BYU Math 320 Readings - Easton Potokar

I did read the entire section. I understood most of it including all the distributions - beta, gamma, uniform and normal. What I feel I'm still lacking is an intuition for the p.d.f. and c.d.f. They seemed pretty abstract in the section and I feel a few examples will do me a lot of good. This started bringing back more from my Stats 121 class. I remember variance being the square of std (I think), and also using chi-squared which was mentioned for things along with the normal distribution. I didn't mind that class, so I'm hoping we head in that direction with stuff we're learning.

I did read the entire section. It wasn't too bad, the distributions all mostly made sense. It's just we're moving so quick and a decent amount of vocab was added in and it's based so heavily on vocab I'm still not super familiar with. I think after being walked through some examples of binomial and poisson distributions I'll get it down pretty quick though. I'm starting to get less and less connections to these sections since I haven't dabbled too much in probability. The only connection I have to these is probably the normal distribution. I also found it pretty cool how the binomial theorem keeps coming up all over the places, in seemingly the most random times.

I did read the entire section. I think the hardest part was just the speed that they cruised through everything. I hadn't really gotten a grasp on what a random variable is or what it is used for, then they rushed right into "X=a", probability mass functions, expectations and variance. I've kinda got a jist of what they all are, but not a super great idea. I'm sure a more detailed overview will solidify everything for me. This section reminds me why I've always intentionally/unintentionally avoided probability! We did some basic counting in high school math, didn't like it much and didn't find it very intuitive, and have basically avoided stats since. The Stats 121 class I took wasn't too bad, so I was getting more comfortable, and now we've dived headfirst into all the unintuitiveness! It'll be good for me though, so I'm doing my best to keep up with it.

I did read the entire section. I think the section was a great idea, it covers many of the things I've been struggling with, hitting on those things where my intuition has been failing. I think all the examples help more than anything, just seeing these things put into practice. I didn't think independence was too bad either, but maybe that's my intuition failing again! One of the examples, about the bomber planes, I had actually heard before in "How to not be wrong" by Jordan Ellenberg. He talks about how mathematician are important basically because they see the world a little differently because of being able to overcome bad intuitions.

I did read the entire section. I think the hardest part for me was just getting an intuition for these things. They're so much different than what's done in an analysis class that I'm used to, that it's going to take time to "build the world". I especially didn't get the chain rule and conditional probability hasn't quite clicked yet either. The other formulas seemed based off those. This once again takes me back to a stats class I took. It was definitely not nearly as deep and definitely not nearly as thorough or fast as we're moving. I think that's for the best, since I didn't feel I learned as much as I could've in that class.

I did read the entire section. I thought most of it wasn't too hard, it's just getting used to new definitions like sample space, events and "discrete probability space". When I thought about the examples enough they made sense, but I wouldn't say I have intuition for them quite yet. I'm sure with more practice that'll come. Naturally, this reminds me a lot of the STATS 121 class I took a while ago. We discussed a few things that came up in the section like probabilities, events, and a few of the example problems. I feel the book is setting a much stronger foundation than what I learned from though.

I did read the entire section. I understood most of the examples when I took the time to read through the thoroughly, but did not get what NP-hard was. It sounded like an NP problem that had a polynomial algorithm? But that sounds like just a P? I didn't really get NP-complete either, so clarification on that is definitely needed as well. The obvious connection probably everyone has is to the million dollar problems. I've had them mentioned in classes before, but never 100% understood them. It's cool to be starting to get what they're about a little bit more, and actually understand them more thoroughly.

I did read the entire section. Similar to last time, I didn't think the content was terribly difficult, but I would probably benefit from see the algorithm in motion a couple of times. I did understand Kruskal's algorithm a lot more quickly than Prim's as well.  In the discrete math class I took we covered spanning trees quick a bit, but we covered complete graphs (graphs where all possible edges are present, I think they're called complete) and possible spanning trees of them. I don't see us going that direction, but finally learning algorithms on how to find spanning trees is super interesting.

I did read the entire section. I think I understand most of the algorithms (BFS and DFS weren't too bad), but the hardest one was definitely Dijkstra's. I definitely noticed none of the word explaining really helped me understand them, but the pictures did lots better and seemed to make things click. It's been really cool to see implementations of these algorithms. I did a bunch of graph theory stuff a while ago in a math class, and did some data structures in another, but we never made it to any very complicated or useful algorithms. It's been super cool to actually see all this stuff I've learned implemented.

I did read the entire section. It wasn't too bad, but this section more than most I feel I need to program some examples myself to think my way through, especially regarding the difference between top-down and bottom-up dynamic programming. Bellman Optimality made sense for the simpler problems, but I lost it for some of the larger ones. This section reminded me quite a of Dr. Jarvis's BYU devotional talk "That's how the light gets in". He starts by talking about the postman problem, and the significant savings by allowing a little bit of error. He then compares it to our everyday lives, where we also must live with a little error. It's made me start comparing some math principles we learn from time to time to gospel principles.

I did read the entire section. I didn't find any of it too hard, maybe a few of the proofs (especially the one describing the complexity of making a heap is O(n)), but I think given some more deep reading I can get them. This is the first section this chapter that has been all new information for me, I've never heard of heaps or priority queues, so I think just some time with the concepts will help me. Since this was all new information for me, I don't have a lot of connections or reflections about it. I am very excited to implement it though in one of the labs.

I did read the entire section. It wasn't too difficult since I've covered some stuff on binary search trees before, but the hard part was definitely AVL trees and the rotation. I think I followed it, but some more concrete examples (which I understand may come from the lab) would be great. Also didn't super follow the proof for the min/max number of nodes in an AVL tree of height h. Like I said, I've done binary search trees in classes before, but it was all in Java. I'm interested to see how they'll be implemented in Python and how difficult the rotation code is going to be. It's cool to see how this could apply to some of my personal projects that I've been working on.