Lectures On The Icosahedron And The Solution Of Equations Of The Fifth Degree
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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 Icosahedron And The Solution Of The Fifth Degree
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Author : Felix Klein
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-12-01
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 2007-12-01 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 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.
Galois Theory
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Author : David A. Cox
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-27
Galois Theory written by David A. Cox and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-27 with Mathematics categories.
Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of prime or prime-squared degree Abel's theorem about geometric constructions on the lemniscates Galois groups of quartic polynomials in all characteristics Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study. Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.
Trends In Singularities
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Author : Anatoly Libgober
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Trends In Singularities written by Anatoly Libgober and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.
Automorphic Forms And Representations
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Author : Daniel Bump
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28
Automorphic Forms And Representations written by Daniel Bump and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.
This book takes advanced graduate students from the foundations to topics on the research frontier.
On The Topology Of Isolated Singularities In Analytic Spaces
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Author : José Seade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
On The Topology Of Isolated Singularities In Analytic Spaces written by José Seade 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 2006-03-21 with Mathematics categories.
Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.
Felix Klein
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Author : David E. Rowe
language : en
Publisher: Springer Nature
Release Date : 2025-05-29
Felix Klein written by David E. Rowe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.
This book presents a historical account of Felix Klein's "Comparative Reflections on Recent Research in Geometry" (1872), better known as his "Erlangen Program.” Originally conceived and written when Klein was collaborating with Sophus Lie, this bold essay initially made little impression on contemporary researchers. Decades later, however, it eventually became a famous classic. Eminent mathematicians hailed Klein’s main message – the role of invariants of transformation groups in geometry – as presaging major developments in mathematics and physics. The first part of this book focuses on the prehistory surrounding Klein’s “Erlangen Program,” stressing the motivations that led Klein to write it. The core of the book (Part II) then presents a new translation of Klein's original text, followed by detailed textual analysis aimed at guiding the reader through its rather terse and opaque prose. Part III deals with its complicated reception history, treated in four periods spanning the years from 1872 to 1930. This culminated during Klein’s lifetime with his efforts to promote the "Erlangen Program” as a framework for interpreting Einstein’s theory of relativity. After his death in 1925, the viability of this framework became a contentious issue among leading differential geometers. Part IV looks back on the transformations in mathematics that led to a modernized interpretation of Klein’s message. The book also explores in depth how the growing fame of the “Erlangen Program” undermined Klein’s friendship with Sophus Lie, leading to a dramatic public break between them in 1893. Beyond the "Erlangen Program” itself, this book deals with many of Felix Klein’s other works. As an introduction to a largely forgotten world of ideas, this study will appeal not only to experts but also to graduate students and all those with a serious interest in the history of modern mathematics.