Section 8.5 due 12/6

I got lost in the proof of Theorem 8.30.

As I was reading this section, I kept thinking about how difficult it would be to come up with these theorems and then to go about proving them. Which comes first: the pattern to see the result of the theorem or the steps that are gone through in the theorem and then check if the idea actually works? Whatever the process is, it seems like it would be really tedious and difficult.

Section 8.3 due 12/1

I don't have specific questions, but I would like some further insight into the Second and Third Sylow Theorems because I don't feel like I understand them.

I like the First Sylow Theorem but I didn't understand it until I read the example. The notation is confusing. They should do something about that.

Section 8.2 due 11/29

I was hoping for an example to accompany more of the theorems because I don't understand them very well.

This section seemed much harder to understand than the previous sections. I just wish I could understand it better so that I could ask more questions.

Review due 11/17

I need to review a lot before taking the exam: right and left cosets, order of groups, subgropus generated by S, cyclic groups, quotient groups, etc.

I would benefit from going over 16, 24,25, or 26 of 7.7 (p. 221).

Section 7.7 due Nov 12

I don't understand the second example on p 218. How is N+(0,0)=N+(1,2) in that example?

It is interesting that cyclic quotient groups G/Z(G) imply that G is abelian. I think that is a interesting correlation.

Extra Credit Colloquim

Dr. Helen Moore talked about her career as a mathematician in the pharmaceutical field. As a researcher, she and a team of other mathematicians try to figure out what the optimal therapy for HIV and Leukemia patients are.

It was a really interesting lecture because I don't generally care about the applications that are shown in math classes--applications that are more geared toward the engineers in the classes. But this showed how math could be applied to helping fight cancer, something that we always think about medical doctors being able to achieve.

It was also interesting because of the importance of precision in the mathematics. Dr. Moore talked about doctors administering drugs to patients--different levels and different combinations of drugs. She said it was important to be accurate in their models because you wouldn't be able to give a person massive amounts of drugs without there being negative effects. (The FDA and drug companies would monitor that more, but it was still important to take into consideration in their models.)

Section 7.6 due Nov 10

Does left/right congruence affect other things? (For example, if there were a "divides" then things might get messy.) Can you further explain the definition of "normal" because they try to make a distinction at the top of p. 212 but I don't understand what they are getting at.

I was trying to decide if I like groups or rings better. I think I like groups better. You can define the group operation however you want as long as it follows the guidelines of a group.