MATH 323 Rings and Modules.

MATH 323. Rings and Modules.

Text: Dummit and Foote, "Abstract Algebra".

Section 201, Instructor: Julia Gordon.

Where: MATH 103 (please note the room change).
When: Tue, Th 9:30-11am.
My office: Math 217.
e-mail: gor at math dot ubc dot ca
Office Hours: by appointment.


Review materials for the final exam


There will be weekly homework assignments, posted here every Wednesday, and due the following Thursday.
  • Acknowledgement: Thanks to Shamil Asgarli for writing up solutions to most of the homework problems that will be posted here.
  • Problem set 1 (due Thursday January 16). Solutions.
  • Problem Set 2 (due Thursday Jan. 23). Solutions.
  • Problem Set 3 (due Tuesday Feb. 4). Solutions.
  • Problem Set 4 (due Thursday Feb. 6). Solutions.
  • Problem set 5 (due Thursday, February 14): Section 8.1: problem 10; Section 8.2: problems 1,3,5; Section 8.3: problem 8. Solutions
  • Problem Set 6 (due Tuesday Feb. 25): Section 9.1: Problems 4,6,13, 18; Section 9.2: Problems 1,3,5,8. Solutions.
  • Problem Set 7 (Due Tuesday March 11) -- see the list below:
    • Section 13.1: Problems 1, 3. Also recommended (but not to be written up): problems 2,5, 6,7 from this section.
    • Section 9.4: Problems 1, 2(except b), 6(a,b,c only), 9;
    • Section 9.5: Problems 3. (Also recommended, but not to be written up, is problem 2 -- note that it refers to problem 6 from 9.4, so it makes sense to do these two together).
    • Solutions.
  • Problem Set 8 (Due Tuesday March 18)
    Also recommended but not to be handed in: Secion 10.1, proplems 3, 12, and 15-19. Solutions .
  • Problem set 9 (due Thuesday April 1). Solutions .
  • Propblem set 10 If you want to turn it in, please do so by Tuesday April 8. This problem set is optional -- if you turn in some of the problems, you get extra credit towards homework score, but you do not have to turn it in. Note also a related an elementary Pick's Theorem .
    Solutions. Picture for Problem 3 .

  • Extras

    This is just a loose collection of extra porblems (some hard, some easy) that can be used for review and general curiosity; also some links to things related to, but not covered in the course. Please do not hand in any of these problems. Many problems and links that will appear in this section were communicated to me by Shamil Asgarli.
  • Some number-theoretic extra problems. Solutions . For the discussion of Problem 4, please see this post at Keith Conrad's page (see also the discussion of cyclotomic polynomials in Section 7).
    For notes on Cyclotomic polynomials, see A note on cyclotomic polynomials by Paul Garrett.
  • Some extra problems on Chapter 7. Solutions will be posted here during the break.
  • Here is a general proof that there are 11 rings of order p^2, for a prime p. Later we will recognize some of these rings as quotients of polynomial rings.
  • Notes on Euclidean domains by Keith Conrad (also optional reading). Contains the proof of the example of a PID that is not Euclidean.
  • The optional problem set on Pell's equation (i.e. on units in quadratic integer rings with D>0).

  • Review materials for the midterm (still relevant for the final)

  • The list of topics for the midterm . (I think the best way to use the list is look at the items with closed book, try to recall all the relevant definisions, facts, proofs, and examples, and if any of this is causing difficulty, then read the relevant section again).
  • Last year's midterm . Do not read the solutions, try the problems yourself! Use the solutions only to check your work. Solutions .

  • Detailed Course outline

    Short descriptions of each lecture and relevant additional references will be posted here as we progress. All section numbers refer to Dummit and Foote.