Lectures On The Icosahedron And The Solution Of The Fifth Degree
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Lectures On The Icosahedron And The Solution Of The Fifth Degree
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Author : Felix Klein
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-01-01
Lectures On The Icosahedron And The Solution Of The Fifth Degree written by Felix Klein and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
In this classic of mathematical literature, first published in 1884, Felix Klein elegantly demonstrates how the rotation of icosahedron can be used to solve complex quintic equations. Divided into two parts-"Theory of the Icosahedron" and "The Theory of Equations of the Fifth Degree"-The Icosahedron covers: . the regular solids and the theory of groups . introduction of (x + iy) . statement and discussion of the fundamental problem, according to the theory of functions . the algebraical character of the fundamental problem . general theorems and survey of the subject . the historical development of the theory of equations of the fifth degree . introduction of geometrical material . the canonical equations of the fifth degree . the problem of the A's and the Jacobian equations of the sixth degree . the general equation of the fifth degree Complete with detailed equations and instructive material, The Icosahedron will be valued by experts in higher mathematics and students of algebra alike. German mathematician FELIX KLEIN (1849-1925) specialized in function theory, group theory, and non-Euclidean geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis; Elementary Mathematics from an Advanced Standpoint: Geometry; and Famous Problems of Elementary Geometry.
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree
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Author : Felix Klein
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree written by Felix Klein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This well-known work covers the solution of quintics in terms of the rotations of a regular icosahedron around the axes of its symmetry. Its two-part presentation begins with discussions of the theory of the icosahedron itself; regular solids and theory of groups; introductions of (x + iy); a statement and examination of the fundamental problem, with a view of its algebraic character; and general theorems and a survey of the subject. The second part explores the theory of equations of the fifth degree and their historical development; introduces geometrical material; and covers canonical equations of the fifth degree, the problem of A's and Jacobian equations of the sixth degree, and the general equation of the fifth degree. Second revised edition with additional corrections.
Lectures On The Ikosahedron And The Solution Of Equations Of The Fifth Degree
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Author : Felix Klein
language : en
Publisher:
Release Date : 1888
Lectures On The Ikosahedron And The Solution Of Equations Of The Fifth Degree written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1888 with Icosahedra categories.
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree
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Author : Felix 1849-1925 Klein
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-09
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree written by Felix 1849-1925 Klein and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree
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Author : Felix Klein
language : en
Publisher:
Release Date : 2019
Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Quintic equations categories.
Combinatorics
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Author : M. Hall Jr.
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorics written by M. Hall Jr. and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Combinatorics has come of age. It had its beginnings in a number of puzzles which have still not lost their charm. Among these are EULER'S problem of the 36 officers and the KONIGSBERG bridge problem, BACHET's problem of the weights, and the Reverend T.P. KIRKMAN'S problem of the schoolgirls. Many of the topics treated in ROUSE BALL'S Recreational Mathe matics belong to combinatorial theory. All of this has now changed. The solution of the puzzles has led to a large and sophisticated theory with many complex ramifications. And it seems probable that the four color problem will only be solved in terms of as yet undiscovered deep results in graph theory. Combinatorics and the theory of numbers have much in common. In both theories there are many prob lems which are easy to state in terms understandable by the layman, but whose solution depends on complicated and abstruse methods. And there are now interconnections between these theories in terms of which each enriches the other. Combinatorics includes a diversity of topics which do however have interrelations in superficially unexpected ways. The instructional lectures included in these proceedings have been divided into six major areas: 1. Theory of designs; 2. Graph theory; 3. Combinatorial group theory; 4. Finite geometry; 5. Foundations, partitions and combinatorial geometry; 6. Coding theory. They are designed to give an overview of the classical foundations of the subjects treated and also some indication of the present frontiers of research.
From Spinors To Quantum Mechanics
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Author : Gerrit Coddens
language : en
Publisher: World Scientific
Release Date : 2015-06-29
From Spinors To Quantum Mechanics written by Gerrit Coddens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-29 with Science categories.
From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics.In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.
Finite M Bius Groups Minimal Immersions Of Spheres And Moduli
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Author : Gabor Toth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite M Bius Groups Minimal Immersions Of Spheres And Moduli written by Gabor Toth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich interconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including Takahashi's 1966 proof regarding the existence of isometric minimal immersions, DoCarmo and Wallach's study of the uniqueness of the standard minimal immersion in the seventies, and more recently, he examines the variety of spherical minimal immersions which have been obtained by the "equivariant construction" as SU(2)-orbits, first used by Mashimo in 1984 and then later by DeTurck and Ziller in 1992. In trying to make this monograph accessible not just to research mathematicians but mathematics graduate students as well, the author included sizeable pieces of material from upper level undergraduate courses, additional graduate level topics such as Felix Klein's classic treatise of the icosahedron, and a valuable selection of exercises at the end of each chapter.
Singularities Part 2
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Author : Peter Orlik
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Singularities Part 2 written by Peter Orlik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This work presents the written versions of all but three of the invited talks presented at this Symposium. It contains 2 papers by invited speakers who aren't able to attend.
A Tribute To C S Seshadri
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Author : Venkatrama Lakshmibai
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-24
A Tribute To C S Seshadri written by Venkatrama Lakshmibai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.
C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.