## Beschreibung

### Beschreibung

"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. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY### Inhaltsverzeichnis

Preliminaries.- Preliminaries.- Field Extensions.- Polynomials.- Field Extensions.- Embeddings and Separability.- Algebraic Independence.- Galois Theory.- Galois Theory I: An Historical Perspective.- Galois Theory II: The Theory.- Galois Theory III: The Galois Group of a Polynomial.- A Field Extension as a Vector Space.- Finite Fields I: Basic Properties.- Finite Fields II: Additional Properties.- The Roots of Unity.- Cyclic Extensions.- Solvable Extensions.- The Theory of Binomials.- Binomials.- Families of Binomials.### Portrait

Steven Roman, Ph.D., is a professor emeritus of mathematics at the California State University, Fullerton. His previous books with O'Reilly include Access Database Design and Programming, Writing Excel Macros, and Win32 API Programming with Visual Basic.### Pressestimmen

From the reviews of the second edition: "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. All in all, I recommend this book highly as it is a well-written expository account of a very exciting area in mathematics." (Darren Glass, The MAA Mathematical Sciences Digital Library, February, 2006) "The second edition of Roman's Field Theory ... offers a graduate course on Galois theory. ... The author's approach is mainly standard ... . the merits of such an approach would have been helpful for readers who already know some Galois theory, or for instructors who have to pick a textbook. ... The clarity of exposition and lots of exercises make this a suitable textbook for a graduate course on Galois theory." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1172, 2009)EAN: 9780387276779

ISBN: 0387276777

Untertitel: 2nd ed. 2006.
Book.
Sprache: Englisch.

Verlag: Springer

Erscheinungsdatum: November 2005

Seitenanzahl: 352 Seiten

Format: gebunden

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