| Prerequisites: | Math 8201 or the equivalent, that is, a solid background in group theory, linear and multilinear algebra |
| Instructor: | Victor Reiner (You can call me "Vic"). |
| Office: Vincent Hall 256, Telephone (with voice mail): 625-6682, E-mail: reiner@math.umn.edu |
|
| Classes: | Mon-Wed-Fri 09:05-09:55am, Vincent Hall 209. |
| Office hours: | MWF 10:10-11am, and by appointment. |
| Course content: | This is the second semester of the graduate core class in abstract algebra dealing with the basic algebra rings, modules and fields. |
| Required text (on sale at bookstore): |
Abstract algebra, 2nd edition, by D.S. Dummit and R.M. Foote, Wiley, 1999. |
|
The tentative plan is continue where we left off in the
book:
Chapters 7,8,9 on rings (adding in Groebner bases) Chapters 10,12 on modules Chapters 13,14 on fields and Galois theory We'll cover the following special topic after the algebra prelim exam, if time allows: Chapter 18,19 on representations and characters of finite groups |
|
| Other useful texts (on reserve in Math Library, 3rd floor of Vincent Hall): |
Algebra, by M. Artin, Prentice Hall, 1991. Topics in algebra, by I. N. Herstein, Xerox College Publishing, 1975. Algebra, by S. Lang, Addison-Wesley, 1993. Field and Galois Theory, by P. Morandi, Springer-Verlag GTM #167, 1996 |
| Homework: | As in the fall, there will be homework assignments due every two weeks
in class on Fridays during the semester, starting with Friday
February 1 (see table below). There should be a total of 6-7 assignments,
which will count for 40% of the course grade.
The assignments will mainly be exercises from the book.
Late homework will not be accepted.
I encourage collaboration on the homework, as long as
each person understands the solutions, writes them up in
their own words, and indicates on the homework page with
whom they have collaborated. I'll expect you to make at least some attempt on all of the homework problems. However, there will generally be more problems assigned than is possible for the grader to look at and comment on, and many of them will be very short and easy. I'll try to hand out brief solutions or solution outlines after each assignment. |
| Exams: | There will be two take-home midquarter exams to be handed out on a date to be announced later, each contributing 15% to the grade. There will be a take-home final exam worth 30% of the grade given either during the last week of class or during exam period. In contrast to the homework, there is to be no collaboration allowed with other humans allowed on any of the take-home midquarter or final exams. |
| Assignment | Due date | Problems |
|---|---|---|
| 1 | Fri 2/1 |
7.1 # 27 7.2 # 5,7,8 7.3 # 2,3,5,13,17,26,29,30,31,33,34 7.4 # 7,8,11,15,16,18,25,26,28, 30,31,32,37,38,39 |
| 2 | Fri 2/15 |
7.5 # 3,4,5 7.6 # 1,2,3,4,5 8.1 # 2,3,4,5,9,10,12 8.2 # 1,2,3,4 |
| 3 | Fri 3/1 |
8.3 # 5,6,7,8(a) (don't do 8(b),(c)) 9.1 # 5,6,7,9,13,14 9.2 # 1,2,3,4,5,6,7,8 9.3 # 2 9.4 # 2,3,5,11,12,13,14 9.5 # 1,3 |
| 4 | Fri 3/29 |
10.1 # 8,11,12 10.2 # 6,13 10.3 # 2,4,5,9,10,11 12.1 # 1,2,3,4,6,13 12.2 # 3,4,10,17,18 12.3 # 5,16,17,22,24,25,26,32,37 |
| 5 | Fri 4/12 |
13.1 # 1,5 13.2 # 3,5,7,8,12,14,16,18 13.4 # 1,2,3 13.5 # 7,9,10 |
| 6 | Fri 5/3 |
13.6 # 3,4,5,6,8,9 14.1 # 4,7 14.2 # 3,4,5,11,13,17,18,29,31 14.3 # 1,3,4,9,10 |
| Exam | Due date | ||
|---|---|---|---|
| Midterm 1 | Fri 3/8 | Midterm 1 | |
| Midterm 2 | Fri 4/19 |
Midterm 2 + extra practice problems on modules over a PID. |
|
| Final Exam | Fri 5/10 | Final exam |