Galois Theory and Its Algebraic Background

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Sprache: Englisch

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Beschreibung

This textbook contains a full account of Galois Theory and the algebra that it needs, with exercises, examples and applications.

Über den Autor

D. J. H. Garling is Emeritus Reader in Mathematical Analysis at the University of Cambridge and Fellow of St John's College, Cambridge. He has fifty years' experience of teaching undergraduate students and has written several books on mathematics, including Inequalities: A Journey into Linear Analysis (Cambridge, 2007) and A Course in Mathematical Analysis (Three volumes, Cambridge, 2013-2014).

Inhaltsverzeichnis

Part I. The Algebraic Background: 1. Groups; 2. Integral domains; 3. Vector spaces and determinants; Part II. The Theory of Fields, and Galois Theory: 4. Field extensions; 5. Ruler and compass constructions; 6. Splitting fields; 7. Normal extensions; 8. Separability; 9. The fundamental theorem of Galois theory; 10. The discriminant; 11. Cyclotomic polynomials and cyclic extensions; 12. Solution by radicals; 13. Regular polygons; 14. Polynomials of low degree; 15. Finite fields; 16. Quintic polynomials; 17. Further theory; 18. The algebraic closure of a field; 19. Transcendental elements and algebraic independence; 20. Generic and symmetric polynomials; Appendix: the axiom of choice; Index.

Details

Erscheinungsjahr:	2021
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9781108969086
ISBN-10:	1108969089
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Garling, D. J. H.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 12 mm
Von/Mit:	D. J. H. Garling
Erscheinungsdatum:	22.07.2021
Gewicht:	0,343 kg