| 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 209. |
| Office hours: | Mon and Wed 8:00-8:50am and Thur 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: |
Math 8201-8202 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, do a tiny bit of Chapters 15 or 17 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) Some multilinear algebra resources: How to lose your fear of tensor products, by T. Gowers, an HTML page The tensor product demystified, by Tai-Danae Bradley, a nice blog Expository papers, by K. Conrad, blurbs Multilinear algebra, by D.G. Northcott, our library link Tensor Spaces and Exterior Algebra, by T. Yokonuma, Amer. Math. Soc. 1992 The Wikipedia page on group properties Peter Webb's materials on symmetry: a survey talk, notes on wallpaper patterns and group cohomology |
| 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. 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 Wednesdays at the beginning of class; see table below for assignments. There should be a total of 5 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 |
|---|---|---|
| Homework 1 | Wed Sept 25 |
1.1 # 9, 25,31 1.2 # 17 1.3 # 15,18 1.4 # 11 1.6 # 4,5,6,7,18 1.7 # 21,23 2.1 # 6,7,16 2.2 # 7,10 2.3 # 5,15,16,23 2.4 # 11,13,14,15,19 2.5 # 8 |
| Homework 2 | Wed Oct 9 |
3.1 # 14, 25, 36, 42 3.2 # 9, 10, 18, 21, 23 3.3 # 3, 8, 9, 10 3.4 # 5 |
| Midterm exam 1 | Wed Oct 16 | Here is Midterm Exam 1. |
| Homework 3 | Wed Oct 30 |
4.1 # 1,2,3 4.2 # 7,9 4.3 # 17,25,30 (removed #6 which makes no sense!) 4.4 # 7, 8(a,b), 9, 16 4.5 # 13, 16, 30, 33, 34 5.1 # 5 5.4 # 2, 8, 15 5.5 # 8 6.3 # 4 |
| Homework 4 | Wed Nov 13 |
11.1 # 6,7,8,9 11.2 # 9, 11, 12, 36, 37 11.3 # 2,4 11.4 # 6 +Exercise 2 from these extra linear algebra exercises |
| Midterm exam 2 | Wed Nov. 20 | Here is Midterm Exam 2. |
| (Homework 5) | (Wed Dec. 4) |
We removed this homework entirely, partly due to a snow day: Exercises 1,3,5,6,7 from these extra linear algebra exercises Exer. 11.5 from book However, we will discuss it, along with some prelim practice problems, at an extra meeting on Study Day, Thursday Dec. 12, 9:05am-noon, in our usual room (VinH209). |
| Final exam | Wed Dec. 11 | Here is the Final Exam |