M 380 D Algebra 57080

CLASS HOURS AND LOCATION: MWF 1:00-2:00 PM, RLM 11.176

OFFICE HOURS: MW 9:30-11:00 AM

TEXTBOOK: D. Dummit and R. Foote, Abstract Algebra, Third Edition, Wiley 2004. 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. 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 on 2/26 in class and a final exam on 5/9 at 2pm in RLM 11.176.

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: 30% homework + 30% midterm + 40% final.

NOTE: No class on 2/24 and 2/28. No class on 4/21

Homework

• Section 13.1, problems 1,3. Section 13.2, problems 3,5,11,14,18. Section 13.4, problems 4,5. Due 1/24 (extended to 1/27).
• Section 13.5, problems 1,2,5,8. Section 13.6, problems 2,6,8,10. Due 2/3.
• Section 14.1, problems 1,3,6,8,9,10. Section 14.3, problems 1,3,5. Due 2/10.
• Section 14.2, problems 1,3,5,8,12,17,18,27,29,31. Due 2/21.
• Section 14.4, problems 2,5. Section 14.6, problems 2,3,12,22,29,38,46,48. Due 3/19. (Also, read section 14.6, problems 30,31,32).
• Section 14.7, problems 2,4,7,11,14,16,18. Due 3/26.
• Section 14.9, problems 2,3,4,5,6,7,10,11. Due 4/4.
• Do all problems of the 2013-01-Algebra-B and 2013-08-Algebra-B prelims. Prelim page. Due 4/25.

Links

• Pictures of Galois groups.
• Transcendence of e and pi from Baker's book.