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Galois Theory (Universitext)

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Synopses & Reviews

Publisher Comments:

The book discusses classical Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it discusses algebraic closure and infinite Galois extensions, and concludes with a new chapter on transcendental extensions. Key topics and features of this second edition: - Approaches Galois theory from the linear algebra point of view, following Artin; - Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity. Review from the first edition: "The text offers the standard material of classical field theory and Galois theory, though in a remarkably original, unconventional and comprehensive manner ... . the book under review must be seen as a highly welcome and valuable complement to existing textbook literature ... . It comes with its own features and advantages ... it surely is a perfect introduction to this evergreen subject. The numerous explaining remarks, hints, examples and applications are particularly commendable ... just as the outstanding clarity and fullness of the text." (Zentralblatt MATH, Vol. 1089 (15), 2006) Steven H. Weintraub is a Professor of Mathematics at Lehigh University and the author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).

Synopsis:

The new edition of this text on classical Galois Theory approaches the theory from the linear algebra point of view, following Artin. It also presents a number of applications of the theory and an expanded chapter on transcendental extensions.

Synopsis:

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.

About the Author

Steven H. Weintraub is a Professor of Mathematics at Lehigh University and author of seven books. This book grew out of a graduate course he taught at Lehigh. He is also the author of Algebra: An Approach via Module Theory (with W. A. Adkins).

Table of Contents

Introduction to Galois Theory.- Field Theory and Galois Theory.- Development and Applications of Galois Theory.- Extensions of the Field of Rational Numbers.- Further Topics in Field Theory.- Transcendental Extensions.- A. Some Results from Group Theory.- B. A Lemma on Constructing Fields.- C. A Lemma from Elementary Number Theory.- References.- Index.

Product Details

ISBN:
9780387875743
Author:
Weintraub, Steven H.
Publisher:
Springer
Subject:
Algebra - General
Subject:
Group Theory
Subject:
Number Theory
Subject:
Algebra - Abstract
Subject:
Galois theory
Subject:
Field theory
Subject:
Quadratic
Subject:
Separable Extensions
Subject:
Symmetric functions
Subject:
Transcendental Extensions
Subject:
Field Theory and Polynomials
Subject:
Group Theory and Generalizations
Subject:
Number Theory <P>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
Subject:
Mathematics-Abstract Algebra
Copyright:
Edition Description:
2nd ed. 2009
Series:
Universitext
Publication Date:
20081121
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
226
Dimensions:
235 x 155 mm

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Related Subjects


Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Number Theory

Galois Theory (Universitext) New Trade Paper
0 stars - 0 reviews
$67.25 In Stock
Product details 226 pages Springer - English 9780387875743 Reviews:
"Synopsis" by , The new edition of this text on classical Galois Theory approaches the theory from the linear algebra point of view, following Artin. It also presents a number of applications of the theory and an expanded chapter on transcendental extensions.
"Synopsis" by , 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.
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