UNIVERSITY OF MINNESOTA 
SCHOOL OF MATHEMATICS

Math 8201: Graduate abstract algebra

Fall 2010

Prerequisites: Previous exposure to undergrad abstract algebra (groups, rings, fields) will be helpful, else things will go by too quickly. Mathematical maturity, including understanding of rigor, is a necessity.
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 20. 
Office hours: Tues-Thur 9:05-9:55am, and Mon 11:15-12:05am 
Required text: Abstract algebra, 3rd edition, by D.S. Dummit and R.M. Foote, Wiley, 2004.
Course content: Math 8201-2 is a one-year graduate core sequence in abstract algebra dealing with groups, vector spaces, rings in Math 8201, then more rings, modules, and field theory in Math 8202.
By the end of Math 8201-8202 we hope to cover as much as possible of the following chapters in the Dummit and Foote text:
Chapters 1-6 on groups
Chapter 11 on vector spaces (adding in spectral theorems)
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.
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.
Also, here were some practice problems from old prelims containing mostly material from this first semester course.
Homework: There will be homework assignments due every two weeks on Friday at the beginning of class; see table below for assignments. There should be a total of 6-7 assignments, which will count for 35% 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.
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 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. 
Homework and exams
Assignment Due date Problems
Homework 1 Fri Sept 24 1.1 # 9, 25,31
1.2 # 17
1.3 # 15,19
1.4 # 11
1.6 # 4,5,6,7,18
1.7 # 12,21,23
2.1 # 6,7,17
2.2 # 7,14
2.3 # 5,15,23,26
2.4 # 12,13,14,15,19
2.5 # 8
Homework 2 Fri Oct 8 3.1 # 14, 34, 36, 42
3.2 # 4, 9, 18, 19, 21
3.3 # 1, 3, 8, 9, 10
3.4 # 5
(6.3 # 2,4,7 was removed from the HW)
Midterm exam 1 Fri Oct 15 Here is Midterm Exam 1
Homework 3 Fri Oct 29 4.1 # 1,2,3,8,10
4.2 # 7,8,9
4.3 # 6,17,25,30
4.4 # 7, 8(a,b), 9, 16
4.5 # 5, 13, 16, 30, 33, 34
5.1 # 5
5.4 # 2, 15, 19
5.5 # 8
(6.1 # 3,9,10 was removed from the HW)
Homework 4 Fri Nov 12 11.1 # 5,6,7 (10 removed; done in class)
11.2 # 9, 11, 12, 36, 37
11.3 # 2,4
11.4 # 6
+Exercise 2 from these extra linear algebra exercises
(11.5 was moved to HW 5)
Midterm exam 2 Fri Nov. 19 Here is Midterm Exam 2
Homework 5 Fri Dec. 10 11.5 # 12, 13
Exercises 1,3,5,6,7 from the extra linear algebra exercises
7.1 # 5, 12, 14, 15, 25, 26
7.2 # 3,4,5,7

(these problems got moved to next semester:
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)
Final exam Fri Dec. 17 Here is the final exam
Back to Reiner's Homepage.