Mathematics 322, Introduction to algebra,
Section 101.
SeptemberDecember 2013, Leonard S. Klinck Building, rm. 460,
TuTh 14:0015:30

Instructor :
Zinovy Reichstein
Office: 1105 Math Annex
Phone: 8223929
Email: reichst at math.ubc.ca
Textbook : Joseph Gallian,
Contemporary Abstract Algebra,
8th edition.
Course description :
Math 32223 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.

Preliminaries on integes, congruences, sets, maps and equivalence relations.

Definition and first properties of a group,

Cyclic and permutation groups.

Subgroups, cosets, and Lagrange's Theorem.

Homomorphisms, normal subgroups, quotients,
and simple groups.

Group actions, pgroups and Sylow theorems.

Finite abelian groups.
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 2327. 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 2327. Problems 58, 64
Pages 5458. Problems 22, 30, 36, 50. In problem 50 "multiple of 5" should
read "multiple of 4".
Pages 6875. Problems 4, 16, 48, 80
Solutions to Problem Set 2
Problem Set 3. Due in class Tuesday, October 8.
Pages 8792. Problems 8, 14, 22, 30.
Pages 118123. Problems 2, 8, 24, 28, 32, 46.
Solutions to Problem Set 3
Problem Set 4. Due in class Tuesday, October 29.
Pages 138142. Problems 2, 4, 12, 36.
Pages 156160. 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 156160. Problems 52, 56.
Pages 200205. 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 421425. Problems 8, 10, 18, 20, 26, 36, 46, 54
Solutions to Problem Set 6
Problem Set 7. Due in class Thursday, November 28.
pp. 234236. Problems 2, 4, 8, 10, 12, 22, 24, 30.
p. 238239. 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