1. Difficult
I find it most difficult with material likes this to focus on the overall idea that is being presented in the text and proofs. I get so caught up and easily confused by the letters, equations and words that many times it seems to go in one ear and out the other. I know that right now most of what we are learning is mostly review, but even with material where I know the answers and I have already understood the overall concept I still get caught up on the details and it is difficult for me to completely judge in my head what the book is actually trying to say.
It is also difficult for me to completely see or judge why or how a proof actually proves something. Often times when I read a theorem, especially when it is overly simple, I think, oh that is such a basic fact, how on earth could you prove it? And then the books proof's strategy is a process or something that I wouldn't have even thought to come up with for the answer.
2. Reflective
I really enjoy reading about simple basic facts and why they are true. Of course sometimes I loose focus because the topic gets a little deeper than I would prefer, but most of the time it is great! It gives me a sense of security about some basic math facts that I know to be true. It is also fascinating to how all of the parts are related to one another. For example, it did not occur to me that the gcd of two numbers can obviously be written as a linear combination of the two numbers. I think I always new that, but I never really acknowledged it until know. Now that makes me curious, because I know that we used linear combinations all the time in Math 313. So I am interested to see how this course uses this information and what we have learned in Math 313 to relate it to abstract algebra.
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