Instructor: |
Monty (or William)
McGovern
Office: Padelford C-450; grader office PDL C-34 Phone: 206-543-1149 Email: mcgovern@math.washington.edu Office Hours: drop in, or by appointment, Padelford C-450; grader office hours W 1:30-2:20, 3:30-4:20 |
Lectures: |
Monday, Wednesday & Friday, 9:30-10:20 a.m., Padelford Hall C-36 |
Required Text: |
Abstract Algebra, by Dummit and Foote, (3d ed., Wiley, 2004). |
Prerequisites: |
Math 505 or the equivalent. |
Grading: |
Your grade will be based on weekly homework, counting 50%, and a final exam, counting 50%. The final exam will be comprehensive. If you cannot complete a homework assignment on time, you can turn it in by 4:00 on the day it is due to Pal's mailbox. PLEASE turn in WHATEVER YOU CAN rather than nothing. In the final you may use two letter-sized pages (one sheet front and back of notes in your own handwriting). class. |
Incompletes and Drops: |
The grade of Incomplete will be given ONLY if a student has been doing satisfactory work until the end of the quarter and then misses the final exam for a documented illness, religious reason, or family emergency. |
What to Expect: |
I will cover Dedekind domains and finitely generated modules over them, generalizing the theory of finitely generated modules over a PID in the fall quarter (Section 16.3 in the text). I will then move on to two further ways to define dimension of commutative rings and further material in algebraic geometry, covering some material in other books (which I will copy and hand out). In particular I will treat some of the basic properties of projective varieties. This term you will be making presentations in class about some topic of interest to you that uses algebra in some way. |
Due: | Problems: |
Apr 1 |
16.1.9,12; 16.3.11-13: review 16.2, read 16.3 |
Apr 8 |
16.1.13,14; 16.3.20,22,23: finish 16.3 |
Apr 15 |
choose a partner and a topic for presentation: read handout
from Atiyah-Macdonald |
Apr 22
|
work out the structure of G(A) for A=k[x,y]/(x^3-y^2) and
k[x,y,z]/(y^2-xz,x^2y-z^2,x^3-yz), with respect to the maximal
ideal M at the origin in both cases; show that dim A[x] = dim A + 1
if A is Noetherian and lies between dim A+1 and 2dim A+1 in
general: start the handout from Chap. 11 of Atiyah-Macdonald |
Apr 29 |
no homework: finish Chapter 11 of Atiyah-Macdonald |
May 6 |
no homework: start handout from Hartshorne |
May 13 |
turn in date for presentations; optional: show that A^1 and P^1
are homeomorphic, but not A^n
and P^n for any n>1; show that the d-uple embedding from P^n to P^N
is an isomorphism onto its image, but P^n and this image have
nonisomorphic coordinate rings; show that the fiber over the origin
of the blowup of any plane curve singular at the origin equals the number
of tangent directions at the origin (terms defined in class):
continue Hartshorne handout |
May 20
|
work on presentation: read Hartshorne handout |
May 27
|
work on presentations: finish Hartshorne handout |