Lectures:
MW 8:40 a.m. - 9:55 a.m. in Vincent Hall 207
Prerequisites:
Math 4281 or equivalent
Instructor:
Christine Berkesch
Office: Vincent Hall 254
Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math8201" in the subject line.)
Office hours:
M 10:00 a.m. - 11:00 a.m. or by appointment (in Vincent Hall 254).
Textbook:
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.


Assessment:
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%
Homework:
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.
Midterms:
There will be two take-home midterm exams. In contrast to the homework, these exams allow no collaboration allowed with other humans besides your instructor. These are open book, library, web, and notes exam; however, outside sources must be cited in order to receive full credit. Your solutions do not need to be typed, but they should be written neatly.
Final exam:
There will be a take-home final exam due at the beginning of class on Wednesday, December 12. In contrast to the homework, on this exam there is to be no collaboration allowed with other humans besides your instructor. 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. Your solutions do not need to be typed, but they should be written neatly.
Disabilities:
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 5   First Math 8201 meeting
October 3   Midterm 1 released
October 10   Midterm 1 due at the start of class
November7   Midterm 2 released
November 16   Midterm 2 due at the start of class
November 28   Final exam released
December 12   Final exam due at start of class
December 12   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 19 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 3 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, October 24 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 7 Problem Set 4:
    11.1 # 6, 7, 8, 9
    11.2 # 9, 11, 12, 36, 37
    11.3 # 2, 4
    11.4 # 6
Wednesday, November 28 Problem Set 5:
    11.5 # 13
    7.1 # 5, 12, 14, 26
    7.2 # 5
    7.3 # 4, 13, 17, 26, 28


Links

Christine Berkesch  ***  School of Mathematics  ***  University of Minnesota