Algebra - I
MATH 5613      Fall 2007

Course Syllabus: [pdf]

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Exam dates:
     1st Midterm: October 12, Friday, 3:30 p.m. to 5:30 p.m.    Practice exam paper: [pdf]
     2nd Midterm: November 30, Friday, 3:30 p.m. to 5:30 p.m.    Practice exam paper: [pdf]
     Final Exam : December 12 (Wed), 8:00 a.m. to 9:50 a.m.

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Weekly Syllabus:

1. (Week of Aug 19)
     Aug 20: Distribute syllabus; get started on groups.
     Aug 22: subgroups, cosets, normal subgroups.
     Aug 24: homomorphism theorems.
     Homework 1: [pdf]    (Due Aug 29)
2. (Week of Aug 26)
     Aug 27: Homomorphism theorems, cotd.
     Aug 22: Cyclic groups; Semidirect products.
     Aug 24: Permutation and alternating groups.
     Homework 2: [pdf]    (Due Sep 5)
3. (Week of Sep 2)
     Sep 3: Labor day; University holiday.
     Sep 5: S_n and A_n, cotd; Group actions.
     Sep 7: Basic theory of groups acting on sets.
     Homework 3: [pdf]    (Due Sep 12)
4. (Week of Sep 9)
     Sep 10: Group actions, cotd.
     Sep 12: Sylow theory.
     Sep 14: Exercises with Sylow theory.
     Homework 4: [pdf]    (Due Sep 19)
5. (Week of Sep 16)
     Sep 17: Direct products and direct sum.
     Sep 19: Nilpotent groups.
     Sep 21: Solvable groups.
     Homework 5: [pdf]    (Due Sep 28, Friday)     Solutions
6. (Week of Sep 23)
     Sep 24: Free abelian groups.
     Sep 19: Finitely generated abelian groups.
     Sep 21: f.g. abelian groups, cotd.
     Homework 6: [pdf]    (Due Oct 3)     Solutions
7. (Week of Sep 30)
     Oct 1: f.g. abelian groups.
     Oct 3: Jordan-Holder theorem and Schreier refinement theorem.
     Oct 5: Inverse limits and completions.
     Homework 7: [pdf]    (Due on Oct 17.)     Solutions
8. (Week of Oct 7)
     Oct 8: Fall break.
     Oct 10: Zassenhaus's butterfly lemma and proof of Schreier's theroem.
     Oct 12: Midterm exam 3:30 to 5:30 pm. (The usual class hour will be treated like an office hour.)
     No Homework for this week.
9. (Week of Oct 14)
     Oct 15: Categories.
     Oct 17: Functors.
     Oct 19: Categorical definitions of products and coproducts.
     Homework 8: [pdf]    (Due on Oct 26.)     Solutions
10. (Week of Oct 21)
     Oct 22: Free groups.
     Oct 24: Examples of rings.
     Oct 26: Ideals and ring homomorphisms.
     Homework 9: [pdf]    (Due on Nov 2.)     Solutions
11. (Week of Oct 28)
     Oct 29: Prime and maximal ideals.
     Oct 31: Chinese remainder theorem.
     Nov 2: Localization.
     Homework 10: [pdf]    (Due Nov 9.)     Solutions
12. (Week of Nov 4)
     Nov 5: UFDs and PIDs.
     Oct 31: UFD and PID, cotd.
     Nov 2: Polynomial rings.
     Homework 11: [pdf]    (Due Nov 15 (Thursday), by 5 p.m.)     Solutions
13. (Week of Nov 11)
     Nov 12: Polynomial rings.
     Nov 14: Polynomial rings.
     Nov 16: Oklahoma Centennial; University Holiday.
     Homework 12: [pdf]    (Due Nov 26 (Monday).)
14. (Week of Nov 18)
     Nov 19: Modules, homomorphisms.
     Nov 21: Short exact sequences of modules.
     Nov 23: Thanksgiving Holiday.
     There is no homework for this week.
15. (Week of Nov 25)
     Nov 26: Free modules.
     Nov 28: Free modules (cotd); Student evaluation forms.
     Nov 30: Midterm exam 3:30 to 5:30 pm. (The usual class hour will be treated like an office hour.)
     Homework 13: [pdf]    (Due Dec 7.)
16. (Week of Dec 2 = Dead Week)
     Dec 3: Free modules, cotd.
     Dec 5: Review of group theory.
     Dec 7: Review of Rings and modules.

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Some handouts:
   Automorphism group of a finite cyclic group