4.2, due on February 2

I think the most interesting thing was to see specific examples of how integer rules and proofs can be adapted for F[x]. It helps a lot that the definitions, although they seem completely different in many ways, still mean the same things in F[x]. Such as the gcd still being written as a linear combination only now it's of functions instead of just numbers.
The hardest thing for me is knowing how to start the division algorithm to find the gcd of a function. I know how do use long division to divide polynomials, I just get stuck on the starting point. Or maybe it's obvious and I'm just not yet seeing the connection I need to.

4.1, due on January 31

The best part about this reading is that many of the proofs that we already did for the integers carry over and work almost exactly the same for F(x). I'm also kind of excited to get into this section because it will be proving a lot of the stuff that will be part of my what I teach eventually.
The proof of the division algorithm was pretty long and hard to follow. Partly, it's just difficult to start thinking about polynomials in such a seemingly different way. Although, it did mostly make sense and I think after I read over it again and we talk about it in class it'll get better.

due on January 28

I spend usually around 4 hours on the homework. Lecture and reading definitely prepare me for the homework.

I find it very helpful that there is required reading due before class and rather than being expected to completely know and understand what we've read, we then go over almost everything that was covered in the reading and it makes much more sense this second time though.

To make the class better I could probably schedule a little more time for the reading so that I can read even more slowly and better wrap my mind around the new concepts. Although, I already try pretty hard at this. I feel like all the questions asked by the class in lecture are very helpful and I also like that you take the time to adequately answer all of them. I really don't have too many suggestions, I think the class is going well and certainly better than I expected.

3.3, due on January 26

The most interesting part of this section was that at the beginning I couldn't understand what isomorphism meant and how it could even be useful, but then once they compared it to a function it instantly made so much more sense and I was able to get a better grasp of it. I like the definition and how it is another way of defining a function.
The most difficult thing right now is the different properties "preserved by isomorphism", and also how to prove injection and surjection. I can't keep track of which properties hold between fields and what need to hold for isomorphism, etc.

3.2, due on January 24

In this section I'm starting to have trouble seeing how everything fits together, what implies what, etc. The vocabulary for rings and fields is starting to build up and become slightly confusing. With more exposure, and after Monday's lecture, I feel like most of it will make sense. It's just getting more difficult to visualize and keep things straight in my mind.

The most interesting thing to me about this section is theorem 3.9. If it is a field, it is an integral domain and then that it is only true that if it is an integral domain it is only a field if that integral domain is finite. I think the way that works out and how they proved it is cool.

3.1, due on January 21

What I don't understand from this section is why theorem 3.1 works. I realize they omitted the proof because it is an exercise but I'm just curious how that always works.
I think theorem 3.2 is incredibly useful and I like that I can easily see exactly why it works and how these few axioms prove all of the axioms when S is a subset of R (a ring).

3.1, due on January 19

The most difficult thing for me about this section is all of the new vocabulary and concepts. Some of it has been vaguely introduced in previous classes but there are still a lot of new ideas. Keeping the different definitions separated and straight in my mind is confusing right now, but should make more sense with practice.

The most interesting part of this reading for me is that you can create a ring any way you want, defining the rules of that ring in many different ways. It is also interesting that there are so many connections between the facts we know about integers, integers modulo ( ), and so many of the other sets of numbers we typically explore.

2.3, due on January 14

The most difficult part of this section was understanding the proof of corollary 2.10 and foreseeing how it will be useful.
The most interesting part was theorem 2.8 and the general rules that always hold when n is prime.

2.2, due on January 12

The most difficult part for me is being able to think about equivalence classes given the new notation and to remember the differences in how they work versus integers.
The most interesting part is that you can define addition and multiplication for equivalence classes and prove that almost all of the properties of integers hold.

2.1, due on January 10

The most difficult part of this reading for me to understand was the second part of corollary 2.5 and the proof justifying it.
The most interesting part of the reading is the relationships between congruence and equality, the relatively simple proofs of this, and the simplicity of the two symbols similarity.

1.1-1.3, due on January 7

To me, the most difficult part of the material was understanding the Euclidean Algorithm. The process was a little bit confusing to me and I also don't entirely understand what it does.

One thing pointed out in this chapter that connected with something else from mathematics is that every integer not equal to +/-1 or 0 is the product of primes. This fact is utilized in simplifying radicals. Also, I found these sections interesting because I can see how having a better understanding and stronger foundation of these topics will help me to be a better secondary math educator because it will help me to piece together different algorithms and general math truths.

Introduction, due on January 7

I am a sophomore and a Math Education major.
I have taken Math 290 and Math 313 since calculus.
I'm taking abstract algebra class essentially because it is a required course for my major and will help me have better background knowledge of the things I eventually teach.
My most effective math teacher at BYU was Dr. Gerson because she moved at a good pace and clearly explained all of the topics. My least effective math teacher at BYU was Dr. Conor because he moved too quickly in lecture, it was hard to follow his logic/explanations, and some of the homework he assigned was over repetitive and didn't feel useful.
I love snowboarding and am the 3rd oldest of 8 kids in my family.
Your office hours work great for me! I feel like this will be a challenging class, but you seem like a great teacher!