Galois Theory

1. Front Matter

   Pages 1-10

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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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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.

• Algebra
• Field Theory
• Quadratic
• Separable Extensions
• Symmetric Functions
• Transcendental Extensions
• linear algebra

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)

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

  Steven H. Weintraub

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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