Algebra - I
MATH 5613      Fall 2009

Course Syllabus: [pdf]    Syllabus Attachment, Fall 2009

---

Exam dates:
     Midterm exam: October 19, Monday. Time: TBA.
     Final Exam : December 7, 8:00-9:50 a.m.

---

Weekly Syllabus:
The numbers in parenthesis refers to exercises in Hungerford's Algebra. These are meant to be practice problems. It is a good idea to `dirty' your hands with such exercises.

1. (Week of Aug 17)
        Aug 17: Distribute Syllabus; general introduction; examples of groups. (Section 1.1: 10, 11, 14.)
        Aug 19: Homomorphisms and subgroups (Section 1.2: 2, 3, 4, 9, 15, 18, 19.) Cyclic groups (Section 1.3: 2, 3, 6, 8, 10.)
        Aug 21: Cosets; Lagrange's theorem. (Section 1.4: 1, 6--10, 13.)
        Homework 1: [pdf]   (Due Aug 26)
2. (Week of Aug 24)
        Aug 24: Normal subgroups; homomorphism theorems. (Section 1.5: 1, 2, 8, 9, 10, 12, 14, 15, 19, 20.)
        Aug 19: Very elementary examples. Semi-direct products (Ex. 2.6.1)
        Aug 21: S_n and A_n. (Section 1.6: 2--8, 11, 12.)
        Homework 2: [pdf]   (Due Sep 2)
3. (Week of Aug 31)
        Aug 31: S_n and A_n, cotd.
        Sep 2: Categories and functors. (Section 1.7: 1, 5, 6; Section 10.1: 2, 4a, 5.)
        Sep 4: Categories and functors, cotd.
        Homework 3: [pdf]   (Due Sep 16)
4. (Week of Sep 7)
        Sep 7: Labor day.
        Sep 9: Products and Coproducts. (Section 1.7; Section 1.8: 2, 5, 6, 7, 14.)
        Sep 11: Free groups, generators and relations.
5. (Week of Sep 14)
        Sep 14: Free groups, cotd.
        Sep 16: Free abelian groups. (Section 2.1: 2, 5, 8, 10, 11, 12.)
        Sep 18: Finitely generated abelian groups (Section 2.2: 1, 2, 5, 9, 11--15.)
        Homework 4: [pdf]   (Due Sep 30)
6. (Week of Sep 21)
        Sep 21: Finitely generated abelian groups, cotd.
        Sep 23: Elementary divisor theorem.
        Sep 25: Groups acting on sets.
7. (Week of Sep 28)
        Sep 28: Group actions, cotd.
        Sep 30: Group actions, cotd.
        Oct 1: Sylow theory.
        Homework 5: [pdf]   (Due Oct 5, Monday)
8. (Week of Oct 5)
        Oct 5: Sylow theory, cotd.
        Oct 7: Time to catch up!
        Oct 9: Fall break.
        Homework 6: [pdf]   (Due Oct 14, Wednesday)
9. (Week of Oct 12)
        Oct 12: Sylow theory, cotd.
        Oct 14: Solvable groups.
        Oct 16: Nilpotent groups.
10. (Week of Oct 19)
        Oct 19: Jordan-Holder series.
        Oct 21: Proof of Schrier refinement theorem.
        Oct 23: Review of group theory.
        Homework 7: [pdf]   (Due November 2.)
11. (Week of Oct 26)
        Oct 26: Review of group theory, cotd.
        Oct 28: Problem solving.
        Oct 30: Rings and Ring homomorphisms.
12. (Week of Nov 2)
        Nov 2: Midterm exam based on group theory. Click here for the question paper.
        Nov 4: Ideals.
        Nov 6: Rings and Ideals, cotd.
        Homework 8: Section III.1, Exercises: 3, 5, 6, 7, 8, 13, 14.   (Due November 16.)
13. (Week of Nov 9)
        Nov 9: Prime and maximal ideals.
        Nov 11: Chinese remainder theorem.
        Nov 13: Prime and irreducible elements.
14. (Week of Nov 16)
        Nov 16: Euclidean implies PID.
        Nov 18: PID implies UFD; Noetherian rings.
        Nov 20: TBA.
        Homework 9: Section III.2: 8, 16, 17, 21, 23. Section III.3: 2, 3, 5, 7, 12. (Due November 23.)
15. (Week of Nov 23)
16. (Week of Nov 30)