7.10, due MArch 30th

1. Well, this was a pretty short section, but if I had to choose one of the more confusing things it would actually probably be Thm 7.52. So is it for any n as long as n is not equal to 4? that that s true for? And why not 4? Anyway, that was a little confusing.
2. This section was very interesting just like the ones before it. I like learning this new stuff and although it'll probably take a little while for me to get it down, I really like it.

7.9, due March 27

1. This section was pretty interesting, but I mostly had a hard time understanding the Alternating Groups and Lemma 7.49, those were what I had the most trouble with understanding.
2. This section was very interesting! It was like the first time that most everything was new to me and that we haven't previously gone over, so I'm excited!

Questions, Due March 25th

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

I need to work on a few things before the exam. I just want to go through every section and make sure that I understand everything in it and the examples. I guess one thing that I really need to focus on is section 9.4 since that's the section I didn't do homework for, and I probably need to learn that and really have that down as well.

• 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.

I would really like to see some "examples" problems. Like you know the 1st problem on the test is always for us to give examples, I would just like a lot of examples of the different kinds of groups you can have and stuff like that. I would also like any hard problems that might be on the test to be solved, and yeah :)

7.8, due March 23rd

1. The most difficult part of the section for me was the 3rd Isomorphism theorem and thm 7.44. I know that we learned the 3rd Iso Thm before for rings, but I think that it is just a little confusing, along with some parts of theorem 7.44. So I'm looking forward to class today so that I can understand these things and do well on the test :)
2. I liked this section because I could understand a lot of it, probably since we've gone over stuff just like it before, but for rings. I'm pretty sure that I like groups a lot better than rings.

7.7, due March 20

1. The thing that was most difficult for me to understand in this section was the last theorem, theorem 7.38. I understand what it is saying, I just kinda forgot what Z(G) meant, I know I will probably go look it up, I think it means the center, but I will have to double check. Also, will we have to find the center of the group in order to use this proof? It's not just given to us I don't think, right?
2. I kinda really liked this section because it mostly made sense, and it seemed like we could use a lot of the theorems as shortcuts without having to prove some big long thing.

7.6, due March 18

1. This section was very interesting, but there were a couple things that I didn't quite understand. The first thing is the bold sentence at the top pf page 212. After reading all the examples on the previous page, it did seem like when they say Na=aN implied that na=an for every n in N, but I guess that's not true. I read the other sentence below that one, but I don't like that it changed on me all of a sudden :) The other thing that was a little confusing was theorem 7.34. There are a lot of things that are equivalent to each other there, but I don't quite understand exactly what some of them are saying.
2. This section was interesting because we learned about Normal subgroups, and it's just funny to me as if we hadn't already been learning about normal groups, I guess that they're all abnormal before this secction. I also like that it has a lot of similarities to 7.5 and a lot of the other sections in the book.

7.5, due March 13

1. Ok, for some reason I thought this section was pretty understandable. The theorems weren't very difficult to understand, and I thought that they were pretty straight forward. One question I do have is about thm 7.29 and 7.30; I was wondering why 7.29 said just "every group" whereas 7.30 says "every group G" is there a difference there since they named the group or no? Just curious.
2. I really like the rest of this section because it was the first time that I kinda felt like I understood a lot of it and thought that it was pretty straight forward. I also think that these theorems are pretty cool and very convenient.

7.5, due March 13

1. The most difficult part for me in this section was Thm 7.25 For some reason it just didn't click for me and I need help understanding what it all means.
2. I of course like that we have dealt with congruence class 3 times now, and I hope that with my prior understanding that I can really understand what we're learning now with groups. I also like learning the new things in the section, even though I don't understand everything right away, I hope to better understand them after class tomorrow.

7.4, due March 11th

1. This section also contained a lot of new info even though we've gone over homo and isomorphisms before, there is a lot more to take in. There are a lot of new Thms and def. that I need to read a lot, and try to understand, but I think the most confusing one for me is Cayley's Thm, and since it's a "big name" theorem, I reckon I better know and understand it! So I'll be looking for to going over that in class!
2. Well clearly this section is helpful because we've gone over isomorphisms and homomorphisms time and time again, so if I dind't have the down before, I should surely have them down after going over them for the third or so time. Honestly, I kinda like iso- and homomorphisms, they make sense and they're pretty straight forward. The rest of the stuff is pretty interesting too, I just have to make sure that I understand them! :)

7.3, due March 9th

1. This section was pretty long if I do say so myself. Very interesting though! there were a few difficult parts for me to understand, including the center of a group and theorem 7.17. It's just a lot of new information to take in, and I just probably need to read it a few times through to really understand everything, and to try and retain all the info.
2. I thought this was a very interesting section, a lot of new definitons and theorems that we haven't seen before (like I mean we haven't seen stuff like that really before) SO I do think it is very interesting, I just need to read it again and again and make sure that I understand it!

7.2, due March 6th

1. Ok I really liked this section up to about Theorem 7.8, and then it got a little difficult for me to understand. So that and the corollary on page 178 is what I'll need to be listening especially to in class, so that I can understand it better.
2. I like that we finally have an inverse, yea! I know that sometimes we've written it before, but now I can write it with no problem! I also like that we've learned a lot of this stuff before, and that we're giving more properties to groups.

7.1, due March 4

1. Ok, there are a few difficult things about the rest of this section for me. The definitions on page 167 are a little hard for me to understand. On page 169, I'm confused when it says that "Under multiplication, a nonzero ring is NEVER a group," and then it says that certain subsets of a ring (which are still rings right, or no?) may be groups under multiplication.... I guess I just don't really understand that. Theorem 7.2 is actually a little confusing too, sheesh I'm just having a hard time tonight I guess! I think what I'm having a hard time with is that with groups we talk about the set of all things, right? Like in this theorem, it's the set of all units, not just one. I remember you talking about this on Monday, about how a subset or something is not just a part of the set, but it includes the whole thing, I can't remember exactly what we were talking about, I'll have to ask you. And ok, what's up with all the notation on page 170? I mean diamonds, really? Must we bring in more new terms?? Goodness gracious! I'm going to have to really get this down! I hope it's ok that I see you tomorrow most likely :)
2. I think a lot of this stuff is very interesting! I like learning this new material, but I get some of it, because some of it is similar to what we've learned already. Anyway, I think it is cool and interesting, and hope that I can understand all of it soon!

7.1, due March 2

1. The last example on page 163, that continues onto page 164 was kind of confusing to me when I read it, so I think I'll need a little help understanding that example better.
2. I like that a group has a lot of the same properties as a ring, and so it hopefully won't be too hard to remember what you need to test to see if something is a group or not. I also like permutations, I feel like I understand what those are and how to find them.