- Math 8202,
General Algebra
- Lectures:
- MW 8:40 a.m. - 9:55 a.m. in Vincent Hall 301
- Prerequisites:
- Math 8201 or equivalent
- Instructor:
- Christine Berkesch Zamaere
- 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 a.m. - 11:15 p.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 8202 is the second semester of 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:
- 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.
- Final exam:
- There will be a take-home final exam due (under the door of Vincent 254) at 10 a.m. on Wednesday, May 10. It does NOT need to be typed. Like the midterms, this is an open book, library, web, and notes exam; however, outside sources must be cited in order to receive full credit.
- 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 18 First Math 8202 meeting February 15 Midterm 1 released February 22 Midterm 1 due at start of class March 22 Midterm 2 released March 29 Midterm 2 due at start of class April 17 Department algebra prelim written exam April 26 Final exam released April 26 Last Math 8202 class meeting May 10 Final exam due at 10 a.m. under door of Vincent 254
- 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 1 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), 9Wednesday, February 15 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, 13Wednesday, March 8 Problem Set 3:
10.3 # 5, 9, 10, 11
12.1 # 4, 6
12.2 # 4, 11, 18
12.3 # 16, 17, 26, 32Monday, March 22 Problem Set 4:
13.1 # 1
13.2 # 3, 8, 12, 14, 16, 18
13.4 # 1, 2, 3
13.5 # 7, 9Wednesday, April 12 Problem Set 5:
13.6 # 3, 4, 9
14.2 # 3, 11, 17, 18, 29, 31
14.3 # 5, 10
14.6 # 2
Links