BYU Math 320 Readings - Easton Potokar

I did read the entire section. I didn't feel it was too bad, since I'm a little ahead on the labs, I've done some stuff with the DFT and understood most of what was going on. Maybe it's silly, but I didn't get what the w_n^k's were, just something about roots of unity, but some explicit examples would be nice. Also I didn't follow the proof of the FFT like at all either. In my circuits class currently, we're just starting to make circuits that act as high and low pass filters, and the Fourier Transform seems to fit in their pretty nicely. We've been doing it with the Laplace transform thus far, but I'm excited to see how the Fourier stuff fits in with everything. 

I did read the entire section. I didn't think it was too bad, given I understood the first section well, nothing seemed to be too big of a leap. I didn't follow the proof entirely at the end of the section, but that can probably be attributed to exhaustion. I am still confused about how to construct a Fourier Series given it includes T and w though. This feels like a cross of Laplace transforms and Taylor Series. It has the approximations properties that come from Taylor Series, but it also has some of the transforming that I remember doing w/ Laplace transforms in DifEq and in my circuits class.

I did read the entire section. I thought it actually made a lot of sense, but maybe that's just in contrast to all the probability stuff we wrapped up. Fourier series didn't seem too hard to me (they reminded me of taylor series to some extent), but it definitely wouldn't hurt to see a few concrete examples of it done. My emphasis is actually signal processing, so this is the stuff I'm starting to get into in my concentration classes. We actually did build a filter the section mentions for an audio amplifier, but we largely glossed over the details unfortunately.

I did read the entire section. I didn't find any of it very difficult, it was like a throwback to previous sections on huffman encoding and other algorithms. I think, as usual, just some examples of hashing would help more than anything, although I feel better about this section than I have about one in quite a while. This brings back some of the first labs we did in this class. A bunch of hashing was mentioned in connection to sets and dicts, and it was really cool to get a better grasp of what they are and how are are used. I think it's pretty cool concept and look forward to seeing if there's any other applications or consequences.

I did read the entire section. The part I struggled with most was Inversion Sampling. The theorem didn't seem to click at all, and I never really developed any intuition for it. I think I kinda got rejection sampling, but I definitely still need to give it some more thought. The largest connection I had for this one was probably just the last homework we did. I think we did quite a bit of rejection sampling (if I understand it correctly), and a little bit of inverse sampling in the first problem. I look forward to working hard to get this concepts down.

I did read the entire section. I didn't think it was too bad, the thing I struggled with the most is just following all the symbols in the Monte Carlo problem, but I think I understand how it functions and works. Having it explained thoroughly with some concrete examples will help me solidify things lots. I've heard the Monte Carlo method mentioned a few times in various classes - some CS courses, other math classes, engineering courses, so it's super cool to finally see what it means and does. I really enjoyed that. It's cool algorithms and things like this that really make me enjoy ACME classes.

Overall, I feel ok about this test. I definitely felt way more confident about the last one though. I do appreciate that all the content on this test built upon itself for the most part, so I don't have much to go back and review since it's had to stay pretty fresh. The course as a whole I've really enjoyed (stats is starting to grow on me as I understand it more), and feel the content is excellent, but we move incredibly fast which is frustrating sometimes, but I totally get.

I did read the entire section. It took me a while to come to grips with a lot of it, I had to stop and think about it for a while. I think seeing some examples worked out (as always!) will help me lots. The theory of what is going on with the MAP *mostly* makes sense, but needs some time to settle. The whole conjugacy concept didn't click much at all though. Currently I'm doing some research with the EE department training neural networks, and I'm just starting to get into this type of stuff. I'm just being shown how to train a network and then get a likelihood distribution out of how probable it actually is that the data lands in a certain range.

I did read the section. This section made a lot of sense to me. Through the last couple of sections things have started settling in, and this section with the Central Limit Theorem started really making things click. I think a few examples would help me more than anything, since I think I understood most of the theory. I've heard a few different explanations of why the central limit theorem works, but the one in the book made the most sense from a theoretical standpoint. That it comes from the average of iid events makes a lot of sense to me and really made things click.

I did read the entire section. I felt WAY better about this one than I have about the last few, and it felt good to settle into some of these concepts a bit. All the inequalities and epsilon proofs felt a lot like Math 341, and I feel a lot more comfortable with this stuff. I don't think any of the inequalities or the law of large numbers gave me too many fits. This also felt a lot like a section we had in Math 344 a couple of weeks ago where we just proved a bunch of inequalities. Also slightly off topic, I'm starting to appreciate python plots a lot more as I continue to use them, and am beginning to see how often they come up in the textbooks.

I did read the entire section. I think I picked up on how estimators work as well as MLE. The notation is getting a little out of hand, so I started getting a little lost, but some extra time reeled it in. I think the thing I'm worried about most, is just the shaky foundation this is getting built on. We moved through chapter 5 so quick I don't feel like I understand it as fully as I would like.  Once again I don't have a whole lot of connections to this due to my lack of a stats background. It continues to bring back little things that remind me of Stats 121 that I took, but it's so much deeper I hardly recognize it!

I did read the entire section. Now that I'm getting some of the other distributions under my belt, this section didn't seem as bad. I think I understood the multivariate pmf, but the cmf and pdf went a little over my head. And the covariance I got, but am just a little confused on how to calculate. I think after seeing some concrete examples (if that's possible) worked through, it'll click. Maybe not a super deep connection, but this reminded me of Markov chains we just did in a lab (it's probably supposed to). I'm curious at the relationship the transition matrices in it have with this multivariate random variables.