8.4, due November 30

This was an interesting chapter, seeing more in depth how signal processing and cleanup is done. However it would have been nicer to see the application earlier in the section, rather than just briefly at the end. It might have made it easier to follow what the section was covering.

I really struggled understanding what all the omegas, capital W's, and boldface w's were. Something about forming an orthonormal basis for something, but I don't quite understand what for, let alone what the matrix representation is supposed to be.

8.1, due November 26

This section was incredibly enlightening. I've always wondered how signal processing worked, especially how data could be transmitted through a waveform, and this reading did an excellent job of explaining it simply. It's almost remarkable how simple it can be.

One thing I find concerning is the fact that there are many equations that I had difficulty following. Much of it seems to have allusions to differential equations, which I was grateful I recognized, but the material is still quite dense.

7.2, due November 20

I've always thought hash tables were incredible data structures. While they have their own shortcomings, they still eliminate a lot of the problems faced by other data structures. The fact that they can be used in constant time is neat, and in some ways makes them ideal.

I've studied hashing before, and found them pretty straightforward. It has been a few years since addressing them in a class, and we didn't delve much into the mathematics behind them, so this will be a nice refresher and stepping stone. I noticed that while collisions were mentioned conceptually in the text, there weren't many details about collision handling at all, which I found unfortunate, because there are many neat ways of addressing them.

7.1, due November 19

These last couple sections have been pretty interesting, in that it's neat how randomness can help us approximate things like integrals and irrational numbers with computers, even though computers struggle with such precise calculations. I found rejection sampling to be particularly interesting. It makes sense that samples outside the distribution and subtracting them could be used to approximate the difference between the area of two curves, but I wouldn't think it to be blatantly obvious.

As interesting as this material is, it's surrounded by some very intimidating equations, theorems, and definitions. I really don't know how much of it I need to understand for this section, and how much I can just accept and move on.

7.1, due November 16

I enjoyed reading through this chapter because it crosses back into some of the familiar territory of numerical methods and estimations, such as Simpson's Rule. It's neat because it's easy to see the applications of random algorithms, such as estimating pi or finding the area under a complicated curve.

I still struggle to see the bridge between statistics/probability and this material, however. For example, how does the indicator random variable play in to estimating an integral? Also, how do we know how to set up these estimations? The intuition to follow is a lot easier than it is to reproduce.

6.5, due November 12

Unlike the previous sections on probability, this one was less conceptually straightforward. I'm having a hard time even following the first example given in the section. This section also seems particularly dense, which has me concerned whether the material covered in a single lecture will help me feel comfortable with my understanding when I begin working on the homework problems.

As much as I've struggled with chapter 6, I've developed an incredible appreciation for probability and statistics. Seeing the application of such practices in the real world has been more helpful in guiding my intuition than anything else, and it's made it worth it. Still, I've been happy to see the end of this chapter.

6.3, due November 9

Certainly the most difficult thing recently has been taking the time to actually complete these blog posts. With the massive amount of time needed to complete the homework I often find myself working on assignments into the early hours of the morning, because I prioritize them over the readings. By the time I finish the homework after midnight it's already past the due date for the blogs. It's also difficult to reconcile sacrificing time I could be working on the assignment when the reading material will be covered in class anyway.

After going over this section I appreciated seeing distributions we've already become familiar with. As with virtually all of the probability and statistics content, having clear examples to work through is incredibly helpful. It is especially useful knowing exactly which parameters plug in to which parts of an equation and what each of those parameters entail.