- Math 8201,
- MW 8:40 a.m. - 9:55 a.m. in Vincent Hall 1
- Math 4281 or equivalent
- Christine Berkesch Zamaere
- Office: Vincent Hall 254
- Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math8201" in the subject line.)
- Office hours:
- M 12:15 p.m. - 1:15 p.m., W 10:00 a.m. - 11:00 a.m., or by appointment (in Vincent Hall 254).
- Abstract Algebra by David S. Dummit and Richard M. Foote, Third Edition, John Wiley and Sons, Inc., 2004. (errata here)
- 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 8201-2, 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, some of Chapters 17-18
- Other useful texts:
- Abstract Algebra: The basic graduate year, by R. Ash, text in PDF
- Abstract Algebra online, by J. Beachy, 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, HTML page
- Expository papers, by K. Conrad, available here
- Tensor Spaces and Exterior Algebra, by T. Yokonuma, Amer. Math. Soc. 1992.
- The wiki page on group properties
- Peter Webb's materials on symmetry: a survey talk, notes on wallpaper patterns and group cohomology
- Written prelim preparation:
- One goal of this course is preparation for the Math PhD's program 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 are some practice problems from old prelims compiled by Vic Reiner that contain mostly material from the first semester course, that is, group theory and linear algebra.
- The course grade will be based on the homework, two midterms, and a
take-home final exam. These will be weighted as follows:
Homework 35% Midterm exams (x2) 20% each Final exam 25%
- Weekly problem sets are posted under homework below. Problem sets will be collected in class on Wednesday approximately every other week. Late homework will not be accepted, but early hard copy submission is permitted.
- All homework must be typed using LaTex. I am willing to provide a template to get you started.
- 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 problem or whole assignment with whom they have collaborated.
- There will be two in-class midterm exams. No collaboration, books, or technical aids are allowed for these exams.
- Final exam:
- There will be a take-home final exam due at the beginning of class on Wednesday, December 7. In contrast to the homework, on this exam there is to be no collaboration allowed with other humans. In contrast to the midterms, this is an open book, library, web, and notes exam; however, outside sources must be cited in order to receive full credit.
- Students with disabilities, who will be taking this course and may need disability-related accommodations, are encouraged to make an appointment with me as soon as possible. Also, please contact UMN's Disability Services to register for support.
September 7 First Math 8201 meeting October 12 Midterm 1, in class (over material covered by end of lecture on Friday, 10-07) November 16 Midterm 2, in class (over material covered by end of lecture on Friday, 11-11) November 28 Final exam released December 5 Final exam due at start of class December 14 Last Math 8201 class meeting
- Remember that all homework must be typed using laTex and you
should indicate when and with whom you have collaborated on each
problem or the whole assignment. Please check back, as these
assignments are subject to change.
Due date Assignment Wednesday, September 21 Problem Set 1:
1.1 # 9, 25
1.3 # 15, 18
1.4 # 11
1.6 # 4, 6, 18
1.7 # 21, 23
2.1 # 6, 7
2.2 # 7, 10
2.3 # 5, 16, 23
2.4 # 11, 14, 15, 19
2.5 # 8
Wednesday, October 5 Problem Set 2:
3.1 # 14, 25, 36, 42
3.2 # 9, 10, 18, 21, 23
3.3 # 3, 8, 9, 10
3.4 # 5
Wednesday, November 2 Problem Set 3:
4.1 # 1, 2, 3
4.2 # 7, 9
4.3 # 6, 30
4.4 # 7, 8(a,b), 9, 16
4.5 # 13, 16, 30, 33, 34
5.1 # 5
5.4 # 15
5.5 # 8
6.3 # 4
Monday, November 21 Problem Set 4:
11.1 # 6, 7, 8, 9
11.2 # 9, 11, 12, 36, 37
11.3 # 2, 4
11.4 # 6
Wednesday, December 14 Problem Set 5:
11.5 # 13
7.1 # 5, 12, 14, 26
7.2 # 5
7.3 # 4, 13, 17, 26, 28