ACME Volume 2 2018

The trickiest thing for me in this section is keeping the terminology straight. I sometimes get paths and walks mixed up, which matters in proofs about cycles. I find the various names for trees interesting. It is easy to see where many of them came from, but the way they are mixed and matched can be unexpected. The definition of leaf node right after parent and child nodes makes me laugh because it makes me imagine childless people as leaves.

This section was pretty straightforward. I can't think of anything that was difficult. It was interesting to see all the different ways to apply paths and graph theory.

I don't understand why we care that the log of the gamma function is twice differentiable and convex. I can see why we would care about those things about the gamma function, but I'm not sure why we care about the log. I think it is cool that we can find ways to take discrete functions and extend them to the real line (or the complex plane.) So much of life is extending our experiences to broader applications, that I enjoy seeing it in math. For assignments without coding sections, I will usually spend an hour or two on the assignment. If there is a coding problem, it will probably add at least an extra hour (often more) to the assignment. (But you probably shouldn't use me as a benchmark.) The repetition (reading, lecture, homework, lab) is helpful. I'm not sure what I would change.

The Master Theorem is interesting, but I still don't feel confident figuring out temporal complexity in the first place, but I do think I'm getting better. It is interesting reading about how much faster various algorithms are for the same task. It leaves me wanting to do a better job coding things up. But that feels like wanting to write an elegant proof: lovely when you can see it, but non-trivial to figure out much of the time.

If I am not careful, I get the last two corollaries mixed up. It is easy to forget that Corollary 1.9.19 is mod p-1 not mod p. I laughed when they named the appropriate corollary "Freshman's Dream".

The thing I find most difficult in this section is following the proofs. While they make sense, they are not as intuitive as the proofs we've done in the past for me. I found it funny that I was mildly surprised for a second that the Euclidean algorithm came from Euclid. Apparently I thought it had to be from China because in my head it is irrevocably connected to the Chinese Remainder theorem.

I found it most difficult to follow all the combination stuff at the end. It makes sense, but takes more effort to follow. I do find it neat the way that we have so many ways to write down patterns we see in the world. And once we write it down, it is often easy to find it in unexpected places around us. That is how I feel about combinations.

This section the most difficult part was following the spatial complexity arguments. I follow it but it isn't obvious to me. It was nice to see some examples like the labs we have been coding. It made following the code in the chapter easier because I had already thought about that problem.

The most difficult part of this section for me is figuring out how the indices change when the order of summation is switched. It seems weird switching summation so easily after all the carefulness of switching integrals and infinite sums. Clearly it is fine, since everything is finite. But apparently I have a built in warning sign about switching sums.

The most difficult part of the section for me was not slipping into straight derivatives and integrals but instead thinking through the sums. Straight derivatives and integrals don't quite work. I think it is satisfying when telescoping series make everything simple.

Introduction: I have both a bachelor's degree and a master's degree in Math from BYU. I am auditing and a non-degree seeking student. (So I have no year in school or major...) I have had Math 290, 313, 314, 341, 371, 342, 334, 541, 553, 542, 554, 532, 641, 655, 571, 642, 572, 586, 513R (Mathematical Biology), 651, and 652. (updated numbers except for those that are no longer taught.) I chose to do ACME because it sounds fascinating. I want to know how to apply the math I know to the real world. Programming is not something I am strong in, but it is important for most applications. My theoretical background is good, but I want to branch out and have other options. And as I work to figure out what to do next with my life, I want options. One of my professors years ago would sit in front of the classroom and read the book to me. (I was the only student in the class.) It was not so helpful. I wish he would have supplemented the material rather than just sticking so closely...

1. Yes, I read the assignment. The most difficult part of the material is finding the temporal and spatial complexity. I'm not confident in my counting. I don't know how to figure out the complexity of operations like list.pop(). The other difficult part is thinking on that level and parsing the dense sentences. I haven't done much of that for a while. 2. It is interesting trying to code things like subtraction when I know that the way I know how to do it is not efficient. Being aware of complexity is interesting when I don't know enough programming to write lower complexity programs.