October 31, 2016

Difficult: I could use more explanation of theorem 7.4
Reflective: It's interesting that nonzero rings under multiplication, yet the nonzero elements of a field are an abelian group under multiplication.

October 28, 2016

Difficult: I'm having a difficult time understanding why we study grous at all. They seem like simpler rings, pretty much.
Reflective: so the operation can be any operation at all as long as it meets the listed criteria. So we don't have to necessarily have addition or multiplication or anything. ...that's interesting.

October 21, 2016

Difficult: If you could go over the examples in the book (and maybe more examples), that would be great.
Reflective: The analogy on page 149 about the sculptures/photographs was very helpful.

October 17, 2016

Reflective: why the need for generalization with congruence?

Difficult: I think over all I don't see the need for this so I'm having a hard time grasping the general concept.

October 14, 2016

Difficult: I need some explanation on extension fields.
Reflective: I had no idea abstract algebra could clarify (or even make possible) so many other branches of math that aren't abstract algebra like the complex numbers in this example.

October 10, 2016

Difficult: I didn't really understand thm 5.5
Reflective: I had never thought polynomials and modulos ever went together! Granted, I've never thought about their union much, but it just never occurred to me that it was possible.