Math 427 (Rezk, 1:00 MWF, Section G, 147 Altgeld).

Office hours

Resources

• Dummit & Foote, Abstract Algebra, 3rd ed.. ISBN-10: 0471433349, ISBN-13: 978-0471433347. Errata are available here.

  This is a big book, with a very wide range of topics. We will certainly not be able to cover them all. The preliminary plan is to cover chapters 1-14.

An online algebra textbook by Robert Ash.

I have created a Facebook discussion group, Math 427 Fall 2009, for the course. This is a public group.

Syllabus

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 R_a and F_a 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.

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576