# M 380 D Algebra (#55630)

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

CLASS HOURS: Mon, Wed, Fri, 9:00 -- 10:00, RLM 9.166

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

TEXTBOOK: D. Dummit and R. Foote, Abstract Algebra, Second Edition, Prentice Hall, 1999 (but now being sold by J. Wiley). Check out Foote's web page for the errata.

SYLLABUS: This is the second part of the prelim algebra sequence. We will cover part IV and some of part V of the book (plus Ch. 12 on modules over PID's left over from the Fall). This will include: Field theory, algebraic and transcendental extensions, separable and inseparable extensions. Galois theory and applications to classical geometric problems, solvability by radicals and finite fields. Polynomial rings and the Nullstellensatz. .

PREREQUISITES: The first part of the prelim algebra sequence (M380C) or equivalent knowledge.

EXAMS: A midterm (available now with solutions) on Monday, March 20th, 8:00-10:00 AM on RLM 9.166 (covering chapter 13 and chapter 14 up to 14.6, inclusive) and a comprehensive final (available now with solutions) exam on Thursday May, 9th, 9:00-12:00 AM.

HOMEWORK: I will assign homework on a weekly basis and it will be due following week, unless otherwise stipulated. No late homework will be accepted. The two lowest homework grades will be dropped.

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

## Homework assignments

1. Section 12.1, problems 2,5,6,11,20, due 1/25.
2. Section 13.1, problems 1,3; Section 13.2, problems 2,7,14,18,19, due 2/1.
3. Section 13.3, problems 4,5; Section 13.4, problems 2,3; Section 13.5, problems 2,5,10, due 2/8.
4. Section 13.5, problem 7; Section 13.6, problems 1,5,8; Section 14.1, problems 1,6,8, due 2/15.
5. Section 14.2, problems 5,6,11,13,17,29; Section 14.3, problems 6,8, due 2/22.
6. Section 14.4, problems 2,4; Section 14.5, problems 2,7; Section 14.6, problems 29,30, due 3/1.
7. Section 14.6, problems 3,13,48; Section 14.7, problems 1,9, due 3/8.
8. Section 14.7, problems 2,3,8,16; Section 14.8, problems 4,9, due 4/1.
9. Section 14.9, problems 1,2,3,7,13, due 4/8.
10. Section 15.1, problems 1,3,4,13,14, due 4/19.
11. Section 15.2, problems 2,8,9; Section 15.3, problems 1,2,8,10, due 4/26. Last assignment!