1、常用数学符号英文对照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 th
2、an 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
3、)(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 / obel
4、usdivision6 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-t
5、h 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 / definitionExampleanglefo
6、rmed 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
7、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
8、 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 / d
9、efinitionExamplexx 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, k
10、constantlemniscateinfinity 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 = 4xceili
11、ng 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
12、,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,
13、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 pr
14、oduct 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 m
15、atrixmatrix 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)p
16、robability 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
17、)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(
18、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(
19、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)/2
20、Mdsample 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
21、= (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
22、)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 dist
23、ributionf(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
24、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 9,1
25、4,28A 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
26、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,
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