| Prerequisites: | Some previous exposure to undergrad abstract algebra (groups, rings, fields) will be helpful, else things may go by too quickly. Mathematical maturity is a must! |
| 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 207. |
| Office hours: | Mon-Wed 10:10-11:00 AM, Tues 3:35-4:25 PM, and also by appointment. |
| Course content: |
This is the first semester of the graduate core class in
abstract algebra dealing with the basic algebra of
groups, vector spaces, rings, modules and fields.
Roughly speaking the semesters should divide
the topics as follows: Fall: Groups, vector spaces, linear algebra, groups representations, some ring theory Spring: More ring theory, modules, and field theory. |
| Required text (on sale at bookstore): |
Abstract algebra, 2nd edition, by D.S. Dummit and R.M. Foote, Wiley, 1999. |
|
With regard to the book, the (very) tentative plan for the two semesters goes
like this: Chapters 1-6 on groups (adding in some RSA encryption) Chapter 11 on vector spaces (adding in spectral theorems) Chapters 18,19 on representations Chapters 7,8,9 on rings (adding in Groebner bases) Chapters 10,12 on modules Chapters 13,14 on fields |
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| 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. |
| Homework: | There will be homework assignments due every two weeks
in class on Fridays during the semester, starting with Friday
September 21 (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 (this is particularly true for the first assignment). 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 dates to be announced later, each contributing 15% to the grade. There will be a take-home final exam worth 30% of the grade given 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 9/21 |
1.1 # 9,22,25,31 1.2 # 10,17 1.3 # 15,19 1.4 # 7,11 1.6 # 4,5,6,7,18,26 1.7 # 12,21,23 2.1 # 6,16,17 2.2 # 10,14 2.3 # 15,23,26 2.4 # 12,19 |
| 2 | Fri 10/5 |
2.5 # 8,15 3.1 # 5,14,33,36,42 3.2 # 4,9,19,22 3.3 # 1,7 6.3 # 2,4,7 |
| 3 | Fri 10/26 |
3.1 # 27 3.2 # 18, 21 3.3 # 3, 9 4.1 # 1, 2, 3, 10 4.2 # 4, 7, 8, 11 4.3 # 6, 13, 25 |
| 4 | Fri 11/9 |
3.4 # 5, 8 4.3 # 33 4.4 # 7,8,9, 18,19 4.5 # 5, 13, 16, 30, 33, 34, 36 5.1 # 5 5.4 # 2, 14, 19 6.3 # 10 |
| 5 | Fri 11/30 |
6.1 # 3,7,9,10 11.1 # 2,5,6,7,8,9 11.2 # 1,4,9,11,36,38 11.3 # 3,4 11.4 # 6 |
| 6 | Fri 12/14 |
11.5 # 4,10,11,13 7.1 # 5,6,11,14,15,25,26 + some linear algebra problems |
| Exam | Due date | |
|---|---|---|
| Midterm 1 | 10/12 | |
| Midterm 2 | 11/16 | |
| Final Exam | 12/21, by 5PM |