Post 42 make up assignment: Focus on Math talk

This talk is titled "Who's number one? from ranking to bracketology".

The speaker talked first about how often we use ranking algorithms every day (e.g. Google). He discussed how predictive methods aren't trying to predict upsets (usually). They're trying to predict the most likely outcomes.

We talked about how we can graph a sport season and rank teams by wins. Winning percentage isn't as good as when we take into account strength of schedule. Strength of schedule, mathematically, is taken care of with linear algebra. Each game creates a dependency between the two teams, expressed as an equation.

12.4, due on December 8

What was the most interesting part of the material for you?
I think it's cool that the fundamental properties of limits are very similar to properties of other mathematical concepts. Being able to use these additive and multiplicative properties will make proofs much faster.

What was the most difficult part of the material for you?
I had a hard time understanding the proof for Lemma 12.26. The use of the deleted neighborhood in the statement kind of confused me, but I'm sure it will make more sense in class.

12.3, due on December 5

What was the most interesting part of the material for you?
The idea of a deleted neighborhood is something I have never heard of before, even in calculus. But it makes sense that we need to use this, so that the domain of the function doesn't technically need to include the value at which we are evaluating the limit.

What was the most difficult part of the material for you?
I have a hard time figuring out what to choose as the expression for delta. Just like the expression for N from before, it will probably come easier with practice.

12.2, due on December 3

What is the most interesting part of the material for you?
It's interesting how the harmonic series diverges. It seems like it's right on the line between converging and diverging. I hadn't yet seen a proof of this fact until now, so that was good to see.

What is the most difficult part of the material for you?
The hardest part of the section was understanding the proof that the harmonic series diverges to infinity. Don't we know that if something diverges, it either diverges to negative or positive infinity?

12.1, due on December 1

What was the most interesting part of the material for you?
I am excited to do proofs about calculus. I loved the calculus classes I took, and it will be fun to more rigorously understand the concepts.

What was the most difficult part of the material for you?
I have a hard time figuring out what to use for N in the proofs. As we do more practice problems it will make more sense.

Responses to Questions, due on November 25

What have you learned in this course?
In this course, I've learned to become more rigorous in my mathematical understanding. In calculus we focused less on rigor, so this class has been useful in that regard. I have become much more precise and articulate when communicating mathematical ideas.

How might these things be useful to you in the future?
The mathematical rigor I've gained from this class will be essential in the upper-level math courses I take in the ACME program. Being able to show something is true, instead of just applying given theorems, gives a much deeper understanding of the idea.

11.5-11.6, due on November 23

What was the most interesting part of the material for you?
I think the fundamental theorem of arithmetic is really cool, because it makes so much sense and makes comparing numbers much easier. Prime factorization is interesting.

What was the most difficult part of the material for you?
I had a hard time understanding the proof for Corollary 15. Using induction for this doesn't make sense to me, because I don't see why we know the base case works.