It seems to me quite logical on how math classes should proceed. The professor presents some theory, with theorems and their demonstration, as well as definitions and propositions, before venturing into a slew of examples. For some reason, this is completely absent from my classes in Taiwan. The examples. I don’t know what these profs are thinking, but examples are paramount for students to understand some of the theory. OK, my complex analysis prof is good. he gives examples and answers questions well¹.
I’ve spent about 4-5 hours on my algebra homework. I still have another 27 problems to finish¹. Naturally, they get harder as you go along. Kind of annoying. I like writing easier ones first and then moving to harder ones a bit later. I like this to happen in each problem set. For some reason, I had trouble with cyclic groups and had to review the subject matter before completing two problems.
With these types of abstract math, it’s best to stop when you feel it slipping away or when you hit a problem that looks impossible to let it stew and come back to it. This has been my technique for the last few years and it works well. I have to be really careful with the solutions. I have all of the solutions of the problems that I’m doing in Hungerford’s Algebra².
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.