TITLE: Why does higher level mathematics more often than not use Greek lettering?
QUESTION [5 upvotes]: In high school, at least from what I've seen, mathematics courses never use Greek lettering in their description of concepts, with the notable exceptions of $\Sigma$ for summations, $\Delta$ for changes over time, $\pi$ as $3.14159\ldots$, $\tau$ in physics courses, and $\theta$ for basic sines, cosines, and tangents. This behavior is mirrored in typical college placement exams, such as the SAT or AP exams, which also do not typically use any Greek lettering.
Yet, when students enter college, classes and instructors do use Greek lettering, and use it without preamble; they assume students are familiar with such notation. Yet, typical freshman are not familiar with Greek lettering, and are not sure how to draw, pronounce, or think in terms of, such letters.
Is there a specific reason Greek lettering is deferred to the high school $\to$ university transition, and, more generally, for Greek lettering in the first place?

REPLY [15 votes]: Hugh Montgomery once did some thinking-out-loud about the possibility of writing a paper where, whenever he needed a new symbol, he would just take the first letter of the alphabet he hadn't already used. The title would be, On the Riemann $a$-function, and the paper would begin, Let $a(b)=\sum_{c=1}^{\infty}c^{-b}$.... He concluded that the paper would be unreadable. 
The point is that mathematicians have adopted conventions. The convention adopted may not make sense, or may not make any more sense than any of the possible alternative conventions, but once it is adopted it is of enormous value in communication, which is what mathematics is about. Once you have been inducted into the conventions, you can instantly grasp $\zeta(s)=\sum_{n=1}^{\infty}n^{-s}$ because you have so many associations with it, whereas it takes a great effort to understand $a(b)=\sum_{c=1}^{\infty}c^{-b}$.

REPLY [6 votes]: Historically, part of a classical education used to be learning Ancient Greek and Latin, so most college students and above were expected to know the Greek alphabet.
A pure example of this history is the naming of college fraternities with Greek letters.
Today, very few English-speakers learn Greek, so there might be a value to having instructors at least present to students a list of the Greek alphabet, with pronunciations, to make acclimation easier.
Typically, the first Greek letter we learn is $\pi$, followed by $\epsilon$ and $\delta$ in calculus.  Maybe $\Sigma$ and $\Delta$.  But we certainly don't have a systematic intro. I know I couldn't tell you the entire Greek alphabet in order, and still forget the names of some of them, particularly $\xi$ for some reason.  (Note - we don't tend to use the Greek letters that look like their Roman alternates, precisely because we are using the change in alphabet to represent types, and so using those letters would hardly be helpful.)