December 7, 2016

Difficult: So do alternating groups A_n have order 3n?
Reflective: Corollary 8.28 could have been helpful on the last homework.  And 8.31.

I think any named theorem is important out of what we've studied.  I also think general knowledge of rings, groups and quotient rings/groups are fundamental to whatever will show up on the test.

I need work on polynomial rings in general.  Like the proof of Theorem 5.11 would be great.  I don't see any sample problems including polynomials (which I like), but if you're planning on sneaking one in, I'd like to see a similar example :).

In this course I learned how to do mathematical proofs.  To be honest, I probably won't use this much after I graduate next week, but it has helped me stop feeling like I was a complete failure as a math major.  I thought I would go my entire college career and not figure out what every math major is expected to be good at, and I felt so defeated.  But I finally became able to do it this semester, and this class helped immensely.  I can now proudly say I graduated in Math instead of feeling like I just scraped by the entire time.  So that's pretty huge.

November 16, 2016

Difficult: I'm not quite sure what the difference is between what a normal subgroup is (Na=aN) and what it is not (na=an for all n in N).
Reflective: You're right.  That theorem 7.34 is super helpful!  That's a lot easier than going through and showing kind of commutativity every single time.

November 11, 2016

Reflective: It's interesting that we pretty much are doing the same things over and over again.
Difficult: Which makes it more interesting that it gets weirder and harder every time we do it. I'm going to need general explaining of this one.

November 9, 2016

Difficult: Can we go over coming up with factoring permutations?
Reflective: Theorem 7.47 is kind of like how numbers/polynomials can be written as products of primes/irreducibles, except for uniqueness.

November 7, 2016

Difficult: What do they mean by a symmetric group S_n?
Reflective: I think theorem 7.18 is really neat. Like that just works out way too nicely.

November 4, 2016

Difficult: I need help with cyclic groups/subgroups in general.  More examples, more explanation.
Reflective: I love this whole "you only need to check two things to see if a ring/group is a sub-ring/group" thing.

November 2, 2016

Difficult: I don't really get Corollary 7.9.
Reflective: The order of element rules are quite like idempotency.  Is that significant?  Related?

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.

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.)

August 31, 2016, 2.0

1.1
Difficult: Remembering that the Division Algorithm requires b > 0.
Reflective: It seems Corollary 1.2 is an easier-to-remember version of the Division Algorithm.  I like it!

1.2
Difficult: It looks hard to come up with a back-substitution in the Euclidean Algorithm to show the gcd as a linear combination of the two integers.
Reflective: The greatest common divisor is a linear combination of the two numbers it divides.  Does that mean, consequently, that a number cannot be a linear combination of two numbers if it is not a common divisor?

1.3
Difficult: I'm having a hard time understanding Theorem 1.8
Reflective: Why is the Fundamental Theorem of Arithmetic important?  It just seems to be a tautology to me.

August 31, 2016

My name is Katie Jacobson.

I'm a senior graduating in December.

I've taken Math 290, 313, 314, 334, 341, 320, 321, 344, 345, 322, 323, 346, 347 (I did one year of ACME)

I'm taking this class because I switched to the regular Math major so I can graduate sooner.

Dr. Jarvis has been one of my favorite math teachers.  He not only was able to teach well to a class setting, but made time for one-on-one personalized help if needed.  He was great at breaking difficult concepts into simpler sub-concepts that made sense.

I was part of BYU's International Folk Dance team for three years and the Women's Ultimate Frisbee team for a semester.