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Galois Theory

  • Textbook
  • © 2009

Overview

Authors:
  1. Steven H. Weintraub

    1. Dept. Mathematics, Lehigh University, Bethlehem, U.S.A.

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  • Concise and clear treatment of the subject
  • Stresses linear algebra approach
  • Presents further topics in field theory
  • Second edition includes expanded key chapter on transcendental extensions
  • Better format and layout

Part of the book series: Universitext (UTX)

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Table of contents (6 chapters)

  1. Front Matter

    Pages 1-10
    Download chapter PDF

  2. Introduction to Galois Theory

    • Steven H. Weintraub
    Pages 1-6

  3. Field Theory and Galois Theory

    • Steven H. Weintraub
    Pages 1-38

  4. Development and Applications of Galois Theory

    • Steven H. Weintraub
    Pages 1-43

  5. Extensions of the Field of Rational Numbers

    • Steven H. Weintraub
    Pages 1-54

  6. Further Topics in Field Theory

    • Steven H. Weintraub
    Pages 1-30

  7. Transcendental Extensions

    • Steven H. Weintraub
    Pages 1-21

  8. Back Matter

    Pages 1-17
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Keywords

About this book

This is a textbook on Galois theory. Galois theory has a well-deserved re- tation as one of the most beautiful subjects in mathematics. I was seduced by its beauty into writing this book. I hope you will be seduced by its beauty in reading it. This book begins at the beginning. Indeed (and perhaps a little unusually for a mathematics text), it begins with an informal introductory chapter, Ch- ter 1. In this chapter we give a number of examples in Galois theory, even before our terms have been properly de?ned. (Needless to say, even though we proceed informally here, everything we say is absolutely correct.) These examples are sort of an airport beacon, shining a clear light at our destination as we navigate a course through the mathematical skies to get there. Then we start with our proper development of the subject, in Chapter 2. We assume no prior knowledge of ?eld theory on the part of the reader. We develop ?eld theory, with our goal being the Fundamental Theorem of Galois Theory (the FTGT). On the way, we consider extension ?elds, and deal with the notions of normal, separable, and Galois extensions. Then, in the penul- mate section of this chapter, we reach our main goal, the FTGT.

Reviews

From the reviews:

"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." (Werner Kleinert, Zentralblatt MATH, Vol. 1089 (15), 2006)

From the reviews of the second edition:

“The book is a valuable reference, covering many more topics than most of the standard books on the subject.” (Mowaffaq Hajja, Zentralblatt MATH, Vol. 1195, 2010)

Authors and Affiliations

  • Dept. Mathematics, Lehigh University, Bethlehem, U.S.A.

    Steven H. Weintraub

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).

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