Prerequisites: |
Math 8201, or an equivalent discussed with the instructor. |
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 9:05-9:55am, Vincent Hall 206. |
Office hours: | Mon 11:15am-12:05pm Tues 9:05-9:55am Thur 2:30-3:20pm |
Required text: | Abstract algebra, 3rd edition, by D.S. Dummit and R.M. Foote, Wiley, 2004. |
Course content: |
This is the 2nd semester of the Math 8201-2 one-year graduate core sequence in
abstract algebra. Math 8201 dealt with groups, vector spaces, linear and multilinear algebra including spectral theory, and started discussing rings, covering roughly these parts of the Dummit and Foote text: Chapters 1-6 Chapter 11 Chapter 7, Sections 7.1 and 7.2 Math 8202 will continue by discussing more about rings, modules, and field theory, covering these parts of the text: Chapters 7,8,9 on rings (adding in Groebner bases) Chapters 10,12 on modules Chapters 13,14 on fields and if there's some extra time, dip into Chapter 18 |
Other useful texts: |
(on reserve in Math Library, 3rd floor of Vincent Hall) Algebra, by S. Lang, Addison-Wesley, 1993. Algebra, by T. W. Hungerford Algebra, by M. Artin, Prentice Hall, 1991. Field and Galois Theory, by P. Morandi, Springer Grad. Texts in Math. 167. Field extensions and Galois theory, by J.R. Bastida, Cambridge Univ. Press, 1984. |
Written prelim preparation: | One role of this class is to prepare the students for the Math PhD program's
Algebra Written Prelim Exams.
Although we will go a long way toward this goal, those who intend to take the
prelim exam should not miss
Paul Garrett's Abstract Algebra page,
containing links to his book for the class, solutions to many of the typical prelim exam problems,
etc. |
Homework: | There will be 6 homework assignments, mainly exercises from the book, due every two weeks on Friday at the beginning of class; see the table below for the tentative list of assignments. These homeworks will count for 35% of the course grade. 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. |
Exams: | There will be two take-home midquarter exams to be handed out on dates to be announced later, each contributing 20% to the grade. There will be a take-home final exam worth 25% of the grade given just before 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 |
---|---|---|
Homework 1 | Fri Feb. 4 |
7.3 # 2,3,13,17,26,29,30,31,33, 7.4 # 8,11,15,19,26,30,31,32,37,38,39, 7.5 # 3,5 7.6 # 1,2,3,4,5 |
Homework 2 | Fri Feb. 18 |
8.1 # 2(a),3,4,5,9,10,12 8.2 # 1,2,3,4 8.3 # 5,6,7,8(a) 9.1 # 5,7,9,13,14 9.2 # 1,2,3,4,5,6,7,8 |
Midterm exam 1 | Fri Feb. 25 | Here is Midterm Exam 1 |
Homework 3 | Fri Mar. 11 |
10.1 # 8,11,12,18,19,20 10.2 # 6,13 10.3 # 2,4,5,9,10,11 |
Homework 4 | Fri Mar. 25 |
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 |
Midterm exam 2 | Fri Apr. 1 | Here is Midterm Exam 2 |
Homework 5 | Fri Apr. 15 |
13.1 # 1,5 13.2 # 3,5,7,8,12,14,16,18 13.4 # 1,2,3 13.5 # 7,8,9 13.6 # 3,4,5,6,8,9 |
Homework 6 | Fri Apr. 29 |
14.1 # 4,7 14.2 # 3,4,5,11,13,17,18,29,31 14.3 # 1,3,4,9,10 14.6 # 2 (These problems from Chapter 18 got removed from HW6: 18.1 # 3,8,13,15,16,19 18.3 # 2,6,8,9,11) |
Final exam | Fri May 6 | Here is the Final Exam |