20131206

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Today

Hi all. There are no new prep problems for today. Please work on Wednesday's problems. If you are stuck on them, then please instead see the "Helpful Practice Problems" section below.

As a class, let me tell you that you are doing amazing collectively. Even the weakest students have learned so much, and have demonstrated it. I would say that this course has had a higher comprehension of theory than any proof type course I have ever taught. I am dead serious here. And yet, I think many of you don't realize this. You don't realize how far you have come, and how much you have learned. I must apologize for not helping you see the growth you have made in yourselves. We need something to help you realize how far you have come.

• On Friday, I plan to have short interviews, 3-5 minutes, with every student in the class. I'll have them in my office, and they'll start before class starts. I want an opportunity with each of you to let you know the good I've seen in you this semester.
• During class time on Friday, we may have some presentations from students, but a good chunk of class time will be devoted to building your confidence in what you have learned. This is where your book comes in handy. I'll have a collection of problems from the text that I want you to work through together in small groups. Bring your textbook, as we'll need it.
• For the remainder of the semester, right now I'm thinking that we'll have two different tracks of work that you can follow. There will be new prep problems that lead us to the Fundamental Theorem of Finitely Generated Abelian Groups and the Sylow Theorems. The other track will be to instead work on problems (from the text) to build confidence (I'll point you to problems that should do this). You may choose which track you want to follow. I'll find a way to allow both tracks to carry on meaningful discussions in class.

Helpful Practice problems

Please open up your abstract algebra text. Turn to any of chapters 6-10, and look at the homework problems at the end of the chapter. You might want to start in chapter 6 or 7 (do you feel more confident with isomorphisms or cosets - whichever you feel more confident with, start there). Do 5-10 of the homework problems near the beginning of the homework list. Do ones that look interesting to you. Feel free to swap to a different chapters (I'd move to chapter 10 before going to chapters 8 and 9) and do some from each chapter. I think you'll find that you can do much more than you may have thought. You have learned so much as a class and individually, but some of you don't feel like you have. As your teacher, I've been trying to stretch you each day to help you grow. It's worked, but I haven't done a good enough job helping you see that growth. I'm sorry.

Here's a list of some of the problems to work on in each chapter. I sorted them by my perceived difficulty. Some of the "basic" problems are very computational in nature. If you understand how to do the computations, I wouldn't waste time doing them. If you don't know how to do the computations, then do them. Don't forget that there are solutions to many of these problems (or at least partial solutions) in the back of the book.

8.22, 23, 27, 27, 28

For more problems, see AllProblems