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             xy / x multiplied by y
         
(x - y)(x + y)     x minus 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
x ^           x hat
x ¯           x bar
x ˜            x tilde
x i            xi / x subscript i / x suffix i / x sub i
∑ i=1 n a i       the sum from i equals one to n a i / the sum as i runs from 1 to n of the a i
4. Linear algebra           
‖ x ‖    the norm (or modulus) of x
OA →     OA / vector OA
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 )       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
∂ 2 f ∂ x 1 2   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

常用数学术语英语翻译 
    数学 mathematics, maths (BrE), math (AmE)
    公理 axiom
    定理 theorem
    计算 calculation
    运算 operation
    证明 prove
    假设 hypothesis, hypotheses(pl.)
    命题 proposition
    算术 arithmetic
    加 plus(prep.), add(v.), addition(n.)
    被加数 augend, summand
    加数 addend
    和 sum
    减 minus(prep.), subtract(v.), subtraction(n.)
    被减数 minuend
    减数 subtrahend
    差 remainder
    乘 times(prep.), multiply (v.), multiplication(n.)
    被乘数 multiplicand, faciend
    乘数 multiplicator
    积 product
    除 divided by (prep.), divide (v.), division (n.)
    被除数 dividend
    除数 divisor
    商 quotient
    等于 equals, is equal to, is equivalent to
    大于 is greater than
    小于 is lesser than
    大于等于 is equal or greater than
    小于等于 is equal or lesser than
    运算符 operator
    数字 digit
    数 number
    自然数 natural number
    整数 integer
    小数 decimal
    小数点 decimal point
    分数 fraction
    分子 numerator
    分母 denominator
    比 ratio
    正 positive
    负 negative
    零 null, zero, nought, nil
    十进制 decimal system
    二进制 binary system
    十六进制 hexadecimal system
    权 weight, significance
    进位 carry
    截尾 truncation
    四舍五入 round
    下舍入 round down
    上舍入 round up
    有效数字 significant digit
    无效数字 insignificant digit
    代数 algebra
    公式 formula, formulae(pl.)
    单项式 monomial
    多项式 polynomial, multinomial
    系数 coefficient
    未知数 unknown, x-factor, y-factor, z-factor
    等式，方程式 equation
    一次方程 simple equation
    二次方程 quadratic equation
    三次方程 cubic equation
    四次方程 quartic equation
    不等式 inequation
    阶乘 factorial
    对数 logarithm
    指数，幂 exponent
    乘方 power
    二次方，平方 square
    三次方，立方 cube
    四次方 the power of four, the fourth power
    n次方 the power of n, the nth power
    开方 evolution, extraction
    二次方根，平方根 square root
    三次方根，立方根 cube root
    四次方根 the root of four, the fourth root
    n次方根 the root of n, the nth root
    集合 aggregate
    元素 element
    空集 void
    子集 subset
    交集 intersection
    并集 union
    补集 complement
    映射 mapping
    函数 function
    定义域 domain, field of definition
    值域 range
    常量 constant
    变量 variable
    单调性 monotonicity
    奇偶性 parity
    周期性 periodicity
    图象 image
    数列，级数 series
    微积分 calculus
    微分 differential
    导数 derivative
    极限 limit
    无穷大 infinite(a.) infinity(n.)
    无穷小 infinitesimal
    积分 integral
    定积分 definite integral
    不定积分 indefinite integral
    有理数 rational number
    无理数 irrational number
    实数 real number
    虚数 imaginary number
    复数 complex number
    矩阵 matrix
    行列式 determinant
    几何 geometry
    点 point
    线 line
    面 plane
    体 solid
    线段 segment
    射线 radial
    平行 parallel
    相交 intersect
    角 angle
    角度 degree
    弧度 radian
    锐角 acute angle
    直角 right angle
    钝角 obtuse angle
    平角 straight angle
    周角 perigon
    底 base
    边 side
    高 height
    三角形 triangle
    锐角三角形 acute triangle
    直角三角形 right triangle
    直角边 leg
    斜边 hypotenuse
    勾股定理 Pythagorean theorem
    钝角三角形 obtuse triangle
    不等边三角形 scalene triangle
    等腰三角形 isosceles triangle
    等边三角形 equilateral triangle
    四边形 quadrilateral
    平行四边形 parallelogram
    矩形 rectangle
    长 length
    宽 width