Actually, I have this feeling all the time when I’m doing my grad work. If you’ve dabbled in higher-level math at all, you probably have had this feeling too. That’s why we like Greek letters, capital letters, italic letters, script letters, and even a few Hebrew and Danish letters (can you think of which Danish character I’m thinking of?). I know all my Greek letters, not because I know any Greek, but because I’ve been exposed to every single one of them through mathematics. Do you think you could name them all too? If you think you’ve got what it takes, go ahead and try this sporcle quiz :-).
On a more serious note, I do always take the time to introduce new Greek letters, just like any other new notation students haven’t seen before. We practice drawing the symbol, I discuss the difference between the lowercase and capital version of that letter, and we appropriately name the symbol. I go to great lengths to do this because I’ve been in a lot of grad classes where the teacher assumed you knew what his/her squiggles meant on the board. I think it’s the nice thing to do to stop and explain your notation.
Can I think of the Danish letter you mean? Nøpe 🙂
John, I’m glad to know you teach your math students Greek letters. I have rarely, if ever, encountered iota, omicron, or upsilon in math. The following wikipedia article lists at least one use for each Greek letter in math, science, and engineering:
Have you ever taken a class in which the professor or textbook used the same letter, typeset in different fonts, as different variables? For instance, grad-level number theory books do this!
Yes! Let –very common in set theory, analysis, topology.
Lowercase and capital letters are very common too, and sometimes that’s confusing, especially with “s”, “x”, “c”, etc.. High school students are exposed to this as early as geometry as we use lowercase letters for the sides of a triangle and the same letters, capitalized, for the vertices of the triangle.
But what happens when you need so many seperate variables, that not even all the written languages, in all the world, from all time, would even scratch the surface of how many seperately valued variables would be needed to express it as a written problem? (never mind the fact that actually writing it would take lifetimes)
You do what we do in the world of programming: you create variables with actual names. There’s a theoretically infinite number of variable-names, limited only by technical constraints imposed by the programming language. Also, it makes things a lot easier to read. Compare “f(b, i, n) = b * (1+i)ⁿ” with “current_salary(base_salary, number_of_years_employed) = base_salary * (1 + inflation_rate) ^ number_of_years”