9.5 and Final, Due April 11

Difficult: It is difficult for me to understand when something is isomorphic.

Interesting: I think it is interesting that they had us prove Corollary 9.31 in the homework of 9.3 and now here it is as a corollary in 9.5.

Which topics and theorems do you think are important out of those we have studied?
Cauchy's Theorem, First Isomorphic theorem.  Pretty much the ones that were on the midterms.

What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
I definitely need a big review just on every thing that we did at the beginning of the semester with rings and fields.

What have you learned in this course? How might these things be useful to you in the future?
I have learned how important it is to know how things came about in mathematics.  This will be helpful in the future when I am teacher and have my own students and I will be able to study more the mathematics I am teaching and give them a proof of how/why that particular math concept is.

9.3 and 9.4, Due April 8

Difficult:  What is the difference between the centralizer and the center of a group?

Interesting:  The Third Sylow Theorem can be used to determine if a group is simple or has proper normal subgroups.

9.2, Due April 6

Difficult: theorem 7.9. What are the k and the t?

Interesting: The fundamental theorem of finite abelian groups.  Every finite abelian group can be written as a direct sum of prime cyclic groups.

9.1, Due April 4

Difficult:G_i is not a subgroup of the direct product G_1 x G_2 x...x G_n.

Interesting: Direct products are not commutative.