# M 380 C Algebra

INSTRUCTOR: Felipe Voloch (RLM 9.122, ph.471-2674)

CLASS HOURS: Mon, Wed, Fri 10:00 -- 11:00 RLM 10.176

OFFICE HOURS: Tue 9:00 -- 11:00 or by appointment.

TEXTBOOK: D. Dummit and R. Foote, Abstract Algebra, Second Edition, Prentice Hall, 1999. There is an errata.

SYLLABUS: The first two parts of the book. Groups (groups, subgroups, quotient groups, group actions, direct products, solvable groups) and Rings (rings, domains, PIDs, UFDs, polynomial rings, modules).

PREREQUISITES: None, but students who haven't had abstract algebra before are encouraged to talk to the instructor before registering.

EXAMS: A midterm (available now with solutions in pdf or ps format), on October 15th, 10:00-12:00, covering part I of the book and a comprehensive exam (available now with solutions in pdf or ps format) on Dec. 3rd., 10:00-12:00.

HOMEWORK: I will assign homework on a weekly basis and it will be due following week, unless otherwise stipulated.

GRADES: 20% homework + 30% midterm + 50% final.

## Homework assignments

1. Section 1.1, problems 6,7,14,15,22. Section 1.2, problem 18. Section 1.3, problems 1,9,14,16. Due 9/3.
2. Section 1.6, problems 2,4,10,17,26. Section 2.1, problems 1,5,8,10. Section 2.3, problems 6,11,16. Due 9/10.
3. Section 3.1, problems 3,5,11,19,33. Section 3.2, problems 5,8,18. Section 3.3, problems 3,7. Due 9/17.
4. Section 1.3, problem 17. Section 3.4, problems 5,11. Section 3.5, problems 9,10,12. Section 4.1, problems 4,8. Section 4.2, problems 3,8. Due 9/24.
5. Section 4.3, problems 2,9,13,25. Section 4.4, problem 1. Section 4.5 problems 1,8,16,18. Section 5.5, problem 6. Due 10/1.
6. Section 4.5, problems 23, 30, 40. Section 5.2, problems 7, 9, 14. Section 5.5, problems 8, 10.
7. Section 7.1, problems 6,14,26. Section 7.2, problems 3,5. Section 7.3, problems 10,25,26,28,34. Due 10/25.
8. Section 7.4, problems 14,30. Section 7.5, problem 5. Section 8.1, problem 10. Section 8.2, problem 7. Section 8.3, problems 6,11. Due 11/1.
9. Section 9.1, problems 4,14. Section 9.2 problems 4,6. Section 9.3, problem 3. Section 9.4, problems 5,15,19. Due 11/8.
10. Section 10.1, problems 8,9,10,12. Section 10.2, problem 9. Section 10.3, problems 9,10. Due 11/15.
11. Section 12.1, problems 2,5,11. Section 12.2, problems 12,17,20. Section 12.3, problems 19,31. Due 11/22. Last homework!!

Rings of fractions the hard way (in pdf format).