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.
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.
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