Is there a list of typical variable letters to use in a given context?

Question

I try to write math notes as clearly as possible. In practice, this means using letters and notation similar to what the reader is already familiar with.

A real function is often $f(x)$, an angle is often $\theta$, a matrix has size $m\times n$, and $i$ is often an index. The full theoretical list is long and complicated. For example, $\pi$ is very often a constant, but sometimes it's a variable for a permutation. Capital sigma $\Sigma$ can indicate summing a series, but it can also denote a matrix, as in the singular value decomposition. So things like context matter, and a great list would have to include more than just variable names. Another choice to make is how to write an inner product, for example.

Does such a list exist?

Answer 1

In my own experience the letters $a,b,c,d,e$ are reserved for coefficients. $f, g, h$ are functions. $i,j,k$ are indices. (Sometimes $i=\sqrt{-1}$) $l,m,n$ are also indicies (and in particular natural numbers or integers)

$o$ isn't often used, since it can be confused with zero. Though it can be "little"-o for asymptotics.

$p,q$ are usually polynomials or rational functions or primes.

$r, s,t$ are real numbers, variables, or coefficients.

$u,v,w$ are variables used for coordinate transformations of the real variables $x,y,z$. Also $z,w$ are variables in complex analysis.

Capital $A,B$ and $M$ are matrices. $N$ is a natural number. $R$ is a radius or bound. $C$ is a constant. $T$ is a linear operator.

Obviously this depends on the field and person to a large extent. I have always found it amusing how difficult it can be to choose just the right letter for something. I get stuck when I am trying to use a letter for a function after $f,g,h$ are already taken.

Answer 2

I just got: Mathematical Notation which is surprisingly comprehensive for such a thin book. It covers several mathmatical topics. It even has $\LaTeX$ examples. Edit: it even has conventions for notes and blackboards.

Answer 3

If in doubt, use Wikipedia.

This gives a list of mathematical symbols and all the (widely-used) contexts in which they arise:

http://en.wikipedia.org/wiki/List_of_mathematical_symbols.

Another good list for letters (Roman and Greek) is: http://en.wikipedia.org/wiki/List_of_letters_used_in_mathematics_and_science.

This tells you what each letter represents in different branches of maths (and science).

Just for maths, there is: http://en.wikipedia.org/wiki/Latin_letters_used_in_mathematics.

Finally, there is http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering.