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.