Math 122 -- Algebra I-- Fall 2019

Mondays and Wednesdays 12-1:15 SC Hall E

This class is an introduction to abstract algebra. The focus of this semester will be groups, rings, and modules.

Instructor: Brooke Ullery (bullery@math, office SC 503)

Teaching fellow: Zijian Yao (zyao@math)

Course assistants: CJ Dowd (cjdowd@college), Charlie O'Mara (comara@college), Fan Zhou (fanzhou@college), Matthew Hase-Liu (matthewhaseliu@college)

Office hours:

If you can't make it to these, you can come to my (Brooke's) office hours for Math 221 (Tuesday 11-1), but the 221 students will have priority during that time.

Section: Sundays at 7 PM in SC Hall A, run by Zijian.

Text: Abstract Algebra, by Dummit and Foote.

Homework: Problem sets will be assigned weekly (usually due Wednesdays). You should submit them on canvas. You can either type your solutions using latex, or very neatly handwrite your solutions, and scan them. I encourage you to work on the problems together, but you must turn in your own solutions and list the names of your collaborators. You may not use solutions found anywhere online. If you consult any outside source, make sure you clearly cite it.

Exams: There will be one in-class midterm on October 30. You can bring one 3 inch by 5 inch card or piece of paper (two-sided) with notes on it. Here's a midterm study guide. Here are the midterm solutions. There will be a take-home final from December 4-7 or 7-10 (your choice).

Grading: Homework: 60%, Exams: 20% each


Assignments

You should submit each problem set on canvas by 11:59 PM the day it's due. I'll drop your lowest homework score at the end of the semester.

Problem set 1: pdf file, tex file, solutions
Problem set 2: pdf file, tex file, solutions
Problem set 3: pdf file, tex file, solutions
Problem set 4: pdf file, tex file, solutions
Problem set 5: pdf file, tex file, solutions
Problem set 6: pdf file, tex file, solutions
Problem set 7: pdf file, tex file, solutions
Problem set 8: pdf file, tex file, solutions
Problem set 9: pdf file, tex file, solutions
Problem set 10: pdf file, tex file, solutions
Problem set 11 (extra credit): pdf file, tex file, due December 3

Lecture Notes

You can find the lecture notes from class here. I'll post each section after we've covered it, so there may be some notes covering multiple days. Warning: There will inevitably be typos in the notes!

Section 1: Binary operations
Section 2: Groups
Section 3: Dihedral groups
Section 4: Symmetric groups
Section 5: Group homomorphisms
Section 6: Group actions
Section 7: The subgroup criterion
Section 8: Centralizers, normalizers, stabilizers
Section 9: Cyclic groups and cyclic subgroups
Section 10: Subgroups generated by subsets of a group
Section 11: Quotient groups and normal subgroups
Section 12: Cosets and orders of subgroups
Section 13: The isomorphism theorems
Section 14: The alternating group
Section 15: Group actions and permutation representations
Section 16: Groups acting on themselves by left multiplication and Cayley's theorem
Section 17: Groups acting on themselves by conjugation and the class equation
Section 18: Sylow's Theorem
Section 19: Rings
Section 20: Polynomial rings
Section 21: Ring homomorphisms and quotient rings
Section 22: Properties of ideals
Section 23: Euclidean domains
Section 24: Principal ideal domains
Section 25: Unique factorization domains
Section 26: Polynomial rings revisited
Section 27: Fields of fractions and Gauss' Lemma
Section 28: Irreducibility criteria