1.Logic
∃    there exist
∀    for all
p⇒q     p implies q / if p, then q
p⇔q    p if and only if q /p is equivalent to q / p and q are equivalent

2.Sets
x∈A     x belongs to A / x is an element (or a member) of A
x∉A     x does not belong to A / x is not an element (or a member) of A
A⊂B     A is contained in B / A is a subset of B
A⊃B     A contains B / B is a subset of A
A∩B     A cap B / A meet B / A intersection B
A∪B     A cup B / A join B / A union B
A\B      A minus B / the diference between A and B
A×B     A cross B / the cartesian product of A and B

3. Real numbers
x+1     x plus one
x-1      x minus one
x±1     x plus or minus one
xy       x multiplied by y
x - y    x minus y
x + y   x plus y
x/y      x over y
=        the equals sign
x = 5    x equals 5 / x is equal to 5
x≠5      x (is) not equal to 5
x≡y      x is equivalent to (or identical with) y
x ≡ y    x is not equivalent to (or identical with) y
x > y    x is greater than y
x≥y      x is greater than or equal to y
x < y    x is less than y
x≤y      x is less than or equal to y
0 < x < 1           zero is less than x is less than 1
0≤x≤1               zero is less than or equal to x is less than or equal to 1
| x |      mod x / modulus x
x^2      x squared / x (raised) to the power 2
x^3      x cubed
x^4      x to the fourth / x to the power four
x^n      x to the nth / x to the power n
x^−n     x to the (power) minus n
√x        (square) root x / the square root of x
√x 3      cube root (of) x
√x 4      fourth root (of) x
√x n     nth root (of) x
( x+y ) ^2         x plus y all squared
( x/y )^2           x over y all squared
n!          n factorial
Â          A hat
ē          e bar
Ã         A tilde

4. Linear algebra
‖ x ‖         the norm (or modulus) of x
OA →        vector OA
OA ¯         the length of the segment OA
A T           A transpose / the transpose of A
A −1         A inverse / the inverse of A

5. Functions
f( x )          fx / f of x / the function f of x
f:S→T         a function f from S to T
x→y            x maps to y / x is sent (or mapped) to y
f'( x )          f prime x / f dash x / the (first) derivative of f with respect to x
f''( x )         f double-prime x / f double-dash x / the second derivative of f with respect to x
f'''( x )        f triple-prime x / f triple-dash x / the third derivative of f with respect to x
f (4) ( x )    f four x / the fourth derivative of f with respect to x
∂f/∂ x 1      the partial (derivative) of f with respect to x1
∂2f/∂x 12   the second partial (derivative) of f with respect to x1
∫ 0 ∞        the integral from zero to infinity
lim⁡ x→0         the limit as x approaches zero
lim⁡ x→ 0 +     the limit as x approaches zero from above
lim⁡ x→ 0 −     the limit as x approaches zero from below
log e y           log y to the base e / log to the base e of y / natural log (of) y
ln⁡y                log y to the base e / log to the base e of y / natural log (of) y