September 30, 2016

Difficult: I could use some examples finding gcd's of polynomials.
Reflective: This all seems very similar to what we did in normal rings.  Why are we treating polynomials separately?

September 23, 2016

Reflective: This actually stems from the footnote on page 321 about why we started with the [a,b] notation.  That footnote was spot on: if they had started with the easier notation, I would have spent a lot less time on understanding everything and would have just believed it.  I need to not be lazy in learning these "familiar" things, not just taking believing them because I've already used it.
Difficult: I don't quite get Theorem 9.31.

September 21, 2016

Homework assignments generally take around 2 hours-- probably 1.5 hours on the main bulk and the other bit on one or two tricky spots.

I think going through proofs in class and breaking down how to tackle them and what format is the most intuitive has really helped.  After an entire BYU career of not handling proofs well, I finally think I'm starting to get decent at them!

In class, I love the examples and walking through proofs.  If there's a lot of content in a chapter and we have to choose between hitting every definition, theorem, and other stuff from start until we have to stop class or hitting more on proofs and examples, I would choose the latter.

September 19, 2016

Difficult: I could use some clarification on Images and preservation by isomorphism.
Reflective: In all my different math classes, I have NEVER had injection, surjection, and isomorphism explained so clearly as in this book.  I actually can for sure say what they are now!

September 16, 2016

Difficult: I don't quite get the proof of Theorem 3.11 and why the integral domain has to be finite.
Reflective: I'm starting to see why the distinctions between fields and integral domains and commutative rings with identity are important.

September 14, 2016

Reflective: I like how proving a set is a subring takes fewer axioms than proving it's a ring!  I love/hate these kinds of proofs because they're usually relatively easy, but they're also tedious.  The shorter set of axioms is always appreciated. :)
Difficult: At the same time, I can see myself making a mistake such as the one in the note right after Theorem 3.2; I might mistakenly make trivial assumptions (i.e. a+x=0 has a solution) instead of proving what actually needs to be proven (i.e. the solution of a+x=0 is in the set).

September 9, 2016

Difficult: I had a hard time understanding the proof of Corollary 2.10.
Reflective: What does modular algebra do for us?  What are some applicable scenarios where this would be useful?

September 7, 2016

Difficult: I'm failing to see how the "not depending on choice of representatives" problem was resolved.
Reflective:  Why add/multiply these congruence classes?  How do we benefit from that?
Fun fact:  I am blogging from several thousand feet in the air.  Airplane wifi is the coolest.

September 2, 2016

Reflective: I thought the method of proving Theorem 2.3 (by using reflexitivity, symmetry, and transitivity) was really slick!  I wouldn't have thought of that.
Difficult: I've always had a tough time remembering what makes up equivalence and what each category means and how to use them.  (Hence why I thought the above proof was neat.)