Final Reflection, due on 4/13

• Which topics and theorems do you think are important out of those we have studied?
• It depends on your definition of important.  I don't foresee the topics covered in this course being very useful in my research.  It may some day become relevant to my research but we'll see.
• 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 on Wednesday.
• I just have to review everything.  Nothing was too difficult.  It was just a lot of material.  So I have to make sure I remember the little computation problems and how to apply the big theorems.
• One thing I have to go over is ideals, maybe principal ideals in particular.
• How do you think the things you learned in this course might be useful to you in the future
• I'm not sure.  See first answer.

8.3, due on 4/11

1.  No love for proofs of Sylow's Theorems, sad day.  Corollary 8.18 seemed very obscure but the proof was straightforward.

2.  The First Sylow Thm was interesting but they were too lazy to prove it.  Cauchy's Theorem was the same thing but k=1.

8.2, due on 4/8

1.  The notation review was fine but I still am not sure what the big deal is about the difference between addition and multiplication.  The proof of Lemma 8.6 was pretty beastly.

2.  Theorem 8.5 was pretty cool and the proof wasn't too bad.  The Fundamental Theorem of Finite Abelian Groups seems pretty fundamental.

8.1, due on 4/6

1.  I'm not sure why this is new chapter it seems like the same stuff we've been doing.

2.  The order of the Cartesian product of groups was very simple.  Lemma 8.2 was pretty nifty.  The proof was very straightforward.

7.10, due on 4/4

1.  At first I thought it was the simplicity of An conjugate transpose but then I noticed that it was a footnote.  I forgot what simple meant.  The proofs in this section were a little hard to follow.

2.  The lack of examples was interesting.  I was surprised this author loves examples.

7.9, due on 4/1

1.  I did not follow the proof of Corollary 7.47 very well.

2.  I really liked the new k-cycle notation because I hated writing out the long things every time in Sn.  The concept of disjoint was very straightforward.  This stuff seems to getting closer to graph theory/network stuff.  Or I'm just barely beginning to see the connection.

7.8, due on 3/30

1.  The idea of the kernel was weird to me because I think of a kernel as the set that is mapped to zero.  But since groups don't have a zero element I guess the next closest thing is the identity.  They skipped the Second Isomorphism Theorem for Groups!

2.  All of the theorems were very straightforward.  I was perfectly okay with the proofs.

7.7, due on 3/28

1.  Theorem 7.37 was a little weird.

2.  It seems like quotient groups are an extension of quotient rings.  Theorem 7.35 was very straightforward and the proof was easy to follow.

7.5, due on 3/25/11

1.  I don't understand why no one other than Jimmer scored in double figures on our team.

2.  Theorem 7.33 was very straightforward.  Theorem 7.34 made lots of sense.  Dr. Doud already proved it in class on Wednesday.

7.6, due on 3/22

1.  I don't understand why they introduce right cosets then left cosets a couple sections later.

2.  The idea of left congruence was pretty simple.  And the idea that it was an equivalence relation was very simple.  The idea of a normal group was very straightforward.

Midterm 2 Response

• Which topics and theorems do you think are the most important out of those we have studied?
• Langrange Theorem
• The general ideas of group theory
• Quotient rings
• What kinds of questions do you expect to see on the exam?
• Well I can tell you one thing I hope we don't have to play sudoku in the testing center.
• A proof or two, even though I like the proofs more
• Judging from the last test we'll probably have to give some examples of different things like finite and infinite groups, subgroups, cosets, etc.
• 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 on Monday.
• I just need to review the concepts more, go over the computational/homework type problems, and look over the important theorems some more.

Math in the Movies

This talk was ok but it wasn't that in depth.  He lightly scratched the surface of some topics that sounded interesting but it was more of a general overview of the movie making process which was boring to me.  He was the man guy who made the chess movie at the beginning of toy story I believe.  That was pretty awesome.  He also had clips of other movies that we're pretty good.

7.5, due on 3/18

1.  The proofs were pretty easy but I didn't realize before the difference between Z4 and Z2xZ2  and between Z6 and S3 but now it's very clear.

2.  This section was pretty straightforward.  The theorems seem very useful.  If you know the order of a group you can tell a lot about it if the order is prime, 4, or 6.

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.