D J H Garling

Galois Theory and Its Algebraic Background

• Gebundenes Buch

Produktbeschreibung

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

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Produktdetails

• Verlag: Cambridge University Press
• 2nd Revised edition
• Seitenzahl: 204
• Erscheinungstermin: 22. Juli 2021
• Englisch
• Abmessung: 234mm x 203mm x 20mm
• Gewicht: 454g
• ISBN-13: 9781108838924
• ISBN-10: 1108838928
• Artikelnr.: 62214711

Autorenporträt

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).

Inhaltsangabe

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.