Review for final, Due Wednesday, April 11

• Which topics and theorems do you think are important out of those we have studied?
• I think that the most important topics that we have studied in the last 3rd of the class have been classifing groups, Lagrange's theorem, the isomorphism theorems for groups and Cauchy's theorem
• 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 in class.
• I need to go through and learn all of the proofs and memorize theorems and definitions
• How do you think the things you learned in this course might be useful to you in the future?
• I don't know how this will be useful in the future. Hopefully it will help me in my upper division courses next year, Number Theory, Cryptography and Combinatorics.

Section 9.4, Due Monday, April 9

The section for today was 9.4: The field of Quotients for an Integral Domain.

This section wasn't that difficult to understand. The hardest part was probably the proof of Lemma 9.26

I thought that this was an interesting argument for the construction of Q the rational numbers.

Sections 8.4, 8.5, Due Friday, April 6

The sections for today were 8.4: Conjugacy and the Proof of the Sylow Theorems, and 8.5: The Structure of Finite Groups.

The most difficult part of these sections was the proofs of th Sylow Theorems.

I thought that the end of 8.5 was interesting when they had a complete classification of all groups of order =< 15.

Section 8.3, Due Wednesday, April 4T

The section for today was 8.3: The Sylow Theorems.

This section wasn't that difficult...maybe because there weren't very many proofs. But the proof of corollary 8.18 was kind of hard to understand.

I thought that this section was pretty interesting. It is neat that we will be able to classify non-abelian groups along with abelian ones.