#26 due October 28th

Difficult- I think I am terrible at understanding this notation! It is kind of confusing. I don't think I understand the binary operation and what that means. I am definitely going to need to get this during the lecture! Also the group tables seem to be a little confusing. I think everything in this class confuses me.


Reflect- The historical note on page 38 is interesting because it relates the groups to other types of math like geometry and some of calc 2 or 3 I believe with LaGrange and permutations. I also like the historical note on page 39. They just add something cool so the text isn't as boring!

#24 due October 24th

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

We have done so much this section geesh! Well I feel like the division algorithm theorem is very important which is number 4.1.7, we used that one a lot. Then the factor theorem is also important. The extension field, K, theorem is important and also cool. And then we learn what an ideal is and we have used it a ton since then so that is important. In what we have done lately the isomorphism theorems have also been very important.

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

I think I need to work on understanding notation, and how to understand what questions are asking me. I will need to review homework problems and examples to know how to better do that. I also need to work on how ideas and theorems relate to each other so when constructing proofs and such I can actually do them. Proofs are what kill me.

#23 due October 21st

I think I am confused on the blog schedule. It says for today to read section 26 but I think that's what we did in class yesterday! So I'm blogging on section 27.

Difficult- Okay I think I do not remember what a proper ideal is so I do not understand the definition of a maximal ideal of a ring. I will look that up though so I can understand this. I think I follow everything else. I am getting really worried for the test though. I also need to figure out what proper nontrivial ideals are.

Reflective- Abstract algebra is really cool the way that primes play into it. Prime ideals seem to be neat. If I can understand them correctly!

#22 due October 19t

Difficult- As you mention, the notation with all of the plus signs is confusing. It requires slowing down and thinking about it for it to make sense, which is fine it just isn't easy right away. I think I am still confused also on what the notation R/I means. Once the lecture turns into the isomorphism theorems with the quotient ring I get very confused. I don't know if maybe once I see the theorems worked out if I'll get it or not but it looks to be really hard.

Reflective- It is neat that the quotient rings were not intended to have anything to do with homomorphisms and isomorphisms yet they do. And it is also cool that we're bringing homomorphisms and isomorphisms back into lectures. The old stuff makes me feel like I at least know something  because this new stuff is confusing to me! I will definitely be in before the exam with questions :)

#20.5

(end of 20)

Difficult- I don't understand how you would do examples 6.1.13-6.1.15. I think I understand the paragraph about principle idea but then I do not get how you do problems with that. The rest of the lecture about congruence seems to make sense though. Cosets might confuse me a little but I think I can figure them out.


Reflective- I think this ideal stuff is cool because it ties together more stuff that we have done previously like subrings, congruence and mod stuff.

#20 due October 12th

Difficult- Okay the definition of the word ideal is confusing. Although I remember you starting to talk about it in class on Monday so it seems familiar and the examples make more sense. I think of all the symbols confuse me . Reflective- The idea of ideal is pretty cool and there are a lot of examples so I think it will be a big topic. This section doesn't seem too bad and I will probably understand it more after class.

#19 due October 10th

Difficult- I don't think I understand how to form the extension field of F or where that comes from. Another part that confuses me is how x^2 + 1 has in Z7 has 49 elements. I don't see how it could. But the notion that a polynomial in Zp with degree k in a filed F[x] has p^k elements is interesting.

Reflective- I think the most interesting part of this lecture is example 5.3.2 which shows [x] is a root of that polynomial in the extension field K even though it is irreducible in Z2. I literally said cool out loud when I read this. This lecture is really interesting and I like it.

#18 due October 7th

Difficult- Well this lesson seems to be pretty straight forward like the ones lately have been. The only thing that seems confusing is that F[x]/(p(x)) contains a subring F* that is isomorphic to F along with the paragraph describing it on the bottom of page one. I know that it gets reworded later but it still kind of seems confusing to me.


Reflective- I am still glad we are using stuff we've seen before in a different way. Really it makes me less worried about this class. Of course I still worry, just not quite as much. I always worry about getting the homework done!

#17 due October 5th

Difficult- Starting at about corollary 5.1.11 I become confused and I don't understand what that corollary is saying or the examples that go along with it. Also definition 5.1.6 makes sense but then I don't get the examples and how you would figure them out. And lastly I don't think I know or remember what disjoint and identical mean.


Reflective- Well once again more stuff we have done is coming back and I like it since I understand it! Well some of it that is but at least it looks familiar. And I especially like that the proofs are basically the same since those are always a challenge for me.

#16 due October 3rd

Difficult- Corollary 23.6 was the only confusing part of this section. I am not quite sure what cyclic means or what the group <F*, .> means and I don't think I get how that relates to the factoring and what we've been doing.

Reflective- I like the factoring part because that is very basic and easy to catch on to. I also like long division so I'm glad we keep using it.