Mathematical Algebraic Structures

Algebraic structures, via Wikipedia
Algebraic structures, via Wikipedia

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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.

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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.

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Using Powerpoint Presentations In Classrooms

My wife teaches university students and she really enjoys using Powerpoint presentations in class³. Most lectures by visiting scholars, as well as research, is usually presented with some kind of presentation. In the math world, it’s usually some Linux-based derivative.

I’ve been going to a class where the professor solely relies on using Powerpoint presentations. I have come to hate them. The reason is that the professor doesn’t understand how much time it takes for students to note down what they see on the slides. Sure, the presentation is made available later on the web, but I like taking notes. That’s how my learning process works. I know that most students work in similar fashion.

The professor shows a theorem, barely explaining it and the rushes through a demonstration. I haven’t even finished noting down the theorem when he’s already midway through the demo. It’s very annoying. The other extremely annoying fact is that the demos, or parts of them, vanish because animation is used in the Powerpoint. Extremely frustrating⁵.

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