In this little tutorial, we’ll expand on what we’ve learned about sets and functions. Specifically, we’ll double-down on the claim that sets are vital to everything we do in mathematics. Functions are not just a way to describe interactions between sets: functions are sets! ...
I saw this movie a little over a week ago, and have been trying to work through how to write a review of it. It is the type of movie that is funny, but speaks to something much broader; as such, I want to make sure the comedic elements do not overshadow the intention of the movie, but also want to commend the way the movie inserts comedy in such a way that goes against modern comedic sensibilities. ...
I recently put a short story I wrote on Amazon. It’s called When You Come Back. You can find a link to it here. When I originally wrote it, mental illness was not necessarily on my mind. But, the majority of its readers have told me it resonates with them to a fairly strong degree. So, I’ve put it up for $1 and any proceeds I receive will go towards The Trevor Project, in support of mental illness assistance. If you’re not interested in the short story, or in providing Amazon with some of the overhead that comes with buying a Kindle book, you can donate to them directly. If you want the story in PDF form, you can contact me.
(Edit, 10/29) This post has been ported to a math-focused blog here. The goal of the change is improved typesetting for me, and improved readability and interaction for you. See this post for more information. This is the next post in the series of posts inspired by my brief work for Mathbook. Previously, we talked about sets. Once we have this basic object, we can start to create, define and communicate relationships and patterns between sets. Mathematics uses the language of a function to describe these relationships. ...
(Edit 6/7/2020) No more Mathbook. I finally discovered the KaTeX plugin for Wordpress, allowing beautiful typesetting once again. (Edit, 10/29) This post has been ported to a math-focused blog here. The goal of the change is improved typesetting for me, and improved readability and interaction for you. See this post for more information. Quite a while ago, an endeavoring individual tried to start an open-source repository of mathematical information called Mathbook. I contributed an article, which I’ll put down in two parts on this blog. It seems that the project has died, although the website is still available. While this is a bit of a shame, I would like to give some of my own little lessons here. The creator’s idea behind Mathbook was to focus on giving people an understanding of why we do math in a certain way. This is missing from mathematical curriculum today, but it is vital to understand that when math was developed, decisions were made for specific reasons. Moving forward, I’ll occasionally add a new post here to that effect. The people in my life don’t always understand the math I learned, so this is part of my effort in showing it. ...
I started my first post-graduation job at Art of Problem Solving this past week. I was an intern here last summer, and I was lucky enough for that to lead to a job. My official role is “Curriculum Developer”. I work on developing their elementary school math curriculum, as that is their current focus. It’s an incredibly good job, with fantastically intelligent and caring people. While it is a great company whose mission I am deeply invested in, and San Diego is a beautiful place to be, these first few days have been very tough. It was weird driving across the country, having a good time, then suddenly getting to work. I’m living on my own, in a room I’m renting (technically an AirBnB) from a nice lady. I know the area from last summer, but I’m still getting over a mental hurdle of actually going out and doing things. Although at the time I write this I’ll have only been here a few days, I’m already feeling antsy. It’s strange. Perhaps the biggest reason for my feelings is that I spent my entire life in Minnesota. I am very rooted there, and despite many friends leaving who have also graduated, there are many people I’ve left behind. I’m leaving the comfortable world of academia to work at a place where I have no true connections. It’s a rather isolating feeling that I am working through. Yet, this is something I correctly anticipated. I have been solidifying Operation: Have a Conversation and Comical Start as ways to keep in contact with people. I’ve reached out to people (or luckily have had them reach out to me) to stay in contact via phone calls or letters. And I also committed to myself that I would write weekly on this blog, and not worry about people reading it. It’s just a good thing to have on my schedule, both for the purpose of self-reflection, and to stop myself from falling idle after I do a day of work. I already reached out to the San Diego Concert Band, a local community band that has fairly open policies for joining. I’ll be rehearsing with them regularly starting next week, which I am incredibly thrilled for. Although my percussion chops are not what they once were, they will improve and I will be better off for having the experience. I also plan on finding a group (or maybe just a person or two) to try and play tennis with. It’s an easy sport to play as long as you have another person, and I definitely enjoy playing it. Ideally I’d find a softball league as well, and I also have a long book list to get through. Despite a touch of melancholy and some misgivings on traveling so far, I am excited for what is to come. Knowing that my time here is rather indefinite, I can feel more comfortable finding my place and joining new things. I have more opportunity to be involved and help myself as I go along. It’s an interesting time.
The other day my girlfriend and I went to see the film Christopher Robin, all about the titular character outgrowing his friends in the 100 acre wood, and slowly finding his way back to childhood. After leaving the movie close to tears (my girlfriend did cry multiple times), here was my one line review: The entire movie was super predictable, but it was so well-done and moving that I didn’t even care. ...
(Edited 6/7/2020 for improved typesetting) Here is one of my favorite “paradoxes” in mathematics. Many students learn it in a first year calculus course. It is called Gabriel’s Horn. ...
This past weekend I had the fantastic experience of playing drumset in a musical put together in only 24 hours. My friend Tim, along with his friend Adam, wrote the entirety of the show. We showed up at Friday on 7pm, with nobody having seen the script or music except the writers. We then performed the musical – lines memorized, music rehearsed, choreography and blocking complete – at 7pm (and 9pm) Saturday evening. I had an extremely good time. The music was engaging and written with some interpretation allowable, as all the members of the pit were experienced in this musical scenario. We had a lot of fun putting things together quickly, and were quite successful in performing our parts within a few hours. The show was broadly a satirical take on the characters from Scooby-Doo. In addition to the normal gang (whose names are never explicitly stated at any point in the show), there is the scapegoat Brian, who is Daphne’s current boyfriend. He is verbally abused throughout the show, with some light slapping. In addition, Scooby-Doo is just a man in a Scooby-Doo outfit (naturally), although an old Hermit we meet at the beginning addresses this fact: ...
The cutting edge of technology is particularly awesome these days. Cars are doing more on their own, phones are surpassing some current computers in their performance, and VR is coming into its own finally. I listen to a lot of tech podcasts, and love messing around with technology, but due to my status as a recent college graduate, I am definitely not maintaining a collection of cutting-edge devices. And that’s okay. First, let’s talk about cars. I recently purchased a post-lease 2015 Honda Civic, LX trim (in other words, the only model more basic comes with a manual instead of a CVT.) The disparity between that car and other higher-end cars from the same year is rather shocking. Sitting in it, I feel super cool. It’s a big upgrade from the 1998 EX-L Honda Accord I had been driving. There’s a “cockpit” feeling to it, good Bluetooth connectivity, and a back-up camera. It’s relatively zippy for a cheap car, and the gas mileage gained by the CVT cannot be beat. Then, I read a Golf R Review by Casey Liss. He is one of three car enthusiasts on the Accidental Tech Podcast. Not surprisingly, the only one I can identify with is John Siracusa, who to my knowledge has mostly driven manual Civics and Accords for his entire life. Casey though, he complained about the lack of assisted driving and automatic parking. The car needs to be fast, it needs a sunroof, and of course Carplay! This was absolutely baffling to me. I just cannot get my head wrapped around why some of these things are important. These three men have attempted to address it on their podcast, but it still does not click with me. Cars can be purchased only so often to be at all reasonable, and so one cannot even stay on the cutting edge. The other issue is that he recently began working from home exclusively, yet sounded very hesitant to become a one-car family. Oh well, to each their own. Now, obviously cars are a very special case of not staying on the cutting edge. I’ve only owned my own car for a few months, and it’ll be a number of years before I can even begin to think about getting another. But phones: now that’s another matter. I’ve had my Galaxy S7 for two years now. Previously, I had a Galaxy S4 for two years, and then some random LG (I think) phone for 4 years throughout high school. In my mind, until I can afford the “every year” phone upgrade, two years is a reasonable time in these days of mostly non-replaceable phone batteries. So, with my S7 really slowing down and the battery life starting to tank, it was time to figure out what to do. Was the newest Galaxy S9 worth the incredible price tag? Did I want to save some money and get a Pixel XL or a new LG phone, each containing last year’s processors, despite them being the newest in the lineup? I ended up choosing a Galaxy S8+. Due to the release of the S9, I got a very good deal on it, and the processing difference (and battery life) between the S7 and S8+ is much larger than the S8+ to a comparable newest generation phone. Once again, I opted to stay on the duller edge of technology. And I am happy with that decision. I tried the S9 in stores, and it truly did not impress me anymore than the S8 does. The S8 was the revolutionary phone (just like the iPhone X, and whatever comes out next will not be quite as lauded). This is what is interesting about technology. So many people are excited to get the newest and best thing. The hype is always there, but the price-to-performance normally isn’t. I spent all of last year in school working on a 4-year old Ideapad and a 5-year old refurbished Thinkpad. They performed admirably for me, because like most people, I’m not doing much heavy-lifting. Being on the dull edge, and looking out at what is available and what others have, can be fun. I don’t think there is anything wrong with living life on some sort of delay with technology. Perhaps as I grow older and make a bit more money, that will change. But for now, I am happy with scouring the internet for good deals, and getting what I actually need for the best price.