#39 due Dec 7

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.

#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.

#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.