MATH 503 (Fall 2007)
## 2007 - 08 Fall

# MATH 503: Algebra I

### Announcements:

- The final exam will be on 22 January
2008 at 13.00. Contents: Everything.
- The second exam will be on 7
January 2008 at 10.00. Contents: 2.4-3.4 (inclusive).
- The first exam will be on 15 November
Thursday. The time and place will be announced later. The exam will be
on sections 1.1-2.2 (inclusive), except 1.7. There will be no lecture on
14 November Wednesday.
** Change in sechedule. **From 22 October on, we will be
meeting on Wednesdays 9.00-12.00.
- The first lecture will be on 20 September 2007, Thursday at
10.40 in M-214.
- The first meeting will take place on 18 September 2007, Tuesday
at 10.00 in M-214.

**Lectures:** After 22 October: Wednesday 9.00-12.00 (M-214).

Before 22 October: Tuesday 8.40-10.10 (M-214), Thursday 10.50-12.20
(M-214)

**Textbook:** Thomas Hungerford, Algebra, Springer-Verlag, 1974.

**Contents:** Groups, quotient groups, isomorphism theorems,
alternating and dihedral groups, (categories), direct products, free
groups, generators and relations. (Free abelian groups, finitely
generated abelian groups.) Actions, Sylow theorems, nilpotent and
solvable groups, normal and subnormal series. Rings, ring homomorphisms,
ideals, factorization in commutative rings, rings of quotients,
localization, principal ideal domains, Euclidean domains, unique
factorization domains, polynomials and formal power series,
factorization in polynomial rings.
Sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, (1.7), 1.8, 1.9, (2.1, 2.2),
2.4, 2.5, 2.6, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6.

**Grading:** will be based on weekly homework assignments, two
midterm exams and a final exam.

**Done in class:**
Week 1: Chapter 0 (2 hrs)

Week 2: Sections 1.1, 1.2, 1.3. (4 hrs)

Week 3: Sections 1.4, half of 1.5. (4 hrs)

Week 4: Sections 1.5, half of 1.6. (2 hrs)

Week 5: Sections 1.6, 1.7 (products and coproducts), 1.8 (direct
products). (4 hrs)

Week 6: 1.8 (weak products), 1.7 (free objects), 1.9 (free groups). (3
hrs)

Week 7: 1.9 (presentations, free products), 2.1, 2.2 (summary). (3 hrs)

Week 8: 2.4, half of 2.5 (3 hrs)

Week 9: No lecture. First exam.

Week 10: half of 2.5, 2.6 (3 hrs)

Week 11: 2.7, 2.8 (3 hrs)

Week 12: 3.1, 3.2 (3 hrs)

Week 13: 3.2, 3.3, 3.4 (3 hrs)

Week 14: Holiday. (Read 3.5.)

Week 15: 3.4, 3.5 (summary), 3.6 (3 hrs)

Week 16: 3.6 (2 hrs)

**Homework:**
Due on October 2: 1.1 (11, 14, 15), 1.2 (6, 15 b,c, 18), 1.3 (3,
6, 8).

Due on October 9: 1.4 (3, 6, 8, 11), 1.5 (10).

Due on October 16: 1.5 (13a, 16, 19, 20), 1.6 (6, 7, 8, 12).

Due on October 24: 1.8 (2, 5, 6 14).

Due on October 31: Three problems assigned in the class, 1.9 (4).

Due on November 7: Four problems assigned in the class, 2.2 (14).

[Because of the exam, next assignments will be due on 28 November.]

Due on November 28: Four problems assigned in the class.

Due on December 5: Two problems, 2.7 (6, 12), 2.8 (9).

Due on December 12: 3.1 (5, 13, 15, 16, 18), 3.2 (2, 10, 11, 19).

Due on December 26: 3.3 (2, 12), 3.4 (1, 2a), 3.5 (7).

Due on January 2: 3.4 (6, 14, 15), 3.5 (8, 9).

*This line last updated on 2 January 2008.*