Math 552 is the second semester of the standard introductory graduate algebra course. A significant portion of the course is devoted to the theory of field extensions, including Galois theory, rings of polynomials, Nullstellensatz, intro to homological algebra, structure of Artin rings. Additional topics are chosen in part based on the interests of the students.
Notices and assignments will appear on this page.
| Due | Assigned Problems |
|---|---|
| 1/31 | V.1 #9, 13a, 19,21(a,c); V.2 #2,4,15 |
| 2/7 | V.2 #7,12; V.3 #5,9,13,19,20 |
| 2/14 | V.4 #2,5,10(a,d),12 V.5 #3,6,11 |
| 2/21 | V.6 #8,11; V.7 #3,5,10; V.9 #1,4 |
| 2/25 | midterm on Galois theory |
| 3/7 | VIII.1 #1,3,4,7 VIII.2 #7,13 VIII.3 #3,8 |
| 3/14 | VIII.4 #1,2,3,8 VIII.5 #1,3,8 |
| 3/21 | Spring Break |
| 3/28 | IV.3 #2,4,5,7,8,10,11 |
| 4/4 | IV.4 #3,11; IV.5 #2(a,b),8(c),9,11(i); X.2 #2 |
| 4/11 | Find a projective resolution over R=F[x,y] of F=R/(x,y); Compute Tor_n(ℤ/8,ℤ/4) for R=ℤ/32, all n≥0 ; Show that R is an injective R-module when R=ℤ/n |
| 4/15 | midterm on commutative rings, modules, homological algebra |
| 4/22 | Group representations supplement, exercise (on p.2) and #1-3 (on p.4) |
| 4/29 | Group representations supplement, prove the Proposition on p.4, and do exercises #4,5,6 |
| 5/2 | midterm on group representations (Classes end) |
Charles Weibel / Spring 2025