7.5, due on 3/16

1.  The only part of the proof of theorem 7.25 that wasn't clear was that "b in G imples b = eb in Kb is a subset of the union of right cosets implies G is a subset of the union of the right cosets."  The red part was unclear.  Is it because b was an arbitrary element of G?  In theorem 7.26 does [G:K] mean the number of distinct cosets?  They explain that in the proof but it seems like they should have explained it before they used it.  If they did I missed it.

2.  The first three results were very straightforward and easy to understand.  Theorem 7.25 was very interesting and the proof was pretty clear.  Apart from the [G:K] part theorem 7.26 was very clear.  I liked the second part of corollary 7.27.

7.4, due on 3/14

1.  Theorem 7.19 was strange to me.

2.  I feel like the 3rd or 4th section of every chapter of this book is called isomorphisms and homomorphisms.  The ideas were very straightforward and sort of repetitive.  Theorem 7.18 was very straightforward and the proof understandable.

Curing Cancer with Math Lecture

First of all, sorry I took so long to write this.  I understand if you don't except it.

Second, I really enjoyed this talk.  I work in IDeA Labs in the CS Dept and we do a lot of mathematical modeling.  One of my friends studied predator-prey models and developed one for leaf cutter ants.  So when the speaker started talking about applying them to cancer I was very interested and followed her quite easily.  It was pretty amazing how she was able to develop the model then optimize the medicine dosage in order to help patients.

7.3, due on 3/11

1.  Theorem 7.11 was a little confusing.  I guess I didn't know that the set being finite implied all the elements were of finite order.

2.  The idea of a subgroup was very straightforward.  The examples were simple enough.  I liked the matrix example on pg 182.  The idea of cyclic subgroups was interesting.

7.4, due on 3/7

1.  Most of the ideas made sense.

2.  When I read the definition of a group I thought it was pretty close to some of the axioms of a ring so Theorem 7.1 was straightforward.  Corollary 7.3 was a clear corollary and it made sense.  Theorem 7.4 made sense and the proof probably isn't too rough.

7.3, due on 3/4

1. I was thrown off that it was not built upon an old idea.  It was sort of unique.

2.  The definition of group was pretty straightforward.  And it was kind of related to the old ideas, that is the axioms for a group are similar to those of a group.

6.3, due on 3/1

1. The idea of a maximal seemed strange to me and I'm not sure of its utility.  The proof of theorem 6.15 was a little much.

2.  Expanding Prime to the structure of R/I is interesting.  Theorem 6.14 was pretty straightforward.  Cor. 6.16 was interesting and the proof was practically trivial.