常用数学符号英文对照Word格式.docx
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±
plus-minus
bothplusandminusoperations
3±
5=8and-2
minus-plus
bothminusandplusoperations
5=-2and8
*
asterisk
multiplication
2*3=6
×
timessign
3=6
·
multiplicationdot
2·
÷
divisionsign/obelus
division
6÷
2=3
/
divisionslash
6/2=3
–
horizontalline
division/fraction
mod
modulo
remaindercalculation
7mod2=1
.
period
decimalpoint,decimalseparator
2.56=2+56/100
ab
power
exponent
23
=8
a^b
caret
2^3
√a
squareroot
√a
=a
√9
=±
3
3√a
cuberoot
3√a
3√8
=2
4√a
fourthroot
4√a
4√16
2
n√a
n-throot（radical）
for
n=3,
n√8
%
percent
1%=1/100
10%×
30=3
‰
per-mille
1‰=1/1000=0.1%
10‰×
30=0.3
ppm
per-million
1ppm=1/1000000
10ppm×
30=0.0003
ppb
per-billion
1ppb=1/1000000000
10ppb×
30=3×
10-7
ppt
per-trillion
1ppt=10-12
10ppt×
10-10
Geometrysymbols
∠
angle
formedbytworays
∠ABC=30°
measuredangle
ABC=30°
sphericalangle
AOB=30°
∟
rightangle
=90°
α=90°
°
degree
1turn=360°
α=60°
deg
1turn=360deg
α=60deg
′
prime
arcminute,1°
=60′
59′
″
doubleprime
arcsecond,1′=60″
59′59″
line
infiniteline
AB
linesegment
linefrompointAtopointB
ray
linethatstartfrompointA
arc
arcfrompointAtopointB
=60°
⊥
perpendicular
perpendicularlines（90°
angle）
AC
⊥
BC
||
parallel
parallellines
AB
||
CD
≅
congruentto
equivalenceofgeometricshapesandsize
∆ABC≅∆XYZ
~
similarity
sameshapes,notsamesize
∆ABC~∆XYZ
Δ
triangle
triangleshape
ΔABC≅ΔBCD
|x-y|
distance
distancebetweenpointsxandy
|
x-y
|=5
π
piconstant
π
=3.141592654...
istheratiobetweenthecircumferenceanddiameterofacircle
c
=
π·
d
=2·
r
rad
radians
radiansangleunit
360°
=2πrad
c
=2π
grad
gradians/gons
gradsangleunit
=400grad
g
=400
Algebrasymbols
x
xvariable
unknownvaluetofind
when2x
=4,then
≡
equivalence
identicalto
≜
equalbydefinition
:
weakapproximation
11~10
sin（0.01）≈0.01
∝
proportionalto
∝
when
kx,k
constant
∞
lemniscate
infinitysymbol
≪
muchlessthan
1≪1000000
≫
muchgreaterthan
1000000≫1
2*（3+5）=16
[（1+2）*（1+5）]=18
{}
braces
set
⌊x⌋
floorbrackets
roundsnumbertolowerinteger
⌊4.3⌋=4
⌈x⌉
ceilingbrackets
roundsnumbertoupperinteger
⌈4.3⌉=5
x!
exclamationmark
factorial
4!
=1*2*3*4=24
|
singleverticalbar
absolutevalue
|-5|=5
f
（x）
functionofx
mapsvaluesofxtof（x）
（x）=3x+5
（f
∘
g）
functioncomposition
g）（x）=
（g（x））
（x）=3x,g（x）=x-1⇒（f
g）（x）=3（x-1）
（a,b）
openinterval
（a,b）={x
a
b}
x∈（2,6）
[a,b]
closedinterval
[a,b]={x
≤
∈[2,6]
∆
delta
change/difference
∆t
t1
-
t0
discriminant
Δ=
b2
-4ac
∑
sigma
summation-sumofallvaluesinrangeofseries
∑
xi=x1+x2+...+xn
∑∑
doublesummation
∏
capitalpi
product-productofallvaluesinrangeofseries
∏
xi=x1∙x2∙...∙xn
e
econstant
/Euler'
snumber
e
=2.718281828...
=lim（1+1/x）x
x→∞
γ
Euler-Mascheroni
constant
γ=0.527721566...
φ
goldenratio
goldenratioconstant
LinearAlgebraSymbols
dot
scalarproduct
b
cross
vectorproduct
A⊗B
tensorproduct
tensorproductofAandB
A
⊗
B
innerproduct
matrixofnumbers
determinant
determinantofmatrixA
det（A）
||
||
doubleverticalbars
norm
AT
transpose
matrixtranspose
（AT）ij
=（A）ji
A†
Hermitianmatrix
matrixconjugatetranspose
（A†）ij
A*
（A*）ij
-1
inversematrix
AA-1
I
rank（A）
matrixrank
rankofmatrixA
rank（A）=3
dim（U）
dimension
dimensionofmatrixA
rank（U）=3
Probabilityandstatisticssymbols
P（A）
probabilityfunction
probabilityofeventA
P（A）=0.5
P（A
∩
B）
probabilityofeventsintersection
probabilitythatofeventsAandB
P（A∩B）=0.5
∪B）
probabilityofeventsunion
probabilitythatofeventsAorB
P（A∪B）=0.5
conditionalprobabilityfunction
probabilityofeventAgiveneventBoccured
P（A|B）=0.3
probabilitydensityfunction（pdf）
P（a
b）=
∫f
（x）
dx
F（x）
cumulativedistributionfunction（cdf）
F（x）=
P（X≤
x）
μ
populationmean
meanofpopulationvalues
μ
=10
E（X）
expectationvalue
expectedvalueofrandomvariableX
E（X）=10
E（X|Y）
conditionalexpectation
expectedvalueofrandomvariableXgivenY
E（X|Y=2）=5
var（X）
variance
varianceofrandomvariableX
var（X）=4
σ2
varianceofpopulationvalues
σ2
=4
std（X）
standarddeviation
standarddeviationofrandomvariableX
std（X）=2
σX
standarddeviationvalueofrandomvariableX
σX
median
middlevalueofrandomvariablex
cov（X,Y）
covariance
covarianceofrandomvariablesXandY
cov（X,Y）=4
corr（X,Y）
correlation
correlationofrandomvariablesXandY
corr（X,Y）=0.6
ρX,Y
ρX,Y
=0.6
summation
Mo
mode
valuethatoccursmostfrequentlyinpopulation
MR
mid-range
MR
=（xmax+xmin）/2
Md
samplemedian
halfthepopulationisbelowthisvalue
Q1
lower/firstquartile
25%ofpopulationarebelowthisvalue
Q2
median/secondquartile
50%ofpopulationarebelowthisvalue=medianofsamples
Q3
upper/thirdquartile
75%ofpopulationarebelowthisvalue
samplemean
average/arithmeticmean
=（2+5+9）/3=5.333
s
samplevariance
populationsamplesvarianceestimator
2
s
samplestandarddeviation
populationsamplesstandarddeviationestimator
zx
standardscore
zx
=（x-x）/
sx
X
distribution
ofX
distributionofrandomvariableX
~
N（0,3）
N（μ,σ2）
normaldistribution
gaussiandistribution
U（a,b）
uniformdistribution
equalprobabilityinrangea,b
U（0,3）
exp（λ）
exponentialdistribution
=λe-λx
x≥0
gamma（c,λ）
gammadistribution
=λcxc-1e-λx
/Γ（c）,
χ
2（k）
chi-squaredistribution
=xk/2-1e-x/2
/（2k/2
Γ（k/2））
F
（k1,k2）
Fdistribution
Bin（n,p）
binomialdistribution
（k）
nCk
pk（1-p）n-k
Poisson（λ）
Poissondistribution
=λke-λ
/
k!
Geom（p）
geometricdistribution
p（1-p）
k
HG（N,K,n）
hyper-geometricdistribution
Bern（p）
Bernoullidistribution
CombinatoricsSymbols
n!
=1·
2·
3·
...·
n
5!
4·
5=120
nPk
permutation
5P3
/（5-3）!
=60
nCk
combination
5C3
/[3!
（5-3）!
]=10
Settheorysymbols
acollectionofelements
A={3,7,9,14},
B={9,14,28}
A∩B
intersection
objectsthatbelongtosetAandsetB
A∩B={9,14}
A∪B
union
objectsthatbelongtosetAorsetB
A∪B={3,7,9,14,28}
A⊆B
subset
subsethasfewerelementsorequaltotheset
{9,14,28}⊆{9,14,28}
A⊂B
propersubset/strictsubset
subsethasfewerelementsthantheset
{9,14}⊂{9,14,28}
A⊄B
notsubset
leftsetnotasubsetofrightset
{9,66}⊄{9,14,28}
A⊇B
superset
setAhasmoreelementsorequaltothesetB
{9,14,28}⊇{9,14,28}
A⊃B
propersuperset/strictsuperset
setAhasmoreelementsthansetB
{9,14,28}⊃{9,14}
A⊅B
notsuperset
setAisnotasupersetofsetB
{9,14,28}⊅{9,66}
2A
powerset
allsubsetsofA
A=B
bothsetshavethesamemembers
A={3,9,14},
B={3,9,14},
A=B
Ac
complement
alltheobjectsthatdonotbelongtosetA
A\B
relativecomplement
objectsthatbelongtoAandnottoB
A={3,9,14},
B={1,2,3},
A-B={9,14}
A-B
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