Field Theory 2nd Edition Steven Roman by Steven Roman 9780387276779, 9780387276786, 0387276777, 0387276785 instant download after payment.

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.

The book begins with a preliminary chapter (Chapter 0), which is designed to be quickly scanned or skipped and used as a reference if needed. The remainder of the book is divided into three parts.

Part 1: Field Extensions

Part 2: Galois Theory

Part 3: The Theory of Polynomials

Appendix: Möbius Inversion

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