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Field Theory
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Field Theory Paperback - 2011

by Steven Roman

From the publisher

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.

This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included.

From the rear cover

This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt

Details

  • Title Field Theory
  • Author Steven Roman
  • Binding Paperback
  • Edition 2nd ed. 2006
  • Pages 335
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Date 2011-09-17
  • ISBN 9781441920959 / 1441920951
  • Weight 1.07 lbs (0.49 kg)
  • Dimensions 9.21 x 6.14 x 0.72 in (23.39 x 15.60 x 1.83 cm)
  • Dewey Decimal Code 512.3

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Graduate Texts in Mathematics - Field Theory (Graduate Texts in  Mathematics, 158)
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Graduate Texts in Mathematics - Field Theory (Graduate Texts in Mathematics, 158)

by Roman, Steven

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California: Springer. Very Good- with no dust jacket. 2011. Second Edition. Original Laminated Wrappers. 1441920951 . Original yellow decorated wrappers. Covers laminated. With library stamps and labels. Slight wear and slight soiling to spine, covers and corners. ; 15.3x23x2 cm; 347 pages .
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Field Theory

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Field Theory
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Field Theory

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Paperback / softback. New. "Springer has just released the second edition of Steven Roman's Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own.
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Field Theory

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Field Theory (Graduate Texts in Mathematics, 158)
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Field Theory (Graduate Texts in Mathematics, 158)

by Roman, Steven

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