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In preparation for an upcoming (not soon) episode of Operation: Have a Conversation, I read the book Tribe by Sebastian Junger. Its description tends to focus on how it explores the way American soldiers who come back from war have trouble integrating themselves back into modern society, as being in the military provides a significant unifying bond that is not felt in today’s Western culture. While I’m not sure what exactly we’ll get into when recording our episode about this book, I’d like to give a couple of thoughts that have lingered with me since I finished reading it earlier today. First, this book is important. I think it would be good for everyone to read. It frames much of how we look at modern society very differently than I had ever perceived. It discusses how panic attacks and depression are evolutionary traits, and how society has developed in such a way to make these afflictions more prevalent. It thoroughly discusses our misunderstanding and mistreatment of PTSD, particularly among those who participated in violent conflicts. This book can be very challenging in certain ways. It opens one’s eyes to a certain hypocrisy with which we live our lives, and also points out reasons to be somewhat afraid for the future of America. It gives some specific ideas about where we tend to fail as a culture and society, and gives some implications for how we can all work toward getting better. It is hard for me to do this book any sort of justice. My thoughts are still unformed and not particularly cohesive. But after reading it, I’m very excited to discuss it with Mikhail and Jack, and hope you’ll take a chance to read it as well. The book is less than 100 pages, and the audiobook (if that’s your style) is only around 3 hours. Yet there is a lot that happens. I highly recommend it.

Updated November 23, 2022 I’m going back through my posts and recategorizing them, and noticed this one. My plan for having a secondary spot for math posts didn’t take off after I moved my blog to WordPress properly, and discovered the excellent $\KaTeX$ plugin for rendering math. Original Post I recently remembered my company, AoPS supports blog creation for their users. In particular, it has the full functionality I’m used to on their message board. In particular, they have native $\LaTeX$ support, in addition to support for the Asymptote vector graphics language. This makes writing math significantly easier on my end, and significantly easier to interact with on the reader’s end. ...

It is still technically Monday, so I’m counting this, but in a sense I have lapsed. It is Monday evening, and so far I’ve been good at having each post written a few days before Monday, and then scheduling it to post at the same time each week. However, I went home to Minnesota this weekend, and thinking of a post to write was not on my mind. So, after the fact, I’ll write a bit about going home. ...

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. ...