When I hear about Autistic Burnout, I feel like it should be a complete cessation of activity, and while I haven’t posted on this blog for about two months, while my overall writing activity has been WAY down, I’ve still been doing stuff. I’ve come to realize that Autistic Burnout is not, in fact, a…
Author: Clio
F4660t
Preamble: The song quotes should not be taken as either approval or condemnation of the respective songs or their artists. I have different personal feelings about each, and in most cases, they’re complicated. “He called me f4660t when I went out for cigarettes.” – Andy Prieboy, “That Was the Voice” This week, I heard a…
Operators
Moderate level definition: An operator is a mathematical symbol takes some defined number of inputs (also called arguments) and returns an output. The first operator that students learn about is \(+\). This operator takes two values and gives their sum. For instance, \(5 + 4 = 9\). The arguments of addition are called the addends;…
FTOC (Informal)
Let \(f_0\) and \(f_1\) be two functions such that \(f_1\) represents the rate at which \(f_0\) is changing with regards to some independent variable \(t\). (If you prefer to read an example first, jump down to that section.) This relationship is typically represented by saying that \(f_1(t)\) is the derivative of \(f_0(t)\), that is: \[f_1(t)=f_0^\prime(t)\]…
An Introduction to Sets
In casual parlance, we often distinguish collections from sets: My comic book collection consists of all the comic books I own, which may include duplicates. It is not an exhaustive collection of every comic book ever produced. However, if I happen to have a set of Groo comics, that means I have every title produced…
What is Algebra, Anyway?
Ask a general person on the street to define mathematics, and they’re likely to say something about manipulating or combining numbers. Ask a mathematician to define mathematics, and they’re likely to talk more about patterns. Here, for instance, is the first sentence of the definition provided by MathWorld: “Mathematics is a broad-ranging field of study…
Locus
A locus (plural loci) is a set of all the points that satisfy a particularly mathematical statement or rule. Such statements or rules can contain any number of distinct variables, but we can only easily graphically represent statements with two or three distinct variables. If a statement contains only one distinct variable, the graph of…
How to Read a Clock
This video and its comments got me thinking about how difficult it really is to read an analog clock: There are multiple comments on TikTok sneering at how inane and unintelligent modern children must be to need more than ten minutes, let alone more than two days, to learn how to read a clock. So…
The Language of Mathematics
Mathematical notation is a language. The study of mathematics is about finding patterns in our universe, but we need a method of communicating those patterns to other people. That’s where notation comes in. Like the languages that we speak, this system of notation did not spring up all at once. It was not the result…
Synthetic Division
Synthetic Division is one of three common techniques for dividing one polynomial by another. The other two are long division and the box method. Of the three methods, students generally prefer synthetic division. It has the advantage of having minimal writing and being strictly algorithmic: Add, multiply, add, multiply…. First, let’s see how it works….