Spring 2018, Math 4581: Abstract Algebra II

Announcements

Wednesday 28 March: On Monday (2 April) we will work on Homework 10, and on Wednesday (4 April) we will have lecture on the class equation, rather than lecture on Monday and review on Wednesday.

Thursday 25 January: From now on, office hours are changed to Tuesdays 2-5pm.

Syllabus

There's lots of information on the syllabus.

Calendar

Jan 8: chapter 1 Jan 10: chapter 2 Jan 12: more chapter 2
Jan 15: no class Jan 17: chapter 3, HW1 due Jan 19: groups, subgroups
Jan 22: permutations Jan 24: test review, HW2 due Jan 26: test on chapters 1--3
Jan 29: work on HW3 Jan 31: orbit/stab thm, HW3 due Feb 2: Lagrange's thm
Feb 5: work on HW4 Feb 7: chapter 5, HW4 due Feb 9: chapter 6
Feb 12: chapter 7 Feb 14: test review, HW5 due Feb 16: test on chapter 4
Feb 19: F[x]/<p(x)> Feb 21: min. polyn., HW6 due Feb 23: p irreducible => field
Feb 26: work on HW7 Feb 28: deg. of extensions, HW7   Mar 2: chapter 9
Mar 5: chapter 10 Mar 7: test review, HW8 due Mar 9: test on chapter 8
Mar 12: spring break Mar 14: spring break Mar 16: spring break
Mar 19: Galois group Mar 21: Gal. permutes roots Mar 23: fixed fields
Mar 26: work on HW9 Mar 28: Galois fund. thm., HW9   Mar 30: normal subgroups
Apr 2: work on HW10 Apr 4: class equation, HW10 due Apr 6: test on Galois theory
Apr 9: work on HW11 Apr 11: quotient groups, HW11 Apr 13: more quotient groups
Apr 16: work on HW12   Apr 18: constructibility, HW12   Apr 20: solvability by radicals
Apr 23: test review
Tues May 1: final exam

Homework

HW1 (due Jan 17): Judson chapter 20 exercises 6, 7, 15, 16.

HW2 (due Jan 24): Solomon ch 2 ex 1; ch 3 ex 1, 2, 6, 7.

HW3 (due Jan 31): Judson ch 3 ex 14, 33, 53; ch 4 ex 30; ch 5 ex 2dfijo, 3bd.

HW4 (due Feb 7): Judson ch 14 ex 2, 3; ch 6 ex 5dfh, 9, 14.

HW5 (due Feb 14): Judson ch 6 ex 11, 12, 17, 18.

HW6 (due Feb 21): Judson ch 14 ex 12, 14.

HW7 (due Feb 28): Judson ch 16 ex 8; ch 17 ex 7, 9, 10; ch 21 ex 1abce, 5.

HW8 (due Mar 7): Judson ch 21 ex 2, 13, 22, 28.

HW9 (due Mar 28): Judson ch 23 ex 1.

HW10 (due Apr 4): Judson ch 21 ex 4; ch 23 ex 6, 9, 22cdef.

HW11 (due Apr 11): Judson ch 10 ex 2 (without factor groups); ch 14 ex 7, 22.

HW12 (due Apr 18): Judson ch 10 ex 1abce, 2, 4.