#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.

#15 due September 30th

Difficult- I followed along pretty well until Theorem 23.15, the Einstein Criterion. I don't get the example or corollary that go along with it either. And then the whole uniqueness of factorization section I don't get as well. A lot of the theorems in this section seem to run together for me, I don't think I'm understanding the main idea of the section.


Reflective- I think the irreducible concept is pretty cool. I followed a lot of the first part of the section and think I can do some of the problems. Something interesting about this section is they leave out or summarize proofs which I thinks shows this section is hard!

#14 due September 28th

Difficult- Well this all relatively makes sense I think since I have seen it before. The trick will be figuring it out using polynomials but that doesn't seem to be too bad. I think I am confused about what a monic polynomial means and when it is monic and when it is not since that's mentioned with the Euclidean algorithm.

Reflective- I think it is great all of this stuff transfers over to polynomials in a field since we have done it before and it makes sense! I also liked this section a lot from last time so I'm glad to see the same things just now with polynomials. I am excited to do the homework... weird.

#13 due September 26th

Difficult- I am confused! I do not understand all the ways a polynomial is different as a ring in Z[x]. This section is like a foreign language to me. There are so many symbols with the sums and then with the mapping. I do follow however what the division algorithm is saying and dividing polynomials so at least I get something. I think understanding the polynomials will take me a little bit but hopefully I can get it.


Reflective- I think the historical note on page 198 is interesting. I think it's cool how the book includes these. It's weird that around 400 years ago x and letters toward the end of alphabet were used to represent indeterminates and this is still true today. I also like the division of polynomials in this section since we did that a long time ago in and it's fun.

#12 due September 23rd

Difficult- I may have spoke too soon on the last blog. I don't get today's section. The start of the section should not say it is quite clear how a structure- relating map of a ring R into a ring R' should be defined because I don't see how it is clear! Okay first that the phi symbol is a map. I remember maps from previous classes, but I don't get what def.18.9 is saying. I am also confused about the abelian groups and how to interpret what <R, +> or <R',+> mean. I remember the terms kernel and isomorphism from previous classes also but I don't follow how rings are relating to these. I also think the examples are confusing. I really hope I get this in class.

Reflective- I don't like this because I don't get it! This section is practically all symbols which is not enjoyable. However looking at example 18.13 helps me to better understand homomorphisms because the example is in numbers and that example makes sense to me.


Questions
1. To study for the exam I went through each lecture we covered. I read the lecture, my notes on that lecture, and looked at the homework problems, especially the ones I missed. I then made note cards about the items on the exam checklist that were covered in that section, and about other things I thought I should memorize. I did this for each section then I started memorizing my note cards. This really helped me to know exactly what things were.
3. Maybe more examples. Some things don't make sense to me until I see different examples of them then things fall into place more.