Jalen Morgan ACME blog

I read the section, and I really enjoyed it. I understood everything, and the proofs were very straight forward. I thought the concepts talked about were interesting, and graph theory is something fun to do. There didn't seem to be anything hard to learn except maybe some vocabulary, but that usually gets explained well during class. The idea of trees seems interesting to me. I just had a code challenge the other day that talked about trees, so it's something very relevant to be learning.

I read the section. One thing I will note is that this is probably the biggest proof for one theorem I've ever seen, and I didn't understand it much. If we have to memorize this, it's going to take a lot of work. I'm pretty overwhelmed by the amount of content we're expected to learn every day. The most interesting part of this section to me was the bottom footnote on page 74.

Primes and Remainders Today I read section 1.9 of our Algorithms and Optimization book. At first glance, I was very intrigued. I saw a bunch of familiar theorems we must have learned in Math 290 or 341, then some unfamiliar theorems came up. Theorems I don't remember learning are the substitution rule and how to do fast modular expansion. It is obvious by the example given, how important these techniques can be. Fermat's little theorem, although not something I've heard of before seems like a fun little equation, and I can already see what kind of problems we'll have in the homework. As always, there are more theorems than I'd have time to memorize. What I'm most struggling with right now is knowing which theorems are worth taking the time to memorize.

I read the section. A lot of the items in this section are things we learned previously in either Math 290 or Math 341. Things like finding the least positive integer and knowing if a divides b are very familiar, and the refresh was interesting to me. I kind of lost it though, when they started talking about how many iterations of the euclidean algorithm we need to solve for the gcd, so that would be the hardest thing for me in this section.

I read the section. What I thought was most difficult is that there are several formulas we need to learn. Most importantly, the binomial theorem and the following corollarys. Besides that, the section was fairly short. What I thought was most interesting was all the n choose k examples. In particular, I was intrigued by how they calculated the number of possible strings of letters formed from the word mississippi. What's even more astounding is how simple it is to calculate it. It's just 11! divided by the number of each individual letter factorial. This is some cool stuff.

I read the assigned reading. The most difficult part I had with the reading is that I haven't taken linear algebra since 2016, so a lot of the linear algebra concepts are not fresh on my mind. It took me a while to remember how to solve for the inverses of matrices and why they're important. I thought the most interesting part of this section was the part that talks about faster algorithms for calculating the multiplication of matrices. It's interesting that there isn't one "best" algorithm either. Using LU decomposition is faster, but has a trade off where numbers can become unstable. QR decomposition is about half as fast but more stable.

I read the assigned reading. I had difficulty in the beginning with changing the order of the summations. It was easy where both summations were from zero to n, but after, with the triangle shaped sets, it was more difficult. The most interesting thing I encountered in the reading was that there are so many ways to modify summations. We can rearrange them, shift the indices, do one then the other, negate summations, factor out values, and transform them to form new ones. Over all, summations have a lot of power to them.

Through reading this section, the most difficult thing was internalizing the formulas. I thought the formula for the fundamental theorem of calculus for sequences made intuitive sense, but some of the steps they took after didn't make easy sense to me. Something I've thought was interesting is how the integral is like a summation, where a summation is adding the elements over a domain of "integer spaces," the integral is adding the elements over an infinite "real space." I've never thought before of a derivative that, like the summation, works with sequences rather than continuous functions. This is interesting.

I read the entire assignment, and the most difficult part of the material was that I didn't quite understand how we are to count the number of operations it takes code. I also had trouble understanding how to compute the spatial resources. What I thought was interesting in this reading was how straightforward the code snippets in the packet were. I would think an extremely efficient algorithm would trade off some readability, but it seems in these examples they are pretty organized and easy to understand.

What is your year in school and major? I'm a junior in the ACME program, I'm not sure yet of the emphasis I'd like to pursue. Which post-calculus math courses have you taken? (Use names or BYU course numbers.) Math 313, Math 314, Math 341, Math 290, Why did you choose ACME? (Be specific.) I chose ACME because I wanted something harder than CS. I've been coding for a long time, and I finally hit the point where math was the next step to be a better programmer. Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly? I thought Dr. Barker was an excellent teacher. This was because he cared a lot about his students. He often asked if we had questions and took time to answer them. He was also interested in everyone's major and futures. Write something interesting or unique about yourself. I also sing in men's chorus, play the viola, and I've been programming video g...