A Classical Introduction To Galois Theory
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A Classical Introduction To Galois Theory
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Author : Stephen C. Newman
language : en
Publisher: John Wiley & Sons
Release Date : 2012-05-29
A Classical Introduction To Galois Theory written by Stephen C. Newman 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 2012-05-29 with Mathematics categories.
Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions. The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through: A study of the solvability of polynomials of prime degree Development of the theory of periods of roots of unity Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic. A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.
Classical Galois Theory With Examples
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Author : Lisl Gaal
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Classical Galois Theory With Examples written by Lisl Gaal 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 1998 with Mathematics categories.
Galois theory is one of the most beautiful subjects in mathematics, but it is heard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout the text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is intended for beginning graduate students who already have some background in algebra, including some elementary theoryof groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity. The book is for students and intends to make them take an active part in mathematics rather than merely read, nod their heads atappropriate places, skip the exercises, and continue on to the next section.
A Classical Introduction To Modern Number Theory
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Author : Kenneth Ireland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Classical Introduction To Modern Number Theory written by Kenneth Ireland 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 2013-04-17 with Mathematics categories.
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
Galois Theory Through Exercises
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Author : Juliusz Brzeziński
language : en
Publisher: Springer
Release Date : 2018-03-21
Galois Theory Through Exercises written by Juliusz Brzeziński and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Galois Theory Of Linear Differential Equations
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Author : Marius van der Put
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Galois Theory Of Linear Differential Equations written by Marius van der Put 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.
Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.
Galois Theory For Beginners
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Galois Theory For Beginners written by Jörg Bewersdorff 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 2006 with Mathematics categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.
Galois Theory Coverings And Riemann Surfaces
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Author : Askold Khovanskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-11
Galois Theory Coverings And Riemann Surfaces written by Askold Khovanskii 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 2013-09-11 with Mathematics categories.
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.
Field Extensions And Galois Theory
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Author : Julio R. Bastida
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28
Field Extensions And Galois Theory written by Julio R. Bastida 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 1984-12-28 with Mathematics categories.
This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.
Fields And Galois Theory
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Author : John M. Howie
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-11
Fields And Galois Theory written by John M. Howie 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 2007-10-11 with Mathematics categories.
A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
Galois Theory
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Author : Steven H. Weintraub
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Galois Theory written by Steven H. Weintraub 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 2008-10-20 with Mathematics categories.
Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.