A Newman, Stephen C. 1952- creator text bibliography Electronic books. nju Hoboken, N.J Wiley 2012 monographic eng

electronic resource

1 online resource. "This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given field), does a solution in terms of radicals exist? That the need to investigate the very existence of a solution is perhaps surprising and invites an overview of the history of mathematics. The classical material within the book includes theorems on polynomials, fields, and groups due to such luminaries as Gauss, Kronecker, Lagrange, Ruffini and, of course, Galois. These results figured prominently in earlier expositions of Galois theory, but seem to have gone out of fashion. This is unfortunate since, aside from being of intrinsic mathematical interest, such material provides powerful motivation for the more modern treatment of Galois theory presented later in the book. Over the course of the book, three versions of the Impossibility Theorem are presented: the first relies entirely on polynomials and fields, the second incorporates a limited amount of group theory, and the third takes full advantage of modern Galois theory. This progression through methods that involve more and more group theory characterizes the first part of the book. The latter part of the book is devoted to topics that illustrate the power of Galois theory as a computational tool, but once again in the context of solvability of polynomial equations by radicals"-- A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials. Stephen C. Newman. Includes bibliographical references and index. Galois theory Mathematics MATHEMATICS Applied Galois theory QA214 512/.32 MAT003000 Newman, Stephen C., 1952- Hoboken, N.J. : Wiley, 2012 (DLC) 2011053469 9781118336670 1118336674 9781118336847 1118336844 9781118336830 1118336836 9781118336816 111833681X 2012005885 10.1002/9781118336816 Wiley InterScience A350873F-43FE-469B-BF3D-1BC1A3E2E2F7 OverDrive, Inc. http://onlinelibrary.wiley.com/book/10.1002/9781118336816 http://onlinelibrary.wiley.com/book/10.1002/9781118336816 DLC 120208 20171115113716.0 ocn775780317 eng