| Prerequisites: | Math 8201 or its equivalent. |
| 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 364. |
| Office hours: | Mon and Wed 8:00-8:50am, Thurs 9:05-9:55am. Also by appt., but Tues pm greatly discouraged. |
| 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, covering roughly these parts of the Dummit and Foote Chapters 1-6 and 11. Math 8202 discusses rings, modules, and field theory, covering these parts of the text: Chapters 7,8,9 on rings Chapters 10,12 on modules Chapters 13,14 on fields and if there's some extra time, dip into Chapters 15, 17 and/or 18. |
| Other useful texts and sources: |
Abstract Algebra: The basic graduate year, by R. Ash, a
text in PDF Abstract Algebra online, by J. Beachy, a set of HTML pages Advanced Modern Algebra by J. Rotman, Amer. Math. Soc. 2010 Algebra, by S. Lang, Addison-Wesley, 1993. Algebra, by T. W. Hungerford, Springer-Verlag, 2003 Algebra: A graduate course, by M. Isaacs, Amer. Math. Society, 2009. Algebra, by M. Artin, Prentice Hall, 1991 (a somewhat lower level book) 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. |
| Dept. written prelims: | 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 homework assignments due every two weeks on Wednesdays at the beginning of class; see table below for assignments. There should be a total of 6 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, posted later, each contributing 20% to the grade. There will be a take-home final exam, posted later, worth 25% of the grade. 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 | Videos |
|---|---|---|---|
| Homework 1 | Wed Feb. 5 |
7.1 # 14,15,25 7.2 # 3,4 7.3 # 2,4,29 (assume Exer. 25 holds),30,31 7.4 # 8,11,19,26,30,31,32 7.5 # 3 7.6 # 1,2,3,4,5 |
|
| Homework 2 | Wed Feb. 19 |
8.1 # 2(a),3,4,5(a),9,10 8.2 # 1,3,5 8.3 # 5,6,7,8(a) 9.1 # 5,7,9,13,14 9.2 # 1,2,4,7,8 |
|
| Midterm exam 1 | Wed Feb. 26 | Here is Midterm Exam 1 | |
| Homework 3 | Wed Mar. 18 |
13.1 # 1,5 13.2 # 3,7,8,12,14,16,18 13.4 # 1,2,3 (moved Sections 13.5, 13.6 to next HW) |
March 16 Zoom lecture on Sec. 13.4 |
| Homework 4 | Wed Apr. 1 |
13.5 # 7,8,9 13.6 # 3,4,5,6,9 14.1 # 4 14.2 # 4,5,11,13,17,18,31 |
March 18 Zoom lecture on Sec. 13.4 March 20 Zoom lecture (still!) on Sec. 13.4 March 23 Zoom lecture on Sec. 13.5 March 25 Zoom lecture on Sec. 13.6 March 27 Zoom lecture on Sec. 14.1 March 30 Zoom lecture on Sec. 14.1, 14.2 April 1 Zoom lecture on Sec. 14.2 April 3 Zoom lecture (still!) on Sec. 14.2 notes (batch 1) notes (batch 2) |
| Midterm exam 2 | Wed Apr. 8 | Here is Midterm Exam 2 | |
| Dept. algebra prelim written exam | Mon. Apr. 13 | Dept. prelims page |
Prelim practice (Mon. Apr. 13 lecture) Prelim practice (Wed. Apr. 15 lecture) Prelim practice notes |
| Homework 5 | Wed Apr. 22 |
14.3 # 3,5,10 14.4 # 2 (assume the extension degree is 8, as on Exam 2) 14.5 # 3,7,10 14.6 # 2 |
April 8 Zoom lecture on Sec. 14.3 April 10 Zoom lecture on Sec. 14.3 April 17 Zoom lecture on Sec. 14.4 April 20 Zoom lecture on Sec. 14.4 April 22 Zoom lecture on Sec. 14.6 April 24 Zoom lecture on Sec. 14.7 April 27 Zoom lecture on Sec. 14.7 notes (batch 3) notes (batch 4) |
| Homework 6 | Wed May 6 |
10.1 # 18,19,20 10.2 # 5 10.3 # 9,10,11 12.1 # 1,2,3,4,6 (removed Section 12.2 # 3,4,11,17,18, and 12.3 # 5,16,17,22,24,26) |
April 29 Zoom lecture on Secs 17. and 12.1 May 1 Zoom lecture on Sec. 12.1 May 4 Zoom lecture on Sec. 12.1 May 6 Zoom lecture on Secs. 12.2,12.3 notes (batch 5) |
| Final exam | Wed May 13 during finals week |
Here is the Final Exam. |