GTM Hungerford’s Algebra vol 73†

Hungerfords Algebra
Hungerford's Algebra

For some reason, our Algebra prof gave us 40 problems to solve. They are all in the first chapter and review comprehensively what I’ve learned in past algebra and algebraic structures classes. Still, 40 exercises, that’s a lot. Seeing as Hungerford’s book is pretty much a reference for graduate students in algebra, I was looking around for solutions to all of the problems since I am unsure if our prof will give us any or if he will give us hints.

I found Dr. James Wilson’s book on Hungerford’s problem sets. It’s available for free here. If it’ no longer there, you can launch a google search and you should find it easily enough.

Part of me almost wants to print it out. It’s 167 pages long. At any copy shop, it will cost about $3 to print that out. That’s including binding. That’s really cool. It will help me out quite a bit. Luckily, I’ve seen most of the subject matter before, so it shouldn’t be a problem. The prof mentioned that he’d take our midterm exam out of this problem set. Sounds good to me. Midterms are in week 9 and we’ve just finished week 3.

commutative diagram
commutative diagram

I’ve heard that these problem sets can be hard. The solutions are a tool. I find that I have to try out any exercise a few times before even considering looking a the solution. Otherwise, I don’t learn anything. In algebra, there’s always a beautiful logic. Today, we saw permutations again. I’m not really fond of them, but the next part of the chapter introduces category theory³.

I wonder if the midterm will be a take-home exam². The prof kept mentioning this in one class, though I didn’t understand what he was saying, it was in Mandarin. That would be fun.

It’s really strange being in class with a the Taiwanese. During the breaks, almost all of them take naps. It’s really weird and humorous. I usually read something. They put their heads down on their desks and cop a few winks of sleep, girls and boys, no exceptions. In my office, everyone has got cushions to nap on. The more enterprising students have fold-away beds and sleeping bags. Until now, I haven’t really spent that much time in my office, as I was pretty busy over the last few weeks. However, homework just started piling up and I’ve got to hit the books over the next few days. As much as I like having an office, things are just better at home. I’ve got a big desk, computer, and laptop, as well all of my reference books¹. Plus, I’m home. It’s more comfortable. If I didn’t have this and was living in a dorm, I guess I’d spend more time at the office.

* * * * *

I’m still looking for an adviser. I’ve got a whole semester to decide. I want to do my thesis in mathematical analysis, topology, measure theory, or abstract analysis. I wouldn’t mind it being in complex variables, as my current prof is definitely the best that I’ve had in that field.

That being said, there’s no rush. If I follow the path that’s been suggested to me, doing a passage au doc by taking the PhD exams next year, I could start a doctorate next year. That would be really awesome. Contrary to Canada and the US, it looks like it’s going to be a lot easier to do this here.

Back to thesis advisers. The adviser that I was considering told me that he isn’t looking for any students. He hasn’t got any right now and he’s waiting to get some funding for research on a project which will keep him busy for the next three years. I interpreted this as a no, which kind of surprised me. I thought that professors would be competing to get prospective grads. Still, the professor is actually an assistant professor and hasn’t published that much, which makes me think about choosing someone else. I’m trying to find someone who’s well published and with a good reputation in analysis.

I’m also trying to secure some kind of funding, by being a research assistant or something like that for a prof. All of the Taiwanese students have to be TAs for a prof. However, it’s paltry pay and I’ve been told that I didn’t need to do it. This leaves me trying to find alternatives funding, since I didn’t get a scholarship. I’m pretty sure that next year I’ll receive one, but until then, I need to find some revenue streams. I’d prefer to find some opportunities to work with a professor and get my name on papers. That would really be cool.

* * * * *

I’m really enjoying annotating my posts. It makes a lot of sense and it enables me to expand on posts once they are written when I edit them. I tend to edit all of my posts at least once or twice before posting them.

* * * * *

[¹]: My home office setup is a bit strange. I’ve set up my desk in the living room, which has kind of been turned into a study, as our extra room has been taken over by our kitty cat. We don’t have a TV nor any home theater system, just a desktop with a 22″ LCD screen on which I do most of my work. I’ve got an’08 13.3 Asus W7J which does the job when I’m on the go.
[²]: That would be cool. I’d ace that. I like when classes are about learning more than if they focus on grades. One of my profs said the following:

-I didn’t talk about grades yet, did I? Well, you don’t have to worry about those.

Which I really liked to hear. There are some neat scholarships available if you score in the top 5 of the class.
[³]: I’ve been looking forward to seeing this mathematical theory in a classroom setting for a while. I don’t have the utmost confidence in my prof, but he’s probably #2 in all of the algebra profs that I’ve had. He’s got some issues with powerpoint presentations, but hey, we can’t be perfect.

[†]: I don’t know why I started out with this post title. Frankly, because I was just relating my recent experience with this book. Since then, the post has diverged somewhat. Still, it’s been titled, so I’ll just keep it for now.

Author: range

I'm mathematician/IT strategist/blogger from Canada living in Taipei.

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