Difficult- Section 37 seems to be pretty straight forward in theorems and examples. Sometimes I don't follow how the book comes up with certain things, but usually when I go back over it I can figure it out. 37.8 Lemma and its associated examples are the ones that cause the biggest challenge for me.
Reflective- I think 37.6 theorem is very interesting as well as 37.8 lemma.
Tuesday, December 7, 2010
Sunday, December 5, 2010
#38 due Dec 5
Difficult- I have followed pretty much everything I think I am confused a little bit about how the conjugates work. I also think I need to review maximal subgroups since that is part of the definition of Sylow subgroups. But most of the rest seems to make sense it is just building on previous knowledge.
Reflective- Well I googled Cauchy to find out more about him and his theorem because I like mathematicians and he is cool. I also like this section a lot because it seems to have a large amount of repeated things like the normal subgroup and primes and order and everything.
Reflective- Well I googled Cauchy to find out more about him and his theorem because I like mathematicians and he is cool. I also like this section a lot because it seems to have a large amount of repeated things like the normal subgroup and primes and order and everything.
Thursday, December 2, 2010
#37 due Dec 2
Difficult- The Cartesian product of sets makes sense I am just really bad at remember exactly what the notation means. I am confused by 11.3 example because I don't see how that relates to anything new in the section because it seems like something we have already done. I do not understand 11.9 theorem very well. So I'm thinking I don't understand the section period. But then I see 11.10 example and that makes perfect sense. So I think it's notation and wording that is holding me up.
Reflective- Gotta love 11.5 Theorem because it goes back to isomorphisms and relatively prime. The historical note is interesting about how findings were finally turned into abstract theory.
Reflective- Gotta love 11.5 Theorem because it goes back to isomorphisms and relatively prime. The historical note is interesting about how findings were finally turned into abstract theory.
Tuesday, November 30, 2010
#36 due Nov 30
Difficult- In the first isomorphism theorem I do not know what canonical means, but I don't know if that is important or not. In all of the theorems I don't follow what they mean exactly. But I do like the figures/diagrams because they are so much easier to understand!
Reflective- I think the 34.4 Lemma! The join term is cool and I think I understand it so gotta love it. The examples are so helpful in understanding what these theorems mean.
Reflective- I think the 34.4 Lemma! The join term is cool and I think I understand it so gotta love it. The examples are so helpful in understanding what these theorems mean.
Sunday, November 28, 2010
#35 due Nov 28
Difficult- There are two million and one symbols in this section! And so I am really confused what the exact definition of a factor group is and what 14.1 theorem means. The 14.2 and 14.3 examples help me understand what a factor group is a little bit more. 14.10 figure is so helpful! I was getting really lost with all the symbols and which meant what. I think the lecture will help me better understand these.
Reflective- I am glad we keep using homomorphisms and isomorphisms since we have used them and know a lot about them. 14.13 theorem we used last section so I know that one, yay!
Reflective- I am glad we keep using homomorphisms and isomorphisms since we have used them and know a lot about them. 14.13 theorem we used last section so I know that one, yay!
Sunday, November 21, 2010
#34 due Nov 21
So yeah I don't really know what I am supposed to be blogging about/if I'm supposed to blog? But I am going to do the exam questions.
Which topics and theorems do you think are important out of those we have studied?
Geesh there are lots. 7.8 Theorem is a big one because because it has 4 parts to it and they are very useful in a lot of proofs and problems we do. LaGrange's Theorem and its corollaries are also very important and are used a lot. I like 6.10 Theorem.
What do you need to work on understanding better before the exam?
I am working on understanding what we did in class Friday. I also am working on proofs of Theorems because I always get lost in them. Just trying to go over everything again before the test!
Which topics and theorems do you think are important out of those we have studied?
Geesh there are lots. 7.8 Theorem is a big one because because it has 4 parts to it and they are very useful in a lot of proofs and problems we do. LaGrange's Theorem and its corollaries are also very important and are used a lot. I like 6.10 Theorem.
What do you need to work on understanding better before the exam?
I am working on understanding what we did in class Friday. I also am working on proofs of Theorems because I always get lost in them. Just trying to go over everything again before the test!
Thursday, November 18, 2010
#33 due Nov 18
Difficult- The evaluation homomorphism confuses me, but if I think of it loud and not use the symbols it makes sense to me. The phi symbol (at least I think that is what it is) with the numbers next to it like the trivial homomorphism, identity map, etc is confusing to me. I follow a lot of the examples but they are somewhat confusing.
Reflective- I like how the division algrorithm comes back into play again! I like 13.12 Theorem because it makes sense and is what you would assume. Also the historical note is interesting as it is neat to read about people who have discovered things, such as cosets being the same.
Reflective- I like how the division algrorithm comes back into play again! I like 13.12 Theorem because it makes sense and is what you would assume. Also the historical note is interesting as it is neat to read about people who have discovered things, such as cosets being the same.
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