Foundations Of Galois Theory PDF Download
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Author | : M.M. Postnikov |
Publisher | : Elsevier |
Total Pages | : 123 |
Release | : 2014-07-10 |
Genre | : Mathematics |
ISBN | : 1483156478 |
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Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.
Author | : Michail M. Postnikov |
Publisher | : |
Total Pages | : 109 |
Release | : 1995 |
Genre | : |
ISBN | : |
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Author | : Mikhail Mikhaĭlovich Postnikov |
Publisher | : Pergamon |
Total Pages | : 0 |
Release | : 1962 |
Genre | : Galois theory |
ISBN | : 9780080096865 |
Download Foundations of Galois Theory Book in PDF, ePub and Kindle
Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of important types of extensions and the field of algebraic numbers. A consideration of relevant facts from group theory leads to a survey of Galois theory, with discussions of normal extensions, the order and correspondence of the Galois group, and Galois groups of a normal subfield and of two fields. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n [greater than or equal] 5. Book jacket.
Author | : Mikhail Mikhailovich Postnikov |
Publisher | : |
Total Pages | : 0 |
Release | : 1962 |
Genre | : Teoría de Galois |
ISBN | : |
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Author | : Stephen C. Newman |
Publisher | : John Wiley & Sons |
Total Pages | : 296 |
Release | : 2012-05-29 |
Genre | : Mathematics |
ISBN | : 1118336844 |
Download A Classical Introduction to Galois Theory Book in PDF, ePub and Kindle
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.
Author | : Emil Artin |
Publisher | : |
Total Pages | : 54 |
Release | : 2020-02 |
Genre | : Education |
ISBN | : 9781950217021 |
Download Galois Theory Book in PDF, ePub and Kindle
The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Author | : John Swallow |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 2004-10-11 |
Genre | : Computers |
ISBN | : 9780521544993 |
Download Exploratory Galois Theory Book in PDF, ePub and Kindle
Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.
Author | : John M. Howie |
Publisher | : Springer Science & Business Media |
Total Pages | : 230 |
Release | : 2007-10-11 |
Genre | : Mathematics |
ISBN | : 1852339861 |
Download Fields and Galois Theory Book in PDF, ePub and Kindle
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
Author | : Tamás Szamuely |
Publisher | : Cambridge University Press |
Total Pages | : 281 |
Release | : 2009-07-16 |
Genre | : Mathematics |
ISBN | : 0521888506 |
Download Galois Groups and Fundamental Groups Book in PDF, ePub and Kindle
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author | : Marius van der Put |
Publisher | : Springer |
Total Pages | : 182 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 354069241X |
Download Galois Theory of Difference Equations Book in PDF, ePub and Kindle
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.