Date

Topic

Remarks

Jan 7

introduction, categories

[DF, Appendix II] and [BCT 1.1]

Jan 9

intro to category theory, functors

[DF, Appendix II] and [BCT Introduction, 1.1]

Jan 14

functors, problem from previous comprehensive

[DF, Appendix II] and [BCT 1.1, 1.2]

Jan 16

faithful, full, free objects, RMod

[DF, Section 10.1 and 10.2]

Jan 21

basis, quotients in categories and modules, direct product/sum, isomorphism theorems

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

Jan 23

CRT (exercise #16,17 DF 10.3), Noetherian modules

[DF, Section 10.3, 12.1]

Jan 28

Rough outline of procedure for SNF on E.D. (with hint how to extend to PID)

[DF Section 12.1, exercises #1619]

Jan 30

Apply SNF to show characterization of modules over PID

[DF Section 12.1, Theorem 4,5]

Feb 4

finish CRT , uniqueness of characterization of modules over PID

[DF Section 10.3 #18, Section 12.1, Theorem 9]

Feb 6

Compute rational canonical form, Jordan canonical form

[DF Section 12.2, 12.3]

Feb 11

computer calculation of rational canonical form (using SNF), injective/projective

[DF Section 12.2, 12.3], [DF Section 10.5]

Feb 13

injective/projective, statement of TFAE for projective modules

[DF Section 10.5]

Feb 18 and 20

Reading week


Feb 25

I won't be able to be there (will need to reschedule)


Feb 27

Midterm


Mar 3

Four characterizations of projective modules

[DF Section 10.5]

Mar 5

Finish projective/injective modules, beginning fields

[DF Section 10.5], [DF Section 13.1]

Mar 10

more about projective/injective modules

[DF Section 10.5]

Mar 12

practice problem


Mar 17

fields and field extensions

[D&F Section 13.1] fields part 1

Mar 19

more fields and extensions

[D&F, Section 13.2, 13.3] fields part 2

Mar 24

splitting fields and algebraic closure

[D&F, Section 13.4] fields part 3

Mar 26

irreducible and separable polynomials

[D&F, Section 13.5]

Apr 2

(Jordan) Galois theory

[D&F, Section 14.1]

Apr 7

finish Galois theory


Apr 14

(Kailun) Grobner bases

