Instructor: Dr. D. Haskell, HH316, ext.27244
Course meeting time: TWF 12:30 - 13:20
E-mail: haskell@math.mcmaster.ca
Office hours: M 13:00-14:00, W, F 11:00-12:00
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,
13:00-15:00. My apologies for this change.
Homework solutions are posted (see below).
FINAL EXAM: Saturday, Dec 11,
7:30-10:30
One of the following two proofs will
be on the exam: Theorem 6.1-Cayley's Theorem or Theorem 9.5-Cauchy'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,
10:00-12:00 in HH109
Revised: see above. OFFICE HOURS: Friday,
Dec 10, 10:00-12:00 (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 4-6 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 6-10 |
NO CLASS |
NO CLASS | introduction, ch 1: symmetries of triangle |
Chapter 0 p. 23 11, 27 |
p23 18, 19 |
| Sept 13-17 | class discussion: symmetry groups read ch 1 p. 39: 13-22 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 20-24 |
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 4-8 |
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 11-15 | ch 6: defn and exs of isomorphisms | catch-up day |
|
||
| Oct 18-22 |
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 25-29 |
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 1-5 |
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 8-12 |
ch 9: factor groups | class discussion: playing with factor groups read ch 9 p. 186: 12-17, 22 ch 9: applications, internal direct products |
ch 10: homomorphisms: defn and exs, |
Chapter 9 p. 186 5, 7, 8, 23 |
|
| Nov 15-19 |
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 6-9 |
Chapter 10 p. 205 3, 15, 31 |
p205 50, 52 |
| Nov 22-26 |
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 29-Dec 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 |