Instructor: Dr. D. Haskell, HH316, ext.27244
Course meeting time: TWF 12:30  13:20
Email: haskell@math.mcmaster.ca
Office hours: M 13:0014:00, W, F 11:0012:00
Course requirements, in brief (consult the course
information sheet for more detailed information).
Homework: 15%
Essay: 5%
Midterm I: 20%
Midterm II: 20%
Final: 40%
ANNOUNCEMENTS
Thursday,
December 16. Final exams are
graded. If you want to drop by in the next few days, you can have a
look at your exam.
Change
to office hours: because of another event scheduled on Friday
morning, I have to move my office hours to Thursday afternoon,
13:0015:00. My apologies for this change.
Homework solutions are posted (see below).
FINAL EXAM: Saturday, Dec 11,
7:3010:30
One of the following two proofs will
be on the exam: Theorem 6.1Cayley's Theorem or Theorem 9.5Cauchy's
theorem for abelian groups. You should work through these proofs from
the text, organising them into the main steps, and remember the main
steps. If you produce a reasonable sketch of the argument, but are not
able to fill in the details for the final exam, you will still get most
of the marks. Otherwise, the exam will be very similar to the midterms.
REVIEW SESSION: Thursday, Dec 9,
10:0012:00 in HH109
Revised: see above. OFFICE HOURS: Friday,
Dec 10, 10:0012:00 (these may get postponed until later in the day)
Nov 29: REVISIONS to Homework 6. The
problems from Chapter 24 will be considered extra credit. You have until
Friday, December 3 to hand them in. Note that this material WILL be
considered fair game for the final exam.
Nov 29: Homework 5 solutions are posted
Nov 8 Homework 3 and 4 solutions are
posted.
Confirmed: Midterm II will be on Friday,
November 19.
Oct 25 The calendar has been
revised. Homeworks 46 have been revised. Homework 3 solutions will be
posted shortly.
Solutions to Homework 2 are posted below.
Oct 11: REVISED midterm 1 date is
Wednesday, 20 October (just as well, since Tuesday the 18th did not
exist). This was agreed to in class last week; sorry for the delay
in posting.
MIDTERM 1 will be on Tuesday, 18 October. It will cover chapters 1
through 5 of the textbook, and material from chapter 0 that we have
covered. You must KNOW definitions. You do not need to be able to quote
most theorems, but should be able to apply them in problems.
Solutions to Homework 1 are posted below.
The due date for Homework 2 is postponed to Wednesday, 6 October 2004.
Assignment dates and midterm
dates are still tentative. Actual test dates and assignment due dates
will be announced in class and posted on this website at least two weeks
in advance.
Homework 1: ch 0: p.
23: 8, 26
ch 2: 6, 28, 14
DUE 21 September 04
Homework 1 Solutions
Homework 2: ch 3: p. 67: 4, 12, 34, 48
ch 4: p.
82: 30, 40, 42
DUE 5 October 04
Homework 2 Solutions
Homework 3: ch 5: p.111:
26, 34, 36
ch 6: p. 129: 24, 26
DUE 19 October 04
Homework 3 Solutions
Homework 4
(revised): ch 6: p. 129:
10, 22, 30
ch 7: p. 145: 16, 22, 38, 46
DUE 2 November 04
Homework 4 Solutions
Homework 5
(revised): ch 8: p. 162: 8, 24
ch 9: p. 186: 10, 26, 36, 42
DUE 16 November 04
Homework 5 Solutions
Homework 6 (revised): ch 10: p.
205: 16, 36, 42, 46
EXTRA CREDIT (may be handed in up to
last day classes) ch 24: p 407: 20, 24, 30, 38
DUE 30 November 04
Homework 6 Solutions
Homework 7 (=extra credit) Solutions
Planned
course schedule (subject to revision):
Dates 
Tuesday  Wednesday  Friday  Recommended (extra) problems  Challenge Problems 
Sept 610 
NO CLASS 
NO CLASS  introduction, ch 1: symmetries of triangle 
Chapter 0 p. 23 11, 27 
p23 18, 19 
Sept 1317  class discussion: symmetry groups read ch 1 p. 39: 1322 modular arithmetic, Z_5 
ch 0: euclidean algorithm, induction 
class discussion: induction p. 24: 20, 21 25 ch 2: defn of group, examples 
Chapter 2 p. 53 9, 15, 23 
p53 33 
Sept 2024 
ch 2: elementary properties of groups ch 3: order of element HOMEWORK 1 DUE ch 0: p. 23: 8, 26 ch 2: 6, 28, 14 
ch 3: subgroup tests 
class discussion: group defn, order read chs 2 and 3 p53: 1, 7, 16, p 67: 1, 2, 3 ch 3: examples of subgroups 
Chapter 3 p. 67 8, 9, 17 
p67 52 
Sept 27 Oct 1 
ch 4: cyclic groups; elem properties 
ch 4: classification of subgroups of cyclic groups, 
class discussion: cyclic groups read ch 4 p82 8, 13, 18, 21 ch 4: corollaries 
Chapter 4 p. 82 2, 4, 5, 6, 15 
p82 61, 64 
Oct 48 
ch 0: functions HOMEWORK 2 DUE ch 3: p. 67: 4, 12, 34, 48 ch 4: p. 82: 30, 40, 42 
ch 5: permutations, cycle notation, products of cycles  class discussion: cycles read ch 5 p. 111: 2, 3, 9, 14, 15 ch 5: rotation group 
Chapter 5 p. 111 7, 19, 31 
p111 50 
Oct 1115  ch 6: defn and exs of isomorphisms  catchup day 


Oct 1822 
ch 6: properties of isomorphisms HOMEWORK 3 DUE ch 5: p.111: 26, 34, 36 ch 6: p. 129: 24, 26 
MIDTERM I (actual date) 
ch 6:
automorphisms 
Chapter 6 p. 129 25, 27, 29, 37 
p129 41, 42, 43 
Oct 2529 
ch 6: Cayley's theorem ch 0: equivalence relations 
class discussion: exs of isomorphisms read ch 6 p. 129: 1, 2, 4, 5, 12 ch 7: cosets, Lagrange's thm 
ch 7: orbit/stabiliser 
Chapter 7 p. 145 7, 9, 12, 25 
p145 36 p165 60 
Nov 15 
HOMEWORK 4 DUE ch 6: p. 129: 10, 22, 30 ch 7: p. 145: 16, 22, 38, 46 
class discussion: equiv relns, cosets read ch 7 p. 25: 46, 47, 48, 49 p. 145: 4, 5, 6 ch 8: external direct products 
ch 8: U(n) as product ch 9: normal subgroups: defn and exs 
Chapter 8 p. 162: 7, 11, 13, 15, 25, 34 
p186 55, 64, 68 
Nov 812 
ch 9: factor groups  class discussion: playing with factor groups read ch 9 p. 186: 1217, 22 ch 9: applications, internal direct products 
ch 10: homomorphisms: defn and exs, 
Chapter 9 p. 186 5, 7, 8, 23 

Nov 1519 
ch 10: properties of homomorphisms HOMEWORK 5 DUE ch 8: p. 162: 8, 24 ch 9: p. 186: 10, 26, 36, 42 
class discussion: playing with homoms read ch 10 p. 205: 5, 6, 8, 10, 14, 19 ch 10: homom thms 
MIDTERM II (actual date) chs 69 
Chapter 10 p. 205 3, 15, 31 
p205 50, 52 
Nov 2226 
ch 8: RSA encryption  ch 24: conjugacy classes, class eqn  class discussion: conjugacy classes read ch 24 p. 407: 1, 3, 4, 48 ch 24: Sylow theorems ESSAY DUE 
Chapter 24 p. 407 15, 17, 28 
p407 36, 42 
Nov 29Dec 3 
ch 24: applications HOMEWORK 6 DUE ch 10: p. 205: 16, 36, 42, 46 ch 24: p 407: 20, 24, 30, 38 
conclusions  class discussion: conclusions 