Mathematics 322, Introduction to algebra, Section 101.
September-December 2013, Leonard S. Klinck Building, rm. 460, TuTh 14:00-15:30

  • Textbook : Joseph Gallian, Contemporary Abstract Algebra, 8th edition.
  • Course description : Math 322-23 is UBC's undergraduate honours abstract algebra sequence. Math 322 is devoted entirely to group theory, with an emphasis on finite groups. The topics I plan to cover are as follows.

    If time permits, I may cover additional topics from the text at the end of the term.

  • Evaluation : Homework assignments will be posted on the course website and collected in class. Late homework will not be accepted. The solutions you turn in should be your own, written in your own words. There will be two midterms and a final exam. The midterms are scheduled for Thursday, October 10 and Thursday, November 7. The final exam is scheduled for 7pm on Wednesday, December 18, in BUCH A202. I will compute the total term mark in two ways,

    Total 1 := Homework (20%) + Midterm 1 (20%) + Midterm 2 (20%) + Final exam (40%), and

    Total 2 := Homework (20%) + Best midterm (20%) + Final exam (60%).

    I will use whichever of these two numbers is higher.

    Midterm 1, with solutions

    Practice Problems for Midterm 2, with solutions

    Midterm 2, with solutions

    Final exam syllabus

    2012 Math 322 final exam

    Solutions to the 2012 Math 322 final exam

  • Students with disabilities : Students with documented disabilities who may need special accommodations should make an appointment with me early in the term.
  • Homework assignments

    Problem Set 1. Due in class Thursday, September 19.
    Pages 23-27. Problems 4, 11, 14, 16, 18, 26, 36, 50, 54, 62

    Solutions to Problem Set 1

    Problem Set 2. Due in class Tuesday, October 1.
    Pages 23-27. Problems 58, 64
    Pages 54-58. Problems 22, 30, 36, 50. In problem 50 "multiple of 5" should read "multiple of 4".
    Pages 68-75. Problems 4, 16, 48, 80

    Solutions to Problem Set 2

    Problem Set 3. Due in class Tuesday, October 8.
    Pages 87-92. Problems 8, 14, 22, 30.
    Pages 118-123. Problems 2, 8, 24, 28, 32, 46.

    Solutions to Problem Set 3

    Problem Set 4. Due in class Tuesday, October 29.
    Pages 138-142. Problems 2, 4, 12, 36.
    Pages 156-160. Problems 10, 12, 26, 34, 38, 48. In Problem 10, HK is defined as { hk | h in H and k in K}.

    Solutions to Problem Set 4

    Problem Set 5. Due in class Tuesday, November 5.
    Pages 156-160. Problems 52, 56.
    Pages 200-205. Problems 6, 14, 38, 52, 62, 64, 70, 78.
    Extra credit Problem: Generalize the assertion of Problem 70 from S_4 to S_n by showing that A_n is the only subgroup of S_n of index 2.

    Solutions to Problem Set 5

    Problem Set 6. Due in class Thursday, November 21.
    Pages 421--425. Problems 8, 10, 18, 20, 26, 36, 46, 54

    Solutions to Problem Set 6

    Problem Set 7. Due in class Thursday, November 28.
    pp. 234--236. Problems 2, 4, 8, 10, 12, 22, 24, 30.
    p. 238--239. Problems 24.
    Problem A: Let G = Z_{360} x Z_{300} x Z_{200} x Z_{150}.
    (a) Find the elementary divisors of G.
    (b) Find the invariant factors of G.
    (c) Find the orders of the torsion subgroups G[2], G[3], and G[5].

    Solutions to Problem Set 7