通用数学符号英文对照.doc

-*常用数学符号英文对照Basic math symbolsSymbolSymbol NameMeaning / definitionExample=equals signequality5 = 2+35 is equal to 2+3not equal signinequality5 45 is not equal to 4approximately equalapproximationsin(0.01) 0.01,xymeansxis approximately equal toystrict inequalitygreater than5 45 is greater than 4strict inequalityless than4 54 is less than 5inequalitygreater than or equal to5 4,xymeansxis greater than or equal toyinequalityless than or equal to4 5,x ymeansxis greater than or equal toy( )parenthesescalculate expression inside first2 (3+5) = 16 bracketscalculate expression inside first(1+2)(1+5) = 18+plus signaddition1 + 1 = 2minus signsubtraction2 1 = 1plus - minusboth plus and minus operations3 5 = 8 and -2minus - plusboth minus and plus operations3 5 = -2 and 8*asteriskmultiplication2 * 3 = 6times signmultiplication2 3 = 6multiplication dotmultiplication2 3 = 6division sign / obelusdivision6 2 = 3/division slashdivision6 / 2 = 3horizontal linedivision / fractionmodmoduloremainder calculation7 mod 2 = 1.perioddecimal point, decimal separator2.56 = 2+56/100abpowerexponent23= 8abcaretexponent2 3= 8asquare rootaa= a9= 33acube root3a3a3a= a38= 24afourth root4a4a4a4a= a416= 2nan-th root (radical)forn=3,n8= 2%percent1% = 1/10010% 30 = 3per-mille1 = 1/1000 = 0.1%10 30 = 0.3ppmper-million1ppm = 1/100000010ppm 30 = 0.0003ppbper-billion1ppb = 1/100000000010ppb 30 = 310-7pptper-trillion1ppt = 10-1210ppt 30 = 310-10Geometry symbolsSymbolSymbol NameMeaning / definitionExampleangleformed by two raysABC = 30measured angleABC = 30spherical angleAOB = 30right angle= 90 = 90degree1 turn = 360 = 60degdegree1 turn = 360deg = 60degprimearcminute, 1 = 60 = 6059double primearcsecond, 1 = 60 = 605959lineinfinite lineABline segmentline from point A to point Brayline that start from point Aarcarc from point A to point B= 60perpendicularperpendicular lines (90 angle)ACBC| |parallelparallel linesAB| |CDcongruent toequivalence of geometric shapes and sizeABC XYZsimilaritysame shapes, not same sizeABC XYZtriangletriangle shapeABC BCD|x-y|distancedistance between points x and y|x-y| = 5pi constant= 3.141592654.is the ratio between the circumference and diameter of a circlec=d= 2rradradiansradians angle unit360 = 2 radcradiansradians angle unit360 = 2cgradgradians / gonsgrads angle unit360 = 400 gradggradians / gonsgrads angle unit360 = 400gAlgebra symbolsSymbolSymbol NameMeaning / definitionExamplexx variableunknown value to findwhen 2x= 4, thenx= 2equivalenceidentical toequal by definitionequal by definition:=equal by definitionequal by definitionapproximately equalweak approximation11 10approximately equalapproximationsin(0.01) 0.01proportional toproportional toyxwheny=kx, kconstantlemniscateinfinity symbolmuch less thanmuch less than1 1000000much greater thanmuch greater than1000000 1( )parenthesescalculate expression inside first2 * (3+5) = 16 bracketscalculate expression inside first(1+2)*(1+5) = 18 bracessetxfloor bracketsrounds number to lower integer4.3 = 4xceiling bracketsrounds number to upper integer4.3 = 5x!exclamation markfactorial4! = 1*2*3*4 = 24|x|single vertical barabsolute value| -5 | = 5f(x)function of xmaps values of x to f(x)f(x) = 3x+5(fg)function composition(fg) (x) =f(g(x)f(x)=3x,g(x)=x-1 (fg)(x)=3(x-1)(a,b)open interval(a,b) = x|axbx (2,6)a,bclosed intervala,b = x|axbx 2,6deltachange / differencet=t1-t0discriminant =b2- 4acsigmasummation - sum of all values in range of seriesxi= x1+x2+.+xnsigmadouble summationcapital piproduct - product of all values in range of seriesxi=x1x2.xnee constant/ Eulers numbere= 2.718281828.e= lim (1+1/x)x,xEuler-Mascheroni constant = 0.527721566.golden ratiogolden ratio constantpi constant= 3.141592654.is the ratio between the circumference and diameter of a circlec=d= 2rLinear Algebra SymbolsSymbolSymbol NameMeaning / definitionExampledotscalar productabcrossvector productabABtensor producttensor product of A and BABinner product bracketsmatrix of numbers( )parenthesesmatrix of numbers|A|determinantdeterminant of matrix Adet(A)determinantdeterminant of matrix A|x|double vertical barsnormATtransposematrix transpose(AT)ij= (A)jiAHermitian matrixmatrix conjugate transpose(A)ij= (A)jiA*Hermitian matrixmatrix conjugate transpose(A*)ij= (A)jiA-1inverse matrixA A-1=Irank(A)matrix rankrank of matrix Arank(A) = 3dim(U)dimensiondimension of matrix Arank(U) = 3Probability and statistics symbolsSymbolSymbol NameMeaning / definitionExampleP(A)probability functionprobability of event AP(A) = 0.5P(AB)probability of events intersectionprobability that of events A and BP(AB) = 0.5P(AB)probability of events unionprobability that of events A or BP(AB) = 0.5P(A|B)conditional probability functionprobability of event A given event B occuredP(A | B) = 0.3f(x)probability density function (pdf)P(axb) = f(x)dxF(x)cumulative distribution function (cdf)F(x) =P(Xx)population meanmean of population values= 10E(X)expectation valueexpected value of random variable XE(X) = 10E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5var(X)variancevariance of random variable Xvar(X) = 42variancevariance of population values2= 4std(X)standard deviationstandard deviation of random variable Xstd(X) = 2Xstandard deviationstandard deviation value of random variable XX=2medianmiddle value of random variable xcov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6X,Ycorrelationcorrelation of random variables X and YX,Y= 0.6summationsummation - sum of all values in range of seriesdouble summationdouble summationMomodevalue that occurs most frequently in populationMRmid-rangeMR= (xmax+xmin)/2Mdsample medianhalf the population is below this valueQ1lower / first quartile25% of population are below this valueQ2median / second quartile50% of population are below this value = median of samplesQ3upper / third quartile75% of population are below this valuexsample meanaverage / arithmetic meanx= (2+5+9) / 3 = 5.333s2sample variancepopulation samples variance estimators2= 4ssample standard deviationpopulation samples standard deviation estimators= 2zxstandard scorezx= (x-x) /sxXdistributionof Xdistribution of random variable XXN(0,3)N(,2)normal distributiongaussian distributionXN(0,3)U(a,b)uniform distributionequal probability in range a,bXU(0,3)exp()exponential distributionf(x)= e-x,x0gamma(c, )gamma distributionf(x)= c xc-1e-x/ (c),x02(k)chi-square distributionf(x)= xk/2-1e-x/2/ ( 2k/2(k/2) )F(k1, k2)F distributionBin(n,p)binomial distributionf(k)=nCkpk(1-p)n-kPoisson()Poisson distributionf(k)= ke-/k!Geom(p)geometric distributionf(k)= p(1-p)kHG(N,K,n)hyper-geometric distributionBern(p)Bernoulli distributionCombinatorics SymbolsSymbolSymbol NameMeaning / definitionExamplen!factorialn! = 123.n5! = 12345 = 120nPkpermutation5P3=5! / (5-3)! = 60nCkcombination5C3=5!/3!(5-3)!=10Set theory symbolsSymbolSymbol NameMeaning / definitionExample seta collection of elementsA = 3,7,9,14,B = 9,14,28A Bintersectionobjects that belong to set A and set BA B = 9,14A Bunionobjects that belong to set A or set BA B = 3,7,9,14,28A Bsubsetsubset has fewer elements or equal to the set9,14,28 9,14,28A Bproper subset / strict subsetsubset has fewer elements than the set9,14 9,14,28A Bnot subsetleft set not a subset of right set9,66 9,14,28A Bsupersetset A has more elements or equal to the set B9,14,28 9,14,28A Bproper superset / strict supersetset A has more elements than set B9,14,28 9,14A Bnot supersetset A is not a superset of set B9,14,28 9,662Apower setall subsets of Apower setall subsets of AA = Bequalityboth sets have the same membersA=3,9,14,B=3,9,14,A=BAccomplementall the objects that do not belong to set AA Brelative complementobjects that belong to A and not to BA = 3,9,14,B = 1,2,3,A-B = 9,14A - Brelative complementobjects that belong to A and not to BA = 3,9,14,B = 1,2,3,A-B = 9,14A Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = 3,9,14,B = 1,2,3,A B = 1,2,9,14A Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = 3,9,14,B = 1,2,3,A B = 1,2,9,14aAelement ofset membershipA=3,9,14, 3 AxAnot element ofno set membershipA=3,9,14, 1 A(a,b)ordered paircollection of 2 elementsABcartesian productset of all ordered pairs from A and B|A|cardinalitythe number of elements of set AA=3,9,14, |A|=3#Acardinalitythe number of elements of set AA=3,9,14, #A=3aleph-nullinfinite cardinality of natural numbers setaleph-onecardinality of countable ordinal numbers setempty set = C = universal setset of all possible values0natural numbers / whole numbers set (with zero)0= 0,1,2,3,4,.0 01natural numbers / whole numbers set (without zero)1= 1,2,3,4,5,.6 1integer numbers set= .-3,-2,-1,0,1,2,3,.-6 rational numbers set= x|x=a/b,a,b2/6 real numbers set= x| - x6.343434complex numbers set= z|z=a+bi, -a, -b6+2iLogic symbolsSymbolSymbol NameMeaning / definitionExampleandandxycaret / circumflexandxy&ersandandx&y+plusorx+yreversed caretorxy|vertical lineorx|yxsingle quotenot - negationxxbarnot - negationxnotnot - negationx!exclamation marknot - negation!xcircled plus / oplusexclusive or - xorxytildenegationximpliesequivalentif and only if (iff)equivalentif and only if (iff)for allthere existsthere does not existsthereforebecause / sinceCalculus & analysis symbolsSymbolSymbol NameMeaning / definitionExamplelimitlimit value of a functionepsilonrepresents a very small number, near zero0ee constant/ Eulers numbere= 2.718281828.e= lim (1+1/x)x,xyderivativederivative - Lagranges notation(3x3) = 9x2ysecond derivativederivative of derivative(3x3) = 18xy(n)nth derivativen times derivation(3x3)(3)= 18derivativederivative - Leibnizs notationd(3x3)/dx= 9x2second derivativederivative of derivatived2(3x3)/dx2= 18xnth derivativen times derivationtime derivativederivative by time - Newtons notationtime second derivativederivative of derivativeDxyderivativederivative - Eulers notationDx2ysecond derivativederivative of derivativepartial derivative(x2+y2)/x= 2xintegralopposite to derivationf(x)dxdouble integralintegration of function of 2 variablesf(x,y)dxdytriple integralintegration of function of 3 variablesf(x,y,z)dxdydzclosed contour / line integralclosed surface integralclosed volume integrala,bclosed intervala,b = x|axb(a,b)open interval(a,b) = x|axbiimaginary uniti -1z= 3 + 2iz*complex conjugatez=a+biz*=a-biz*= 3 - 2izcomplex conjugatez=a+biz=a-biz= 3 - 2inabla / delgradient / divergence operatorf(x,y,z)vectorunit vectorx*yconvolutiony(t) =x(t) *h(t)Laplace transformF(s) = f(t)Fourier transformX() =f(t)delta functionlemniscateinfinity symbol