Universitext

Galois Theory

Authors: Weintraub, Steven

  • 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
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eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-87575-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-0-387-87574-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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).

About the authors

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).

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)


Table of contents (6 chapters)

  • Transcendental Extensions

    Weintraub, Steven H.

    Pages 1-21

  • Extensions of the Field of Rational Numbers

    Weintraub, Steven H.

    Pages 1-54

  • Further Topics in Field Theory

    Weintraub, Steven H.

    Pages 1-30

  • Field Theory and Galois Theory

    Weintraub, Steven H.

    Pages 1-38

  • Introduction to Galois Theory

    Weintraub, Steven H.

    Pages 1-6

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-387-87575-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-0-387-87574-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Galois Theory
Authors
Series Title
Universitext
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-87575-0
DOI
10.1007/978-0-387-87575-0
Softcover ISBN
978-0-387-87574-3
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIV, 212
Topics