4.1, due on 1/31

1.  I found the xa=ax for every a in R part hard to believe.  They don't give a proof of it in the section and they don't give it in the appendix they refer to either, no good.

2.  I thought it was interesting that now we're going to expand to polynomials in rings/fields.  I found the division algorithm applied to fields interesting.  The proofs (that were given) were understandable.

Class Feedback, due on 1/28

• How long have you spent on the homework assignments?  I spend about an hour on the homework assignments.
• Did lecture and the reading prepare you for them? Yes.
• What has contributed most to your learning in this class thus far?  The homework helps.
• What do you think would help you learn more effectively or make the class better for you? Since the reading is mandatory and mostly we just go over the reading in class lately I've been getting bored in class.  So, maybe less reading or different stuff in lecture than in the reading, but I understand that for some people seeing it twice helps them understands.  So I'm not sure.

3.2, due on 1/26

1.  It is a little unclear to me how to show how rings are not isomorphic because how do you show there is no possible function.

2.  I like the idea that now we have functions between our rings.  This will make things more interesting.  It reminds me of switching between the frequency domain.  Pretty much all of the examples were straightforward.  The proofs also were fairly easy to follow.

3.2, due on 1/24

1.  I was a little confused by Theorem 3.5 (7) because on Friday's homework we found a 1r=0 so how would -1ra=-a?  Oh, well by looking at that proof I got it.

2.  I liked the idea that these principles could be applied to any ring.  It seems powerful.  Also all the proofs were very straightforward.  I liked Theorem 3.6 for checking if a subset was a subring because Theorem 3.2 seemed like too much stuff to remember.

p.s. The homework assignment due Friday was a little excessive.  I do not think it was necessary to do addition and multiplication tables for three separate Cartesian products.  After two, maybe even one, it was busy work.

3.1, due on 1/21

1. The first example in this half of the reading was a little confusing not in concept just in utility.  I have no idea why or where you would need the Cartesian product of these two rings but whatever.

2.  Theorem 3.1 seemed very straightforward but I'm still not sure of its utility.  Subrings made sense and seem like they should be useful.  So did subfields.  Theorem 3.2 will be useful in proving something is a subring and the proof was trivial.

3.1, due on 1/19

1. I found all the reading very straightforward and understandable. I thought the 5th example was a little strange. I did not like the fact that it said "take our word for it that Axioms 2,7, and 8 hold."

2.  We are finally getting the point!  I find it very interesting that we will be able to apply general theory to a family of systems that is covered under a group of common features.  I am very interested in linear algebra (I took 570 last semester and it is an important part of my research) so I really liked the 6th and 7th but most the 11th example.  I was reading the field definition and I was thought "matrices don't do this" but then the book showed me a subset where they do, very interesting.

2.3, due on 1/14

1.  The proofs weren't too difficult I just don't like when a proof is so wordy.  It makes it easy to get lost in the words.  This sometimes makes my proofs weaker but I think it is easier to follow.

2.  I like when things come together to make a whole that is very logical.  We are not quite there yet but I feel like we're close with congruence classes (sections 2.1-2.2) no being integrated with primes(section 1.3) and the greatest common divisor (section 1.2).  I am excited to (hopefully) soon be able to see the point of these congruence classes and their utility.

Solomon Friedberg - Boston College - Packing Primes 1/11

I thought it was interesting that I had to come out to Utah to hear someone who could possibly be my neighbor.  Being from Cambridge, BC is only about 15 minutes from my house.  

1.  The speaker introduced some new notation that was a little fuzzy because it was new, such as the pi function and Riemann zeta function.  He also used several words that I did not understand but were spoken too quickly for me to be able to write them down.

2.  I thought it was interesting that not only did he have a homework problem from the second assignment on a slide but his proof was the exact same proof that I had done.  I thought it was interesting that he hadn't seen the Pi (product) function until graduate school because I have already seen it in several instances and I still have a year of undergraduate work left.  The connection that he drew between the pi function and e was interesting.  That relationship was that the number of primes less than or equal to x (pi(x)) was approximately equal to x/lnx.

2.2, due on 1/12

1. The motivation for Theorem 2.6 was a little confusing.  I'm not sure if I totally grasped the point but I'm not too worried about it because I feel like I understand Theorem 2.6.  I also don't really like how they introduced new notation but I'm sure I will get used to it.

2.  I think it is interesting how we are now developing an algebra for congruence classes.  I am still not exactly sure why they are important but hopefully the importance will avail itself soon.  I thought it was pretty sleek how the proof of Theorem 2.6 fell out directly from Theorem 2.2.

2.1, due on 1/10

1. I thought it was strange how the notation [a] could be an infinite number of different sets, depending on the congruence modulo number.  It seems like a subscript could have been added outside of the bracket to indicate the congruence modulo number.  The introduction of the sets of all congruence classes modulo n was not very clear and it was unclear the utility of them.

2. I thought it was interesting how two congruence classes could only be disjoint or identical.  This is slightly counterintuitive but the proof was very straight forward.  I am pretty sure I have seen congruence classes before but it is still unclear to me the usefulness of them.

1.1-1.3, due on 1/7

1. At first it was difficult to follow the Euclidean Algorithm.  It was unclear to me the point of it.  After reading over it again I understood what it was.  The proof seemed fairly straightforward.

2. I think it's funny how we learned about division and prime numbers so long ago and we're still studying them.  I find it interesting how we are deeply evaluating things that are so fundamental.

Introduction, due on 1/7

Junior (Graduation), Senior (Credits)
Major: Mathematics

Post-Calculus Math Courses: Math 290, Math 334, Math 341, Math 343, Math 570.
I am taking this class to fulfill the requirements for the math major.

My most effective math teacher explained difficult concepts well, answered questions concisely, and used the book as a supplement i.e. gave examples/proofs that were not in the book so that we had two sets of examples/proofs.

My least effective teacher did not explain difficult concepts well, got flustered when answering questions, and depended solely on the book only giving examples/proofs that were in the book.

I am a member of the BYU Symphony.

I can only attend Friday's office hours because of symphony rehearsal (1-2:50 MW) but if they were at three I could attend every day.