Lecture schedule for Math 3EE3
The following lecture schedule is tentative and could change as the
term proceeds. Any electronic materials displayed in class will be linked to
the corresponding lecture after the lecture has been given.
Week 1 Jan. 6 - 9
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Examples and properties of rings: Judson 16.1-2; D&F 7.1-3
Week 2 Jan. 13 - 16
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homomorphisms, integral domains and fields of quotients: Judson 16.2-3, 18.1; D&F 7.3, 7.5
Week 3 Jan. 20 - 23
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Rings of polynomials, Homomorphisms, ideals and quotients: Judson 16.3, 17.1-2; D&F 7.4, 9.1 - 9.2
Week 4 Jan. 27 - Jan. 30
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Factorization over a field, Gauss' lemma, Eisenstein criterion: Judson 17.3, 18.2, D&F 9.4, 9.5
Week 5 Feb. 3 - Feb. 6
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field extensions, vector spaces over arbitrary fields: Judson Chap. 20, 21.1; D&F 11.1
Week 6 Feb. 10 - Feb. 13
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More on vector spaces, algebraic extensions, first term test on Feb. 10
Week 7 Feb. 24 - Feb. 27
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Algebraically closed fields, a short discussion of set theory and Zorn's lemma: D&F Appendix pg. 907
Week 8 Mar. 3 - Mar. 6
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Cont'd discussion of set theory, algebraic extensions continued, Judson, 21.1; D&F, 13.1, 13.2
Week 9 Mar. 10 - 13
- Hilbert basis theorem: D&F 9.6,
Week 10 Mar. 17 - 20
- Grobner bases: D&F 9.6, second term test on Mar. 17
Week 11 Mar. 24 - 27
- geometric constructions: Judson, 21.3; D&F 13.3
Week 12 Mar. 31 - Apr. 2
- finite fields: Judson, 22.1; D&F, 14.3
Week 13 Apr. 6 - 8