBMS Regional Conference on Algebraic Geometry, held in Sundance, Utah, in July 1988. The conference focused on algebraic curves and related varieties. Some of the papers collected here represent lecture...

This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between...

This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral wei...

This work covers the proceedings of the NSF-CBMS Conference on 'Spectral Problems in Geometry and Arithmetic' held at the University of Iowa. The principal speaker was Peter Sarnak, who has been a central contributor to developments in this field. The vol...

This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in t...

This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen wit...