MA3202-1 Galois teori
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| Beskjeder: |
19.12: Første møte 8. januar 2007, kl. 12.15, rom B22.
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| Ansvarlig: |
Helge Maakestad.
Rom 944, Sentralbygg II. Telefon 73 59 17 95. E-post: helge.maakestad  math.ntnu.no. |
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| Ukentlige møter: |
Mandag 12.15-14.00 rom B22 og torsdag 10.15-12.00 rom B22. |
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| Litteratur: |
P. B. Bhattacharya, S. K. Jain og S. R. Nagpaul: Basic
Abstract Algebra. Cambridge University Press, Second
edition. ISBN: 0-521-46629-6. J. B. fraleigh: A first course in abstract algebra. Addison-Wesley Publishing Co. 7'th edition. Plan: Her finner dere en foreløpig fremdriftsplan for kursets forelesninger. Jeg vil også poste meldinger om kurset på denne siden. Pensum: Pensum for kurset vil være kap. 11, 15, 16 og 17 i boken "Basic Abstract Algebra" samt deler av kapittel 18. Her finner dere en artikkel om Galois. |
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| Innhold: |
Kap. 11 Unique factorization domains and euclidean domains 11.1 Unique factorization domains 11.2 Principal ideal domains 11.3 Euclidean domains 11.4 Polynomial rings over UFDs Kap. 15 Algebraic field extensions 15.1 Irreducible polynomials and Eisenstein criterion 15.2 Adjunction of roots 15.3 Algebraic extensions 15.4 Algebraically closed fields Kap. 16 Normal and separable extensions 16.1 Splitting fields 16.2 Normal extensions 16.3 Multiple roots 16.4 Finite fields 16.5 Separable extensions Kap. 17 Galois theory 17.1 Automorphism groups and fixed fields 17.2 Fundamental theorem of Galois theory 17.3 Fundamental theorem of algebra Kap. 18 Applications of Galois theory to classical problems 18.1 Roots of unity and cyclotomic polynomials 18.2 Cyclic extensions 18.3 Polynomials solvable by radicals 18.4 Symmetric functions 18.5 Ruler and compass constructions |
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| Eksamen: | Holdes den 30 mai. | ||