Math 427 (Rezk, 1:00 MWF, Section G, 147 Altgeld).
Office hours
See my homepage.
Resources
The primary book for the course will be:
Other useful resources include:
This course is now on Illinois
Compass. Grades are posted there.
I have created a Facebook discussion
group, Math
427 Fall 2009, for the course. This is a public group.
Syllabus
The orgainization of the course is
described here.
Reading and assignments
- Monday 24 August. First day.
- Wednesday 26 August. Read Ash sections I.1 and I.2.
Daily problems I.1 #6 and I.2 #2. (Also look at D&F sections I.1,2,3, if you
have it.)
- Friday 28 August. Read Ash section I.3. (Also look at D&F
section I.6.)
PS1 due.
- Monday 31 August. Read D&F I.4,5,6. Daily problems D&F I.6 #4,
#11, #18.
- Wednesday 2 September. Read D&F I.7. Daily problems D&F I.7 #2,
16, 17.
- Friday 4 September. Read D&F II.1, II.2.
PS2 due (D&F I.4: 11; I.6: 6, 20, 23, 24; I.7: 6, 14, 15, 18). [You
don't have to do I.7 #16 twice.]
- Wednesday 9 September.
Read D&F II.3, II.4. Daily problems D&F II.1: 2; II.2: 3; II.3: 11; II.4: 9.
- Friday 11 September. Read D&F II.5. PS3 due (D&F II.1: 11, 14; II.2: 2, 7,
8, 14; II.3: 21, 22, 23, 25, 26; II.4: 7, 12).
- Monday 14 September. Read D&F III.1. Do problems D&F
II.5: 11; III.1: 11.
- Wednesday 16 September. Read D&F III.2. Do problems D&F
III.1: 31, III.2: 8.
- Friday 18 September. Read D&F III.3.
PS 4 due (D&F II.5: 4; III.1:
3, 6, 9,18; III.2: 5, 6).
- Monday 21 September. Look at D&F VI.3. Do problem D&F
III.3: 3. Handout on free groups.
- Wednesday 23 September. Do the following problem: Let G be
a group, let R be a subset of G, and let S={ grg-1| g in G,
r in R}. Show that the subgroup <S> of G generated by S is a normal
subgroup.
- Friday 25
September. Read D&F
III.4. PS5 due
(changed, Wed 23 Sep; last problem revised).
- Monday 28 September. Read D&F III.5, IV.1, and IV.2. Do
problem IV.1 #2.
- Wednesday 30 September. Do problem IV.2 #2.
- Friday 2
October. Handout on orthogonal
groups.
PS6 due.
(Fixed typo 28 Sept: definitions of Ra and
Fa in (5) were reversed.) Here is
a description of the solution
for the last problem on PS6, together with some additional comments.
- Monday 5 October. Read D&F IV.3. Do problem IV.3 #5.
- Wednesday 7 October. Read D&F IV.4. Do problem IV.4 #3.
- Friday 9 October. PS7 due (D&F III.1 #36,
IV.2 #11,12,13, IV.3 #2, 6, 19, IV.4 # 1, 13).
- Monday 12 October. Read D&F IV.5. Do problem IV.5 #4.
Here are notes on the Sylow theorems.
- Wednesday 14 October. Do problem IV.5 #32.
- Friday 16 October. Read D&F V.1. PS8 due (IV.5 #7, 8, 13,
18, 24, 26,
34, 35; V.1 #4, 10.)
- Monday 19 October. Read D&F V.2. Problem: Let A be a
finite abelian group of order n with exponent m. Use the
classification of finite abelian groups to show that m=n if
and only if A is cyclic.
- Wednesday 21 October. Read D&F V.5. Do problem V.5 #3.
- Friday 23 October. PS9 due (D&F V.2 # 1; V.5 # 1, 5, 6, 7,
8.)
- Monday 26 October. Read D&F VII.1. Do problems VII.1 # 3,
11.
- Wednesday 28 October. Read D&F VII.2. Do problem VII.2 #9.
- Friday 30 October. Read D&F VII.3. PS 10 due (D&F VII.1 #
5, 7, 8, 13, 14; VII.2 # 12, 13.)
- Monday 2 November. Read D&F VII.4, VII.6. Do problems
VII.4 #8, 15.
- Wednesday 4 November. Read D&F VIII.1, VIII.2. Do problem VIII.2 #3.
- Friday 6 November. Read VIII.3. Midterm
due (revised 10/24, 10/28, 10/30).
- Monday 9 November. Read VIII.3. Skim IX.1-5. Do problems
IX.2 #7 and IX.4 #4.
- Wednesday 11 November. Read XIII.1. Do problem XIII.1
#1.
- Friday 13 November. Read XIII.2. PS11 due (D&F VII.3 #7,
12, VIII.3 #5, IX.2 #4, IX.4 #1, 3.)
- Monday 16 November. Do problems XIII.2 #4, 7.
- Wednesday 18 November. No daily problem today.
- Friday 20 November. Read XIII.4. PS12 due (D&F XIII.2 #8, 9, 10, 18,
19. 20. 21.)
- Monday 30 November. Read XIII.5. Do problem XIII.4 # 2.
- Wednesday 2 December. Do problem XIII.5 #2.
- Friday 4 December. PS13 due (D&F XIII.4 # 3, 4, 5; XIII.5 #
5, 7; XIV.1 # 1, 5.)
- Monday 7 December. Read XIV.1, XIV.2. No daily problem.
- Wednesday 9 December. No daily problem.
- Friday 18 December. Final exam
due. (I've corrected typos in statements of 4d and 9.) Here are
solutions to the final. Have
a good break!
Contact info.
email:
office: Illini Hall 242
office hours: Check here.
Last modified 21 December 2009
by Charles Rezk.