Mathematical symbols are used internationally but each country read them in its own way. Moreover it is often difficult to find a comprehensive list.
I know that this question is very broad but I think that it could be useful to a lot of people to know how to read the most often found symbols.
By most general symbols I mean: limits, product/union over sets, integrals, (partial) derivatives, etc.
So this question is really about how to read math aloud. If I need to find the name of a particular notion like "signal processing" I can ask Wikipedia.
Edit: Here is a list of what I would like to see covered in an answer.
- Fraction: a/b is read "a over b" ;
- Functions: f(x) is read "f of x" ;
- Inverse image: f^{-1}(A) is read "the inverse image of A by f" ;
- Direct image: f(A) is read "the direct image of A by f" ;
- Powers: a^n is read "a to the n-th" ;
- Limits: lim_{x -> 0} f(x) = 0 can be read "limit of f of x is 0 when x goes to 0" ;
- Derivative: "df/dx" is read "the derivative of f with respect to x" ;
- Integral: "Integrate f from a to b with respect to x" ;
- Unions and Product of sets ;
- A ⊂ B is read "A susbset of B" ;
- a ∈ A is read "a in A" ;
- quantifiers: forall and exists ;
- symbols big sum and big product (ie. sum from n equals 0 to n = infinity) ;
- binomial coefficient ;
- how the reading of (3 + 2) * 2 differs from 3 + 2*2 ;
- how to read the for basic operations +,×,÷,- in context ;
- P(X|Y) is read "probability of X given Y" ;
- P(X = k) is read "probability that X becomes k" ;
- Square roots, n-th roots ;
- Elementary functions : exp, log, log_a, cos, sin, tan, cosh, sinh, tanh and their inverse.
I tried to be comprehensive on symbols you may find very often. If you think that I forget some very important symbols please notify me.