# Field Theory

- 1 Citations
- 60k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 158)

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Textbook

- 1 Citations
- 60k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 158)

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

Irreducibility Vector space algebra binomial finite field

- DOI https://doi.org/10.1007/0-387-27678-5
- Copyright Information Springer New York 2006
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-27677-9
- Online ISBN 978-0-387-27678-6
- Series Print ISSN 0072-5285
- Buy this book on publisher's site