MATH 504 (Spring 2008)

2007 - 08 Spring

MATH 504: Algebra II

Announcements:

The second midterm will be on 22 May Thursday at 14.40 on field theory. The final exam will be on 19 June Thursday.
The first midterm will be on 3 April Thursday. We will discuss the best time in the class. Contents: Everything we covered on modules.
The third lecture will be on 26 February between 14.40 and 16.30. No lecture on 28 February.
The second lecture will be on 21 February Thursday between 13.40 and 15.30 in M-214.
The first meeting and the first lecture will take place on 19 February Tuesday between 13.40 and 15.30 in M-214.

Lectures: (After March 3) Tuesday: 14.40-16.30 and Thursday: 14.40-15.30. (Place: M-214)

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

Contents: Modules, homomorphisms, exact sequences, free modules, projective and injective modules, tensor products, modules over a PID. Fields, field extensions, the fundamental theorem of Galois theory, splitting fileds, algebraic closure and normality, the Galois group of a polynomial, finite fields, cyclic extensions, radical extensions, transcendence bases.

Sections 4.1, 4.2, 4.3, 4.5, 4.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.7, 5.9, 6.1.

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

Done in class:

Week 1: 4.1, some of 4.2 (4 hrs)
Week 2: rest of 4.2 (2 hrs)
Week 3: 4.3 -- up to 3.10. (2 hrs), 4.5 (1 hr)
Week 4: 4.5 (2 hrs), 4.6 (1 hr)
Week 5: 4.6 (3 hrs)
Week 6: 4.6 (2 hrs), 5.1 (1 hr)
Week 7: 5.1 (2 hrs) and Midterm Exam 1
Week 8: 5.1 (1 hr), 5.2 (2 hrs)
Week 9: Appendix 1, 5.2
Week 10: 5.3
Week 11: 5.3 and Appendix (2 hrs)
Week 12: 5.4

Tentative Plan:

Week 13: 5.4
Week 14: 5.5 and Exam 2
Week 15: No lecture, because of Antalya Algebra Days.

Homework: Due on March 4: Chapter 4, Section 1: 4, 9, 11(a-c). Section 2: 4, 10, 12.
Due on March 11: Section 3: 1, 5. Section 5: 2, 3.
Due on March 18: Section 5: Remaining parts of 2, 3, also 4 and 7. Due on March 25: Section 6: 2 and correct your mistakes in earlier homeworks.

This line last updated on 9 May 2008.