Lectures:
MW 8:40 a.m. - 9:55 a.m. in Vincent Hall 207
Prerequisites:
Math 8201 or equivalent
Instructor:
Christine Berkesch
Office: Vincent Hall 254
Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math8202" 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   40%
Midterm exam   25%
Final exam   35%
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.
Midterm and final exams:
There will be one take-home midterm and a take-home final exam. 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.
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.


January 23   First Math 8202 meeting
March 6   Midterm released
March 27   Midterm due at start of class
April TBA   Department algebra prelim written exam
April 22   Final exam released
May 6   Last Math 8202 class meeting
May 9   Final exam due at 10 a.m. by email


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, February 6 Problem Set 1:
    7.4 # 8, 11, 15, 19, 26, 37
    7.5 # 3
    7.6 # 1, 2
    8.1 # 2(a), 3, 5(a), 9
Wednesday, February 20 Problem Set 2:
    8.2 # 5
    8.3 # 5, 8(a)
    9.1 # 13, 14
    9.2 # 4, 7
    10.1 # 8, 12, 18, 20
    10.2 # 5, 8, 13
Wednesday, March 6 Problem Set 3:
    10.3 # 5, 9, 10, 11
    12.1 # 4, 6
    12.2 # 4, 11, 18
    12.3 # 16, 17, 26, 32
Monday, April 10 Problem Set 4:
    13.1 # 1
    13.2 # 3, 8, 12, 14, 16, 18
    13.4 # 1, 2, 3
    13.5 # 7, 9
Wednesday, May 1 Problem Set 5:
    13.6 # 3, 4, 9
    14.2 # 3, 11, 17, 18, 29, 31
    14.3 # 5, 10
    14.6 # 2


Links

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