Math 302 - Abstract Algebra

Math 302 - Abstract Algebra
Fall 2025
Emily Proctor

Please read the syllabus to learn all the details about the course.

Here is a chronological list of the videos and notes for the semester.

And here is a list of overview questions to help you gain a high-level perspective on the content of our course. I recommend coming back regularly to this list as we move through the semester.

Homework

Due Wednesday, September 10:: Please type (up to) a page about who you are as a mathematician (classes or experiences you've had, anything you've liked, anything you've disliked...) as well as your motivations for taking Abstract Algebra this semester. Be honest; this is just a simple, informal assignment that will help me start to get to know you. If there is anything else you'd like me to know as we start the semester, please include that too. Print out two copies of your page and turn them in at the start of class on Wednesday.; Watch Chapter 0 videos Part 1/notes, Part 2/notes, and Part 3/notes.
Due Wednesday, September 17:: Read Chapters 0 and 1 of Gallian.; If you have not seen induction before, or if you would like a refresher, please watch Chapter 0 video Part 7/notes.; Please also see Chapter 0 videos Part 8/notes and Part 9/notes on functions, focusing on the definitions of a function, one-to-one, and onto.; Complete Problems 1-10 from our problem list.
Due Wednesday, September 24:: Read Chapter 2 of Gallian.; Here is a proof that U(n) is a group.; Complete Problems 11-23 from our problem list.
Due Wednesday, October 1:: Read Chapter 3 of Gallian.; Complete Problems 24-36 from our problem list.
For Monday, October 6:: Read Chapter 4 of Gallian.; You can use Problems 37-42 from our problem list to practice with cyclic groups and the Fundamental Theorem of Cyclic Groups. You don't have to turn them in, but I hope they will be helpful to you as you prepare for the exam. Here are the solutions, so that you can check your work.; Our exam will be six problems. The first will be a proof from the notes, the second will be a homework problem, and the remaining four will be problems that grow from these.; Here is a sample exam and solutions that I hope will be helpful to you as you prepare!
Due Wednesday, October 15:: Read Chapter 5 of Gallian.; Complete Problems 43-53 from our problem list.; Note: I adjusted the order of the problems in our problem list, so if you are working from a downloaded copy, it would be a good idea to refresh and redownload!
Due Wednesday, October 22:: Read Chapter 6 of Gallian.; This group table shows that D_3 and S_3 are isomorphic.; Complete Problems 54-65 from our problem list.
Due Wednesday, October 29:: Read Chapters 7, 8, and 9 (normal subgroups) of Gallian.; Here is a proof that aH=Ha if and only if aHa^{-1}=H.; Complete Problems 66-75 from our problem list.; If you are working with an older copy of our problem list, I have updated it so it's a good idea to refresh and redownload. (It's probably a good idea to do this each week!)
For Monday, November 3:: You can use Problems 76-82 from our problem list to practice with external direct products and normal subgroups. You don't have to turn them in, but I hope they will be helpful to you as you prepare for the exam. Here are the solutions, so that you can check your work.; Our exam will be six problems. The first will be a proof from the notes, the second will be a homework problem, and the remaining four will be problems that grow from these.; The exam will focus on the material since our last exam: permutation groups through normal subgroups. Here is a sample exam and solutions that I hope will be helpful to you as you prepare!; Now is a great time to have a look again at and consider the overview questions linked at the top of this page!; We will have an optional review session on Sunday, November 2, 3:00-4:15pm in Warner 101.
Due Wednesday, November 12:: Read Chapter 9 (factor groups) and 10 of Gallian.; Complete Problems 83-93 from our problem list.; If you are working with an older copy of our problem list, I have updated it so it's a good idea to refresh and redownload!
Due Wednesday, November 19:: Read Chapter 12 of Gallian.; Complete Problems 94-105 from our problem list.; For Problem 97, here is a proof that when N is normal in G, KN is a subgroup of G.
Week beginning November 26:: Happy Thanksgiving!
Due FRIDAY, December 5:: Read Chapters 13 and 14 (ideals) of Gallian.; Complete Problems 106-121 from our problem list.; If you are working with an older copy of our problem list, I have updated it so it's a good idea to refresh and redownload!