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.
Continue reading “Movie Review: BlackKklansman”
New Story and Trevor Project Donations
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.
Mathbook: Introduction to Functions
(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.
Continue reading “Mathbook: Introduction to Functions”
Mathbook: Introduction to Sets
(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.
Introduction to Sets
We will learn the basics of how sets are used in mathematics. It is important to understand basic arithmetic before diving in, but nothing else.
Understanding Sets
In any field of mathematics, it is important to be able to deal with objects and structures. At the lowest level of mathematical objects and structures are sets. Most simply, a set is a collection of objects. We can think of the set of all flowers in Hawaii, or the set of whole numbers between 10 and 37. Typically, we use curly brackets (braces) to denote a set, such as \{1, 2, 3\}. If we are using the same set many times in a row, or talking about a set that cannot easily be written down, we can use some other symbol. Throughout this tutorial we will let S be the set \{1, 2, 3\}, and H be the set of all flowers in Hawaii.
There are certain rules and terms used with sets that allow mathematicians to be consistent when using and talking about sets. For example, we want to know what to call the objects in our sets in general, and how we can write sets.
DEFINITION
Element: Each object or member of a set is called an element of the set. Each element can only occur once in a set. \{1,2,1,3\} is not a valid set since the 1 occurs twice. In addition, the order of elements in a set does not matter. S = \{1,2,3\} = \{3,1,2\}.
To say an element s is in the set S, we write s \in S.
It is also natural to discuss how many elements are in a set.
DEFINITION
Cardinality: The number of elements in a set is called the cardinality of the set. The cardinality is often denoted by putting vertical bars around the set. For example, since S has three elements, we write |S| = 3.
For this tutorial, we will only be looking at sets with finite cardinality; this means we will always be able to list and count every element in the set. Future tutorials may explore larger sets, which becomes an even more powerful (and fun!) mathematical tool.
Often we want to look at some of the elements in a set, but not all of them. For example, we might want the elements of H which are red flowers. This is a very common pattern in mathematics: given an object or structure, how can we look at smaller objects that have a similar structure?
DEFINITION
Subset: If every element in some set A is in a set B, we say that A is a subset of B, and we write A\subset B. For example, the set \{1,3\} is a subset of S.
When doing mathematics, it is good practice to look at the simplest example of any object you are interested in exploring. When it comes to sets, it becomes natural to ask “What if my set has no elements?”
DEFINITION
Empty Set: The empty set is defined to be the set which has no elements. The most common notation is \emptyset, but you may see \{\}, especially in older math texts. This second notation emphasizes it is a set with no elements.
Almost everything you see and do has sets hiding in the background. They are a universal way of communicating mathematical ideas, and are thus very important to understand.
In a future post, I’ll give the second half of this post: Understanding Functions. Once you have established your structure (the set), and have explored some basic ideas (subsets, the empty set), it is important to discuss how you can have two sets interact. The simplest way to have two sets interact is via a function.
New Chapter
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.