Mathematical terminology and notation through a linguistic lens Introduction The first time I attended graduate school was for Linguistics. My first year, I taught English as a Second Language. My most resistant students were Mathematics majors, because many of them held the opinion that mathematics is a universal language. Why bother getting fluent in English?…
Category: Notation
Reflections on Inverse Function Notation
I was thinking about inverse function notation, and that got me thinking about function notation, and that got me thinking about operations and how meh our notation for mathematical operations is. So, let’s start fresh. We’ll pretend we don’t have any operators, just a bunch of numbers and an equal sign. We need to make…
The Problem with Mathematical Notation
Mathematics is beautiful. Mathematical notation, meanwhile, is a horrid mess second only to English itself for its arbitrariness. For instance, basic arithmetic operators have three levels: Addition, Multiplication, and Exponentiation. Addition notation is tidy: We add forward (a + b) or backward (a – b). We call these “addition” and “subtraction” for historical reasons, but…
Naming Variables
First of all, let me get this out of the way: “Hey, you kids! Get off my lawn!” In this post, I comment on the notational shifts from what I was trained in back in the 1980s and what textbooks do now. I was reading Power Puzzles 2 by Philip Carter and Ken Russell when…
Pi aside: Degrees are even worse
Make no mistake: When I run the world, π will be set aside in favor of τ. For those who haven’t heard, there’s a movement to use 6.28318530718… (that is, 2π) as the basic variable relating to circles rather than 3.14159265359…. I personally feel that there’s a strong pedagogical motivation at the secondary education level (specifically, τ is the circumference of…
=
When I was a lad studying mathematics, the equality sign seemed particularly simple: The stuff on the left is equal to the stuff on the right. However, I have since been developing a much more sophisticated perception of the simple little sign. It can indeed be a troublesome symbol, not because of its own meaning…
Logarithmic notation: Mathematics vs. computer programming
One of my concerns as an educator is the way in which peccadilloes of mathematical notation can get in the way of understanding. In the case of logarithms, this has become more troublesome as general education about numeric bases at the secondary level has apparently evolved primarily into an interest of computer programmers. The notation…
PEMDAS and negative numbers
By standard mathematical convention, \(-1^2=-1\). At the same time, students are taught to refer to \(-1\) as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed below. Furthermore, while the first convention is generally taught in high school, the mathematical argument…