Midterm 1 Review: Due Feb 1

1. Most important: the stuff about rings, fields, integral domains.
2. I expect to see question like what is this theorem and how do you prove it.  Proving that something is a ring or a field or a integral domain.  Giving examples of such things.
3. I need to work on knowing how to construct proofs.

10.4, Due Jan 29

Interesting: I understand how the relation ~ works, like the concept behind it and how things are equivalent.

Difficult: I do not understand how the idea of ~ relates to everything else in the section.

Due Jan 27

How long have you spent on the homework assignments? Did lecture and the reading prepare you for them? 

I have spent between an hour to 2 hours on homework assignments.

What has contributed most to your learning in this class thus far?

It has been really helpful to do the reading before hand that way in class I can really focus on the parts that I didn't understand in the reading and not have the lecture be the first time that I am learning it.  I do also use the internet a lot for help.

What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)

For myself I should probably go to office hours and get help from either you or the TA when I have questions.

3.3, Due Jan 25

Difficult: The relabeling part was confusing to me.  Can't you just take any two sets and relabel one to match the other and it will work.  I guess I don't understand the purpose.

Interesting: Isomorphism and Homomorphism kind of seem like proving something is one to one or onto just with different names and maybe a little bit more properties.

3.2, Due Jan 22

Difficult: Not really understanding why we can't just subtract.  I mean isn't subtraction and a negative the same idea?

Interesting: It's nice to see that the stuff we learned about units and zero divisors also applies to rings.

3.1, Due Jan 20

Difficult: The example 20 was hard for me to follow, but maybe that was just because I was unsure what the Z[sqrt 2] meants.

Interesting:  It is very nice that in order to prove something is a subring of a ring you only need to verify four of the axioms.

3.1, Due Jan 15

Difficult: I am confused because the definition of a ring is a nonempty set R equipped with two operations and in most cases that is addition and subtraction, but then there is the commutative ring that looks like it just has to satisfy multiplication.  So what is necessary for something to be a ring and can something be called a "ring" in general if it is just commutative?

Interesting: I thought it was interesting that the idea of rings can be applied to things that may not be numbers or number classes.

2.3, Due Jan 13

Difficult:  What is going to be difficult in this chapter is remembering that they aren't going to be using brackets when talking about classes.  I think it is going to cause a lot of confusion for me.

Interesting:  It's interesting to see the comparison between just regular integers and the classes.  For example when we say 2*3=0 that is not true in the integers because neither 2 or 3 is 0 but it is true in the classes because the class of 6 is 0.  So in order for the multiplication of integers to be 0 one of the integers has to be zero but for classes they can both be non zero and still equal 0.

2.2, Due Jan 11

Difficult:  It is still unclear to me how you find the classes so it is making it hard for me to see what you get when you add classes and when you multiply classes.

Interesting:  It is nice that the properties of arithmetic hold true for the classes as well.

2.1, due Jan 8

Difficult:  The whole mod n concept.  It says that a and b are congruent if their difference is 0 and equivalent if their difference is a multiple of 0.  Doesn't that make everything equivalent to each other? What is the point of the mod n.

Interesting: It's nice that the reflexive, symmetric and transitive properties hold true for congruency.

1.1-1.3, due Jan 6

What was difficult for me to grasp was the primes and unique factorization chapter.  I also am just unsure how to know when you do a proof by contradiction or need to prove it two ways.  I know that kind of goes back to Math 290 but it has been a while since I have taken that class.  Also from the reading it seems to me that 0, +1,-1 are not prime or composite. Is that correct.  That's something I have never been really sure about.
Something that I found very helpful was the way to find out if a big number is prime with out dividing it by every number between 0 and itself.  The one where n has no prime divisors less than or equal to the square root of n.  It could have come in handy in earlier math classes.

Introduction, Due on Jan 6th

I am in my fourth year of college and I am studying Mathematics Education.  I have taken Math 290, Math 313, Math 314, and Math 334.  I am taking this class because it is a requirement for my major.  The math teacher that was really great was one of my high school math teachers.  His name is Mr. Barkdoll and I had him for two years.  He really cared about my success in school and I was able to go to him for help in deciding which classes to take and which ones would benefit me at the time.  He believed in me.  He also took the time to get to know his students and he made mathematics fun with different games that continued throughout the year.  One of my favorite professors at BYU was Professor Villamizar.  He really cared about how we did in class and would come and talk to us and tell us what we could do to improve.  He made himself available and he new me by name and didn't forget me after the semester was over. A little bit about me, I am from Arizona, I am the oldest of 5 girls, I love singing, and being out doors hiking and camping. I am available for the hours provided.