6.3, Due Feb 29

Difficult: I am not understanding example one.  What would be in P=(6)?

Interesting: That an ideal may have more than one maximal ideal.  Because when I read maximal I think maximum, and most things don't have more than one maximum.

6.2, Due Feb 26

Difficult: Saying that something is a homomophic image is still a bit confusing to me.

Interesting: It's interesting that pi is a special homomorphism the natural homomorphism, but what makes it so special.  Why can we say that is true for pi but nothing else?

6.1,6.2, Due Feb 23

Difficult: There are so many new terms and it is getting really overwhelming and I am having a difficult time seeing how they really all differ because all of the rules seem to hold for whatever we are talking about. Why do you need a special name for a+I?

Interesting:  I found it hard to find something interesting because I was so lost in the reading.

6.1, Due Feb 22

Difficult: I feel like an ideal is the same thing as saying something is commutative. What is the difference between the two?

Interesting: Proving that something is an ideal doesn't seem to difficult to understand.

5.3, Due Feb 19

Difficult: The term extension field is a little bit confusing to me. Is the extension field the roots of f(x)?

Interesting: It is interesting yet still confusing to me that a root can be [x], because to me that is a variable and I don't see how that can be put in the place of a variable to call it a root, because I feel like you are just back at the beginning.

5.2, Due Feb 17

Difficult: I'm still not quite understanding how to find the congruence classes of a polynomial.

Interesting: It's interesting that polynomials can have units and identities as well.

5.1, Due Feb 16

Difficult: I'm still a little bit confused as to the relationship between congruence classes and remainders.

Interesting: It's nice that the properties for congruence classes carries over from the integers to polynomials.

4.5 and 4.6, Due Feb 12

Difficult: When it says that A polynomial is irreducible in the complex polynomials if and only if it has degree 1, is that essentially saying that every polynomial in the complex polynomials is reducible except for the ones that are degree one?

Interesting:  I like Eisenstein's Criterion. It makes deciding whether a polynomial is reducible or not very easy. But it's annoying that it doesn't work in mod n.

4.4, Due Feb 10

Difficult: Are roots and remainders of polynomials the same thing?

Interesting: It is interesting that you can say if a polynomial is irreducible it has no roots.  I mean that makes sense, but what is interesting is that a polynomial can be reducible but still have no roots.

4.3, Due Feb 8

Difficult: Just to be clear, the associates of a polynomial are the essentially like units in the integers?

Interesting: Polynomials can be "prime" we just call them irreducible.

4.2, Due Feb 5

Difficult: I am just a little bit confused with what it says in example 2.  I agree that x^2+1/3x+2 is the gcd of that polynomial.  But what is confusing is that it says that it is "a" gcd of the polynomial.  Does that mean that there can be multiple gcds of a polynomial?

Interesting: multiples of polynomials that divide a polynomial also divide the same polynomial.

4.1, Due Feb 3

Difficult: I'm a little bit confused as to what the elements of R[x] are.  Are they the coefficients of the polynomial or are they the values of what x can be?

Interesting:  We are using all of the properties of polynomials learned in high school and then just using them to determine fields and integral domains and such.