Second Course in Abstract Algebra, MATH 516, Fall 2010

Instructor: Daniel Groves, 538 SEO e.mail

Course webpage: http://www.math.uic.edu/~groves/teaching/2010-11/516/

Course hours:

MWF, 2:00-2:50AM, Room 203, Stevenson Hall.

Office hours:

MW 1pm (You can always make an apointment by e.mail or try stopping past my office.)

Text: "Abstract Algebra" by Dummit and Foote.

The current edition is the third. However, if you can find the second edition on the cheap, this should be fine for you. (Let me know and I can translate exercise numbers)

Course description:
The plan is to cover most of the material in Chapters 1 - 12 of Dummit and Foote.
This may prove to be too ambitious, in which case the plan will be revised along the way.
This is a second course in abstract algebra, so it would be good if you knew about groups, rings and fields already, as well as things like homomorphisms, subgroups (subrings, etc.), kernels, quotients. However, I will start from scratch so this is not absolutely necessary. (I'll just go quite quickly through the basic material.)
You should also know about things like equivalence relations, and the material in Chapter 0 of Dummit and Foote.

Assessment: Homework sets will be due approximately every two weeks, starting Wednesday, August 8 (Monday August 6 is Labor Day and there is no class). (In weeks when homework is not due, exercises will be set that you should attempt. Of course, in an ideal world you would do all of the exercises in Dummit and Foote...)
There will be a take home final exam, and possibly a take home midterm.
The relative weightings of these items will be discussed in class.

Homework sets:
  • Week 1 (not for turning in): Dummit and Foote. Chapter 1.2 #5, #9, #10, #11, #12, #13. Chapter 1.3: #10, #14, #15, #18, #19. Chapter 1.4: #1, #2, #3, #5, #6, #10, #11.

  • Week 2. Due Wednesday, September 8, at the beginning of class: Dummit and Foote. Chapter 1.7, #8, #9, #10. Chapter 2.2, #12. Chapter 3.5, #2, #12. Chapter 4.1, #7, #8.

  • Week 3 (not for turning in): Dummit and Foote. Chapter 1.6, #5, #6, #9, #19, Chapter 2.4, #14, #15. Chapter 3.1, #2, #11, #14. Chapter 6.3, #2, #5, #6, #11.

  • Week 4. Due Monday, September 20, at the beginning of class: Dummit and Foote. Chapter 2.2, #5, #14, Chapter 2.3, #15, #18, #25, Chapter 3.1, #41.

  • Week 5 (not for turning in): Dummit and Foote. Chapter 3.3, #3, #8, #9. Chapter 3.4, #4, #5, #11. Chapter 4.6, #1, #5, #6.

  • Week 6. Due Monday, October 4, at the beginning of class: Dummit and Foote. Chapter 4.2, #11, #12. Chapter 4.4, #1, #7. Chapter 4.5, #8, #18, #19, #20.

  • Week 7 (not for turning in): Dummit and Foote. Chapter 5.1, #10, #17, Chapter 5.5, #1, #2, #8, #9, #15, #18, Chapter 6.1, #7, #16, #25.

  • Week 8. Due Monday, October 18, at the beginning of class: Dummit and Foote. Chapter 7.1, #5, #6, #13, #14, #23, #24.

  • Week 9 (not for turning in): Dummit and Foote. Chapter 7.1, #26, #27, Chapter 7.2, #3, #4, #5, Chapter 7.3, #6, #10, #11, #13, #18, #19, #26

  • Week 10. Due Monday, November 1, at beginning of class: Dummit and Foote. Chapter 7.4, #15, #30, #31, Chapter 7.5, #5, Chapter 7.6, #3, Chapter 8.1, #4, #6.

  • Week 11 (not for turning in): Dummit and Foote. Chapter 8.1, #9, #11, Chapter 8.2, #1, #3, #8, Chapter 8.3, #1, #8, Chapter 9.1, #4, #5, #6, #14, Chapter 9.2, #5.

  • Week 12. Due Monday, November 15, at the beginning of class: Dummit and Foote. Chapter 9.2, #7, Chapter 9.3, #4, Chapter 9.4, #2, #9, Chapter 9.5, #3, Chapter 10.1, #8, #15, Chapter 10.2, #8.

  • Week 13 (not for turning in): Dummit and Foote. Chapter 10.2, #9, #10, Chapter 10.3, #4, #5, #11, Chapter 10.4, #2, #4, #5, #8, #9.

  • Week 14. Due Monday, November 29, at the beginning of class: Dummit and Foote. Chapter 10.4, #12, #18, #20, #24. Chapter 10.5, #3, #6, #10, #27.

  • Take home final. Due Friday, December 10, 2pm.

    No collaboration is allowed on the final. You may refer to Dummit and Foote, but no other sources other than lecture notes and homework assignments. You may refer to results proved in the main text of Dummit and Foote, or in lectures, and you may refer to exercises from Dummit and Foote which were assigned during the semester (whether or not they were turned in for grading, and whether or not you successfully answered them), but no other results unless you prove them. You should give specific references for results you assume in this way.

    Questions for the final:
    Dummit and Foote. Chapter 3.2, #19. Chapter 4.2, #14. Chapter 4.3, #30 Chapter 5.5, #10. Chapter 6.1, #22. Chapter 7.4, #37. Chapter 8.3, #5. Chapter 9.5, #7. Chapter 10.3, #15. Chapter 10.5, #28.