9.4, due February 27

1. This section wasn't so bad, I did get a little confused, however, on Lemma 9.29. I guess maybe the notation threw me off a bit, or maybe I just need to read it a few more times to understand it better. ALso, theorem 9.31 was a little confusing for me. I idn't really understand what it meant by F is a field of quotients, and then there is just a lot in that theorem to take in. ANyway, I'll just read them more and more and try to understand them.
2. I like how we're sticking with some of the same notation, like on the top of page 321, the equivalence class of (a,b) is a/b, kinda ilke the congruence classes of functions. Then other than that I like this section, because most of it I felt I understood, and that's always good!

Questions, Due February 25th

• Which topics and theorems do you think are important out of those we have studied?

I think most of the topics that we have studied will be important for the test, and the general message of most the theorems, especially the ones given to us in class to study.

• What do you need to work on understanding better before the exam?

There are a few things that I need to brush up on and work on understanding before the exam. Mostly some of the theorems and the examples so that I can know what I should be looking for and doing for the test.

• Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Wednesday.

Haha, how about problems 2, 6, 10, 13, and 15 from section 6.3... just kidding, unless you want to. :) I'll probably be up to your office anyway for help. Besides the ones I said already, I can't really think of one off the top of m head, but I'll be sure to have one for class.

6.3, due Feb 22

1. Ok, the most difficult part of this section for me was the theorems about something being maximal. I understand the definition of maximal, but then I just think I'm getting a little confused with the theorems. Like Thm 6.15, so I understand that if M is an ideal in a comm. ring R with identity, then M is maximal if R/M is a field. So going on to corollary 6.16, in a comm ring R with identity, evey maximal ideal is prime. So does that mean that whenever R/M is a field (along with the other condition) that M is always a maximal ideal, and it's prime?
2. I like that I've seen things in this section before, such as the definition of prime on p154, that is the same as the one we had in chapter 2 I think, so that's nice. It has been a pretty interesting section too, inda fun to read about.

6.2, due Feb 20th

1. The most difficult thing for me in this section was still probably the notation, just getting used to how everything is written, and telling myself that they're really not adding in a coset, and stuff like that. A few of the theorems were a little confusing at first , but I think I might understand them a bit. Theorem 6.2 is a little difficult for me to completely grasp, but I"m sure I should get it after class today.
2. I like that we're talking about homomorphisms and isomorphisms again, I understand things when they talk about that. I just still like how they continue to build on previous sections and add new knowledge to each section. I liked the definitions we learned in this section. I think I understand them, but we'll see in class today.

6.2, due February 18th

1. Ok, the book called it out on this one. Page 146, the definitions of addition and multiplication of cosets in R/I. I guess it might be one of those things that you just have to make yourself learn without understanding it completely. Like when the teacher says, "That's just how it is..." I understand it is the definition and everything, but I want to add the I's together and get 2 I's and multiply the other multiplication rule out... I guess it might be something that I just have to memorize and learn without really completely understanding. Along with that, I don't like that there are 3 entirely different meanings to the plus sign; plus is plus people! Anyway, I'm sure you'll explain it tomorrow and I'll get it!
2. I like how we've gone over all this stuff before except that now we're using ideals and hopefully I'll get used to that and understand it. I'll try to not read too far ahead, except for that I'm curious... So I will, I just won't tell you about it until Thursday night. :)

6.1, due February 17th

1. Well I guess that the most difficult part of this section for me was the definition of ideal. I know that this is what the entire section is on, and I think I understand what it means, but I'm not positive. Is it basically saying that it is a commutative subring of R except that the different elements, a,r, are from the 2 different rings I and R? I'm just a little hazy on it, but I think I will understand it if I go through it a few more times.
2. I really liked this section even though I didn't quite understand the first definition, because it is basically stuff that we've already gone over except with different rings. So hopefully after I understand exactly what an ideal is, it will all click even more!

5.3, due February 12th

1. The most difficult thing in this chapter for me was the definition of an extension field. And then that wasn't good that I didn't understand that definition because it was used in the rest of the theorems after that. So after class when we go over what it is, I'm sure I'll understand it a lot better and then be able to understand the rest of the other theorems more clearly.
2. The cool thing about this section is that it matches section 2.3, except for that we're dealing with functions. So hopefully with the prior knowledge of that previous section, I will be able to understand this section a little better

5.2, due February 11... My Birthday!!!!

1. The most difficult thing for me in this section is about the same thing as last section, I'm having a hard time getting used to the way we denote the congruence classes modulo p(x). Every time I read a theorem or a proof, I feel like I understand it until I see that symbol and my mind automatically tells me that we're dividing p(x). I know it's something that I just need to get used to and stop whining about, but it's giving me a hard time!
2. Like the other sections we've been discussing, I really like how we build on the previous information, and particularly on chapter 2 in this chapter. It boosts my confidence to read something that I've already done in the integers, and it helps me to think that I can understand it and do it with functions!

5.1, due February 9th

1. Luckily, this section seemed to be ok, since we've already had these theorems and corollaries in chapter 2. One thing that I don't quite understand why we do, and that I'll have to get used to is the way we denote the congruences classes modulo p(x) on p 122. I don't get why we denote it like that cause to me it looks like we're dividing the function by p(x). Anyway, that's what I don't really understand and am going to have t get used to
2. I really like how this is mostly like chapter 2, except that we're dealing with functions now, but it helps because I've already done stuff like this, so hopefully it won't be too bad.

4.5 & 4.6, due February 5th

1. First of all, anything with a name that looks like Einstein's name in it already turns me away from even trying to understand it! After last semester in Physical Science and the whole theory of relativity thing, I'm done with Einstein, or anything that looks like his name, even if it is Eisenstein. But honestly, that is probably what I don't understand in these two sections, it's confusing to me. But I'll keep reading it and looking at the examples until I figure it out!
2. I like learning new things, and these sections were pretty interesting! The irreducibility just keeps going and going! It's traveling into the rationals, reals, and now the complex numbers! Good stuff! I like how each section builds on the former, because it helps you learn and understand a little better.

4.4, due February 4th

1. I think I understood most of this section (of course I always think that until I start to do the homework :) ) but one thing I had a question about was on page 103 where it proves corollary 4.17 and then goes onto say how the converse is not always true except for degrees 2 & 3, I was wondering if those were the only 2 degrees for which the converse is true?
2. I really liked this section, because I feel like I know what we're talking about for the most part, roots! I knew how to find roots, and hopefully I still know how to find them. :) Anyway, I this section has been very interesting, and I'm eager to see how interesting I'll find the homework to be.... But I like that I'm understanding the remainder and factor theorems, along with most of the corollaries. I'll just have to see how the homework treats me, and what I can learn in class.

4.2 & 4.3, due February 2nd

1. For section 4.2, on part that I wasn't sure about was the bold sentence underneath the first example on page 90, where it talked about if f(x) divides g(x), then cf(x) also divides g(x) for each nonzero c contained in f. I was just wondering what c is. Is it any just any integer multiplied by f(x) like a coefficient, or does if have it have to be in f(x)? That was just a little confusing to me.
For section 4.3, at first I wasn't getting what they meant exactly by irreducible until I looked at the asterisk at the bottom of page 95, and then I realized that it's just another name for "prime," but that when using polynomials, we say irreducible, so that made a lot more sense. I think I just need to see some more examples to really understand everything in these 2 sections.
2. In section 4.2, I like how we are talking about the gcd again, except this time we're using functions, hopefully I will be able to understand it a little better since we've worked with the gcd before, same with the definition of relatively prime.
In section 4.2, I also like how we've dealt with things like this before, but now we're just using functions, I think I just need to see a few examples to understand these things better.