常用数学符号英文对照

than or equal to y ( ) parentheses calculate expression2 ×(3+5) = 16inside first[ ] brackets calculate expression[(1+2)×(1+5)] = 18inside first+ plus sign addition 1 + 1 = 2−minus sign subtraction 2 −1 = 1±plus - minus both plus and minus3 ±5 = 8 and -2operations±minus - plus both minus and plus3 ±5 = -2 and 8operations* asterisk multiplication 2 * 3 = 6×times sign multiplication 2 ×3 = 6 ·multiplicationmultiplication 2 ·3 = 6dot÷division sign /division 6 ÷2 = 3 obelus/ division slash division 6 / 2 = 3–horizontal line division / fractionmod modulo remainder calculation 7 mod 2 = 1. period decimal point, decimal2.56 = 2+56/100separatora b power exponent 23= 8a^b caret exponent 2 ^ 3= 83√a cube root 3√a ·3√a ·3√a = a3√8 = 24√a fourth root 4√a ·4√a ·4√a ·4√a = a4√16 = ±2n√a n-th root(radical)for n=3, n√8 = 2% percent1% = 1/100 10% ×30 = 3‰per-mille1‰= 1/1000 =0.1%10‰×30 = 0.3ppm per-million1ppm = 1/1000000 10ppm ×30 = 0.0003 ppb per-billion1ppb =1/100000000010ppb ×30 = 3×10-7ppt per-trillion 1ppt = 10-1210ppt ×30 = 3×10-10 Geometry symbolsSymbol Symbol Name Meaning / definition Example ∠angle formed by two rays ∠ABC = 30°measuredangleABC = 30°spherical angle AOB = 30°∟right angle = 90°α= 90°deg degree 1 turn = 360deg α= 60deg ′prime arcminute, 1°= 60′α= 60°59′α= 60°59′″double prime arcsecond, 1′= 60″59″line infinite lineAB line segment line from point A to point Bray line that start from point Aarc arc from point A to point B = 60°⊥perpendicular perpendicular lines (90°angle) AC ⊥ BC| | parallel parallel lines AB | | CD≅congruent to equivalence of geometric shapes and size ∆ABC≅∆XYZ ~ similarity same shapes, not same size ∆ABC~ ∆XYZΔABC≅ΔΔtriangle triangle shapeBCD|x-y| distance distance between points x and y | x-y | = 5πpi constant π = 3.141592654...c = π·d =is the ratio between the circumference andin range ofseries∑∑sigma doublesummation∏capital pi product -product of allvalues in rangeof series∏ x i=x1·x2·...·x ne e constant / Euler's numbere =2.718281828...e = lim (1+1/x)x , x→∞γEuler-Mascheroni constantγ=0.527721566...φgolden ratio golden ratioconstantπpi constant π =3.141592654...is the ratiobetween thecircumferenceand diameter of acirclec = π·d = 2·π·rLinear Algebra SymbolsSymbol Symbol Name Meaning / definition Example ·dot scalar product a · b×cross vector product a × bA⊗B tensor product tensor product of A and B A⊗Binner product[ ] brackets matrix of numbers( ) parentheses matrix of numbers| A | determinant determinant of matrix Adet(A) determinant determinant of matrix A|| x || double vertical bars normA T transpose matrix transpose (A T)ij = (A)ji A†Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji A*Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji A-1inverse matrix A A-1 = Irank(A) matrix rank rank of matrix A rank(A) = 3 dim(U) dimension dimension of matrix A rank(U) = 3Probability and statistics symbols Symbol Symbol Name Meaning / definition Example P(A) probabilityfunctionprobability of event A P(A) = 0.5P(A∩B) probability ofeventsintersectionprobability that ofevents A and BP(A∩B) = 0.5P(A∪B) probability ofevents union probability that ofevents A or BP(A∪B) = 0.5P(A | B) conditionalprobabilityfunctionprobability of event Agiven event B occuredP(A | B) = 0.3f (x) probabilitydensity function(pdf)P(a ≤ x ≤ b) = ∫f (x) dxF(x) cumulativedistributionfunction (cdf)F(x) = P(X≤ x)μpopulationmean mean of populationvaluesμ = 10E(X) expectationvalue expected value ofrandom variable XE(X) = 10E(X | Y) conditionalexpectation expected value ofrandom variable Xgiven YE(X | Y=2) = 5var(X) variance variance of randomvariable Xvar(X) = 4σ2variance variance of populationvaluesσ2 = 4std(X) standarddeviation standard deviation ofrandom variable Xstd(X) = 2σX standarddeviation standard deviationvalue of randomvariable XσX=2median middle value of random variable xcov(X,Y) covariance covariance of randomvariables X and Ycov(X,Y) = 4corr(X,Y) correlation correlation of randomvariables X and Ycorr(X,Y) = 0.6ρX,Y correlation correlation of randomvariables X and YρX,Y = 0.6∑summation summation - sum of all values in range of series∑∑doublesummationdouble summationMo mode value that occurs most frequently in populationMR mid-range MR = (x max+x min)/2 Md sample median half the population isbelow this valueQ1lower / firstquartile 25% of population are below this valueQ2median / secondquartile 50% of population are below this value = median of samplesQ3upper / thirdquartile 75% of population are below this valuex sample mean average / arithmeticmeanx = (2+5+9) / 3 = 5.333s2sample variance population samplesvariance estimators2 = 4s sample standarddeviation population samples standard deviation estimators = 2z x standard score z x = (x-x) / s xX ~ distribution of X distribution of randomvariable XX ~ N(0,3)N(μ,σ2) normaldistributiongaussian distribution X ~ N(0,3)U(a,b) uniformdistribution equal probability inrange a,bX ~ U(0,3)exp(λ) exponentialdistributionf (x) = λe-λx , x≥0gamma(c,λ) gammadistributionf (x) = λc x c-1e-λx /Γ(c), x≥0χ 2(k) chi-squaredistributionf (x) = x k/2-1e-x/2 /( 2k/2 Γ(k/2) )F (k1, k2) F distributionBin(n,p) binomialdistributionf (k) = n C k p k(1-p)n-kPoisson(λ) Poissondistributionf (k) = λk e-λ / k!Geom(p) geometricdistributionf (k) = p(1-p) kHG(N,K,n) hyper-geometricdistributionBern(p) BernoullidistributionCombinatorics SymbolsSymbol Symbol Name Meaning / definition Examplen! factorial n! = 1·2·3·...·n5! = 1·2·3·4·5 = 120 n P k permutation 5P3 = 5! / (5-3)! = 60n C kcombination 5C3 = 5!/[3!(5-3)!]=10Set theory symbolsSymbol Symbol Name Meaning / definition Example { } set a collection of elementsA = {3,7,9,14},B = {9,14,28}A ∩B intersection objects that belong to set A andset BA ∩B = {9,14}A ∪B union objects that belong to set A orset BA ∪B ={3,7,9,14,28}A ⊆B subset subset has fewer elements orequal to the set{9,14,28} ⊆{9,14,28}A ⊂B proper subset / strictsubsetsubset has fewer elements thanthe set{9,14} ⊂{9,14,28}A ⊄B not subset left set not a subset of right set{9,66} ⊄{9,14,28}A ⊇B superset set A has more elements orequal to the set B{9,14,28} ⊇{9,14,28}A ⊃B proper superset / strictsupersetset A has more elements thanset B{9,14,28} ⊃{9,14}A ⊅B not superset set A is not a superset of set B{9,14,28} ⊅{9,66}2A power set all subsets of Apower set all subsets of AA =B equality both sets have the samemembersA={3,9,14},B={3,9,14},A=BA c complement all the objects that do not belong to set AA \B relative complement objects that belong to A and notto BA = {3,9,14},B = {1,2,3},A-B = {9,14}A -B relative complement objects that belong to A and notto BA = {3,9,14},B = {1,2,3},A-B = {9,14}A ∆B symmetric difference objects that belong to A or Bbut not to their intersectionA = {3,9,14},B = {1,2,3},A ∆B ={1,2,9,14}A ⊖B symmetric difference objects that belong to A or Bbut not to their intersectionA = {3,9,14},B = {1,2,3},A ⊖B ={1,2,9,14}a∈A element of set membership A={3,9,14}, 3 ∈Ax∉A not element of no set membershipA={3,9,14}, 1∉ A (a,b) ordered pair collection of 2 elementsA×B cartesian product set of all ordered pairs from Aand B|A| cardinality the number of elements of set AA={3,9,14},|A|=3#A cardinality the number of elements of set AA={3,9,14},#A=3aleph-null infinite cardinality of natural numbers setaleph-one cardinality of countable ordinal numbers setØempty set Ø = { } C = {Ø} universal set set of all possible values0natural numbers / wholenumbers set (withzero)= {0,1,2,3,4,...} 0 ∈01natural numbers / wholenumbers set (without 1= {1,2,3,4,5,...} 6 ∈1zero)integer numbers set = {...-3,-2,-1,0,1,2,3,...} -6 ∈rational numbers set = {x | x=a/b, a,b∈} 2/6 ∈real numbers set = {x | -∞< x <∞} 6.343434∈= {z | z=a+bi, -∞<a<6+2i∈complex numbers set∞, -∞<b<∞}Logic symbolsSymbol Symbol Name Meaning / definition Example ·and and x·y^ caret / circumflex and x ^ y& ampersand and x & y + plus or x + y∨reversed caret or x∨y| vertical line or x | yx' single quote not - negation x'x bar not - negation x¬not not - negation ¬x! exclamation mark not - negation ! x~ tilde negation ~ x ⇒implies⇔equivalent if and only if (iff)↔equivalent if and only if (iff)∀for all∃there exists∄there does not exists∴therefore∵because / sinceCalculus & analysis symbolsSymbol Symbol Name Meaning / definition Example limit limit value of a functionεepsilon represents a very smallnumber, near zeroε→0e e constant /Euler's number e = 2.718281828...e = lim (1+1/x)x ,x→∞y ' derivative derivative - Lagrange'snotation(3x3)' = 9x2y(n)nth derivative n times derivation (3x3)(3) = 18 derivative derivative - Leibniz's notation d(3x3)/dx = 9x2second derivative derivative of derivative d2(3x3)/dx2 = 18xnth derivative n times derivationtime derivative derivative by time - Newton's notationtime secondderivativederivative of derivativeD x y derivative derivative - Euler's notationD x2y second derivative derivative of derivativepartial derivative ∂(x2+y2)/∂x = 2x ∫integral opposite to derivation ∫f(x)dx∫∫double integral integration of function of 2variables∫∫f(x,y)dxdy∫∫∫triple integral integration of function of 3variables ∫∫∫f(x,y,z)dxdydz∮closed contour /line integral∯closed surface integral∰closed volume integral[a,b] closed interval [a,b] = {x | a ≤ x ≤ b}(a,b) open interval (a,b) = {x | a < x < b}i imaginary unit i≡√-1 z = 3 + 2i z* complexconjugatez = a+bi→z*=a-bi z* = 3 - 2iz complexconjugatez = a+bi→z = a-bi z = 3 - 2i∇nabla / del gradient / divergenceoperator∇f (x,y,z) vectorunit vectorx * y convolution y(t) = x(t) * h(t)Laplace transform F(s) = {f (t)}Fourier transform X(ω) = {f (t)}δdelta function∞lemniscate infinity symbol。