Date

Topic

Remarks

Jan 4

introduction, categories

[DF, Appendix II]

Jan 8

intro to category theory

[DF, Appendix II]

Jan 10

functors, free objects, Rmod

[DF, Appendix II, Section 10.1, 10.2]

Jan 15

free objects, Rmod, quotients

[BCT, Sec 1.2, p. 70], [DF, Section 10.2, 10.3]

Jan 17

Notherian <=> submodules are f.gen.

[DF, Section 12.1]

Jan 22 and 24

I can' be there, class to be rescheduled


Jan 29

Use of Smith normal form for E.D.

[DF, Section 12.1]

Jan 31

Smith normal form for P.I.D., classification existence

[DF, Section 12.1]

Feb 5

Uniq PID module classif., f.g. ab. grps, rational can form

[DF, Section 12.1 and 12.2]

Feb 7

Computing the rational canonical and Jordan forms of a matrix

[DF, Section 12.2 and 12.3] + Sage

Feb 12

snow day


Feb 14

Projective, injective and flat modules

[DF, Section 10.5]

Feb 19 and 21

Reading week


Feb 26

Practice for midterm


Feb 28

Midterm


Mar 5

finish projective/injective modules, begin fields

[D&F, Section 10.5, Section 13.1]

Mar 7

algebraic extensions, constructible numbers

[D&F, Section 13.2, 13.3]

Mar 12

splitting fields and algebraic closure

[D&F, Section 13.4]

Mar 14

irreducible and separable polynomials

[D&F, Section 13.5]

Mar 19

(Kel) begin Galois theory

[D&F, Section 14.1]

Mar 21

perfect, separable, cyclotomic fields, ${\mathbb F}_{p^n}$

[D&F, Section 13.5 and 13.6]

Mar 26

(Kel) finish Galois theory

[D&F, Section 14.2]

Mar 28

review for final


Apr 2

(Daniel) Hilbert's Nullstellensatz

[D&F, Section 15.2, 15.3]

Apr 4

(Daniel) Hilbert's Nullstellensatz, problem solving


Apr 9

(Oskar) Grobner bases

[D&F, Section 9.6]
