scp Math 421 -- Abstract Algebra I -- Fall 2022

Math 421 -- Abstract Algebra I -- Fall 2022

This course is an introduction to abstract algebra, specifically groups and rings. For additional course details, see the syllabus.

Lecture: Tuesday and Thursday 11:30 AM - 12:45 PM in MSC E406

Instructor: Brooke Ullery (bullery@emory, office MSC E416)

Office hours (subject to change):

Text: Abstract Algebra, by Dummit and Foote (3rd edition).

Homework: There will be homework assigned after each class. It will not be collected or graded. Instead, there will be a weekly quiz covering the homework material. The homework assignments are available below and will be updated after each lecture. I encourage you to work on the problems together and to come to office hours if you need help or have any questions.

Quizzes: There will be a short (10 minute) quiz at the end of each Thursday class, except the first Thursday (8/25) and dates of the midterm exam. The quiz questions will be very similar to the homework problems from that week. Notes, books, or electronic devices may not be used when taking the quizzes. Your lowest two quiz grades will be dropped. No makeup quizzes will be given. If you miss a quiz, that will be one that you drop. For illness that impacts your attendance for more than two weeks, contact the Office of Undergraduate Education (OUE) and Brooke as soon as possible and we will consider your situation on a case by case basis.

Exams: The 75-minute midterm exam will take place during class on October 20. The final exam will be cumulative and take place on December 13, 11:30 AM - 2:00 PM. Notes, books, or electronic devices may not be used when taking any of the exams. Makeup exams will be given only in extreme situations, with justification verified by the OUE.

Grading: 20% quizzes, 35% midterm, 45% final exam

Masks: Masks in class and office hours are encouraged but not required.


Here I'll post which sections we cover each day of lecture, the corresponding lecture notes (once we finish that section), and the assigned homework problems. Keep in mind the lecture notes from one class may not be posted until after the following class if we stop in the middle of a section.

Date Topics covered Homework Comments
Thursday 8/25 Binary Operations, started Groups Read sections 0.1-0.3, Problem set 1 Bring a paper square to class on Tues. (about 3 inches)
Tuesday 8/30 Groups Problem set 2
Thursday 9/1 Finished Groups, started Dihedral Groups Problem set 3 Quiz 1 solutions; Dihedral groups notes will be posted next Tuesday
Tuesday 9/6 Dihedral Groups, started Symmetric Groups Problem set 4
Thursday 9/8 Symmetric Groups, started Group homomorphisms Problem set 5 Quiz 2 solutions
Tuesday 9/13 Group homomorphisms, started Group actions Problem set 6 Note updated office hour times
Thursday 9/15 Group actions Problem set 7 Quiz 3 solutions
Tuesday 9/20 Subgroup criterion, started Centralizers and normalizers Problem set 8 Office hours tomorrow are 3:30-4:30 in my office
Thursday 9/22 Centralizers and normalizers, started Stabilizers of group actions Problem set 9 Quiz 4 solutions
Tuesday 9/27 Stabilizers of group actions, started Cyclic groups Problem set 10
Thursday 9/29 Cyclic groups Problem set 11 Quiz 5 solutions
Tuesday 10/4 Noncyclic subgroups Problem set 12
Thursday 10/6 Started Quotient groups Problem set 13 Quiz 6 solutions; quotient group notes will be up next week
Tuesday 10/11 - no class Fall break
Thursday 10/13 Quotient groups Problem set 14 Quiz 7 solutions, exam next week covers through noncyclic subgroups
Tuesday 10/18 Midterm study guide Review day
Thursday 10/20 Midterm solutions
Tuesday 10/25 Normal subgroups Problem set 15
Thursday 10/27 Started Cosets and orders of subgroups Problem set 16 Quiz 8 solutions
Tuesday 11/1 Cosets and orders of subgroups Problem set 17
Thursday 11/3 Products of subgroups Problem set 18 Quiz 9 solutions
Tuesday 11/8 The Isomorphism Theorems, started Alternating groups Problem set 19
Thursday 11/10 Alternating groups, started Group actions and permutation representations Problem set 20 Quiz 10 solutions
Tuesday 11/15 Group actions and permutation representations, started Groups acting by left multiplication Problem set 21
Thursday 11/17 Groups acting on themselves by left multiplication and Cayley's theorem Problem set 22 Quiz 11 solutions
Tuesday 11/22 Started Groups acting by conjugation Catch up on past problem sets
Thursday 11/24 - no class Thanksgiving
Tuesday 11/29 Groups acting on themselves by conjugation and the class equation Problem set 23
Thursday 12/1 Conjugacy in symmetric groups Quiz 12 solutions
Tuesday 12/6 Final exam study guide Last day of class -- review day