Over the past couple of weeks at work, I’ve been working on revising some of the exams for our elementary school curriculum. This has been an interesting task full of challenges. One thing I’m constantly working on is putting myself in the headspace of a bright, but still young, elementary school student. What wording can I allow in problems? How long can a problem be before we’re testing their reading comprehension instead of their math? How many problems should there be? How many problems of a certain level of difficulty? There are so many questions to discuss, but one is a bit more fundamental than all others, and can help inform the answers to each subsequent question. What do we want our test to test? ...

Now that I’m working full-time, I’m getting used to spending significantly more time focusing consistently than when I was in school. Back in college, I could break up my work as I saw fit, take rests and roam around, or just slack off a bit any given day. That does not go over particularly well in an actual working environment. ...

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. ...