Section 6.1 (1st part), due February 25

What was most difficult?
The most difficult thing is some of the notational characteristics, like the top of page 146 and in general, this stuff is just getting a bit hard to keep track of...abstractions, definitions, etc.

Reflections
What the heck is meant by the first example on page 146?! I hope I don't get murdered on the test...

Section 6.1 (2nd time), due Feb 23

What was most difficult?
The most difficult thing was (nothing new), just the new vocab and I'm not sure I like the notation a+I...I think in general the notation in this subject can be a bit misleading.

Reflection
Nothing is super difficult, it's just a pain to have class two days in a row! But at least we had a long weekend to do the previous assignment (of course I didn't use my time effectively...long weekends encourage relaxation...bad news).

Section 6.1, due February 22

What was most difficult?
The most difficult thing is understanding the bigger picture of what we're doing, and why ideals are relevant. The next most difficult thing is having to remember and understand more, very specific definitions.

Reflection
We'll see how things go in class... I'm interested to learn about ideals, but also scared because supposedly things are going to get harder yet before they get easier, though class hasn't been too hard just yet.

Section 5.3 Due, February 18

What was most difficult?
The most difficult part is still understanding modular arithmetic in these fields.
The last assignment wasn't very clear or helpful. Also, I missed lecture Wed so I didn't get any good info. I'm hoping tomorrow's lecture can help.

Reflection
I thought the discussion about complex numbers was kind of cool. I think Complex Analysis (well, parts of it) is pretty cool so it was just neat to see we could get the set of complex numbers buy using these fields.

Section 5.2, due February 16

What was most difficult?
The most difficult part was the paragraph at the top of page 126...I just feel lost right there.

Reflection
I have been super, super busy in other classes, with tests and projects so it's been hard to keep up the reading for the last two days. Things are just pretty stressful and I hate having to choose between sleep/my health and keeping my head above water. After tomorrow things should settle down and hopefully I can get into the groove I was in before the test for this class.

Section 9.4, due February 11

What was most difficult?
The thing that was most difficult was the notation [a,b] for a/b, because
I'm so used to the latter notation. However, towards the end of the section they switched, which made things easier. In general, what has been difficult and further exemplified in this reading, was how they took something so intuitive and give us these super specific, strange names for everything. This makes me over-think everything and when I try to remember the definition, I feel confused until I remember the aspects that are more in line with my intuition. But, this is mathematics, so it's no real surprise, just a bit obnoxious at times.

Reflection
It will be fun/interesting to do some of what we've been doing, but with rational numbers now.

February 9 Reading Assignment

Topics/Theorems I think are most important
I think rings and polynomials are most important, and the named theorems associated with each. Also, the counting in Z mod n is important, but that's pretty easy so I'm not too worried about it. The Division Algorithm (also the DA in F[x]) will be important, perhaps most importantly for using it prove things. The Remainder Theorem and Factor Theorem will be important.

What kind of questions do I expect to see?
I expect (and hope) the questions are similar to those on the homework, which are usually very straightforward, though they require a thorough understanding of how the theorems and corollaries can be used to find new results. I expect questions such as prove...(blah blah blah) is irreducible, or find the linear combination of the gcd of these two numbers (or polynomials), etc.

What do I need to work on better before the exam?
I need to memorize the definitions better, and be able to command them. Some of them right now, I still have to refer to the text, so I need to get those down pat and understand the nuances and what is what so I can move through the material a bit more confidently. I feel like I know most of the other stuff pretty well, it's just that I forget the EXACT definition at times.

Section 4.4, due February 7

What was most difficult?
I have a hard time choosing what was most difficult because this section was pretty straightforward, especially when compared to the last section. Friday's lecture cleared that up though and I'd be lying if I was to make up something from this reading that was hard.

Reflection
I think there are some cool theorems in this section, namely The Remainder Theorem and The Factor Theorem. I had just never really thought about finding the remainder by evaluating the function at the point a from the factor (x-a).
Surprisingly, I am thinking this class is pretty cool. Even though I'm more of an applied mathematician, and analysis is a bit more directly related, I HATE analysis and I think Algebra is much more interesting and fun, so far at least. At least Algebra is doable by HUMANS, and the hw isn't impossible to figure out, though it is challenging enough.

What was was most difficult?
The thing that is most difficult right now is that there are so many new terms and concepts...they are just piling on and when I'm doing the reading, I feel like my head is going to explode and I don't have time to process it all. Reading just makes me look forward to lectures so much more.

Reflection
As mentioned, the reading is confusing, but once I've been to lecture and when working on problems, it's not really that bad.