Section 4.2, Due Wednesday, February 1

The section for today was 4.2: Divisibility in F[x].

I thought that the most difficult part of this section was the proof of Theorem 4.5 which claims a unique gcd of any two functions f(x), g(x).

I thought that it was very interesting and convenient that the properties of divisibilty practically transfer straight over to Polynomials. Most of the proofs are exactly the same, except that for the monic condition on the gcd.

Section 4.1, Due Monday, January 30

The section for today was 4.1: Polynomial Arithmetic and the Division Algorithm.

I found the proof of the Division Algorithm for polynomials to be the most difficult part of the reading. I'd appreciate going over it in the lecture.

I thought that it was interesting that polynomials can be examined in terms of rings. I'm amazed at how interconnected math can be.

Due Friday, January 27

I spend about one to two hours on each assignment. I think that the reading and lectures are generally good at preparing me for the homework, but sometimes there is a disconnect between what I hear in class/read in the textbook and what I am asked to do in the homework. I think that the lectures should bridge that gap instead of just repeating what is in the chapter. Reading the textbook and then soldifying that information in lecture has been the most beneficial to my learning thus far. As I said before, I think lectures should address the coming homework more. But I do like what you are doing already (going over the section & the proofs), but I would appreciate a little heads up for the homework too.

3.3, Due Wednesday, January 25

The section for today was section 3.3: Isomorphisms and Homomorphisms.

I thought that Theorem 3.12 was pretty confusing. I wasn't able to follow the proofs very well. Hopefully they will make sense tomorrow in class.

I thought that the concept of isomorphisms and homomorphisms was very interesting. I particularly liked the analogy that they drew to Roman Numerals. I took Math 300, The History and Philosophy of Math, and we explored a lot of different numeral systems. I mean any different numeral system, or more abstractly, language systems are isomorphisms, very interesting stuff.

3.2, Due Monday, January 23

The section for today was 3.2: Basic Properties of Rings.

I thought that the concept of "units" was kind of confusing. It would be helpful if you went over that in class.

I thought that the reading was pretty interesting. I liked the introduction, which reminded the readers that far more properties are used in Z than just the ring axioms. So naturally, there will be more properties that apply to rings in general.

The rest of 3.1, due Friday, January 20

The section for today was the second half of 3.1, Definition and Examples of Rings.

I didn't think that this was particularly difficult, but if I had to choose something, I'd say theorem 3.1. I'd like to see the proof of that.

I thought that it was an interesting section. I liked learning about subrings. I liked the last example; it was so simple and logical.

3.1 (first half), due Wednesday, January 18

The reading for today was the first half (through page 48) of section 3.1.

The most difficult part for me in this section was the part with the matrices and why they are rings. But upon carefully reading it, I was able to understand.

This was a very interesting section. I particularly liked the introduction to chapter 3. I was very interested to learn why this discipline is called abstract algebra. I thought that it was just because it was going to be very difficult. But, according to the book, it is called abstract because the "common core of essential features" is "abstracted" from different systems so that they can be more easily compared/examined. Very interesting!