Basic Math Symbols (Algebra Geometry Statistics etc.)

Basic mathematical symbols

SymbolSymbol NameMeaning / definitionExample
=equals signequality5 = 2+3
5 is equal to 2+3
not equal signinequality5 ≠ 4
5 is not equal to 4
approximately equalapproximationsin(0.01) ≈ 0.01,
x ≈ y means x is approximately equal to y
>strict inequalitygreater than5 > 4
5 is greater than 4
<strict inequalityless than4 < 5
4 is less than 5
inequalitygreater than or equal to5 ≥ 4,
x ≥ y means x is greater than or equal to y
inequalityless than or equal to4 ≤ 5,
x ≤ y means x is greater than or equal to y
( )parenthesescalculate expression inside first2 × (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)×(1+5)] = 18
+plus signaddition1 + 1 = 2
minus signsubtraction2 − 1 = 1
±plus – minusboth plus and minus operations3 ± 5 = 8 and -2
±minus – plusboth minus and plus operations3 ± 5 = -2 and 8
*asteriskmultiplication2 * 3 = 6
×times signmultiplication2 × 3 = 6
·multiplication dotmultiplication2 · 3 = 6
÷division sign / obelusdivision6 ÷ 2 = 3
/division slashdivision6 / 2 = 3
horizontal linedivision / fraction 
modmoduloremainder calculation7 mod 2 = 1
.perioddecimal point, decimal separator2.56 = 2+56/100
abpowerexponent23 = 8
a^bcaretexponent2 ^ 3 = 8
asquare roota · a  = a√9 = ±3
3acube root3a · 3√a  · 3√a  = a3√8 = 2
4afourth root4a · 4√a  · 4√a  · 4√a  = a4√16 = ±2
nan-th root (radical) for n=3, n√8 = 2
%percent1% = 1/10010% × 30 = 3
per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3
ppmper-million1ppm = 1/100000010ppm × 30 = 0.0003
ppbper-billion1ppb = 1/100000000010ppb × 30 = 3×10-7
pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10

Geometry symbols

SymbolSymbol NameMeaning / definitionExample
angleformed by two rays∠ABC = 30°
 measured angle ABC = 30°
 spherical angle AOB = 30°
right angle= 90°α = 90°
°degree1 turn = 360°α = 60°
degdegree1 turn = 360degα = 60deg
primearcminute, 1° = 60′α = 60°59′
double primearcsecond, 1′ = 60″α = 60°59′59″
 lineinfinite line 
ABline segmentline from point A to point B 
 rayline that start from point A 
 arcarc from point A to point B = 60°
perpendicularperpendicular lines (90° angle)AC ⊥ BC
| |parallelparallel linesAB | | CD
congruent toequivalence of geometric shapes and size∆ABC≅ ∆XYZ
~similaritysame shapes, not same size∆ABC~ ∆XYZ
Δtriangletriangle shapeΔABC≅ ΔBCD
|xy|distancedistance between points x and yxy | = 5
πpi constantπ = 3.141592654…

 

is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r
radradiansradians angle unit360° = 2π rad
cradiansradians angle unit360° = 2π c
gradgradians / gonsgrads angle unit360° = 400 grad
ggradians / gonsgrads angle unit360° = 400 g

Algebra symbols

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
equivalenceidentical to 
equal by definitionequal by definition 
:=equal by definitionequal by definition 
~approximately equalweak approximation11 ~ 10
approximately equalapproximationsin(0.01) ≈ 0.01
proportional toproportional toy ∝ x when y = kx, k constant
lemniscateinfinity symbol 
much less thanmuch less than1 ≪ 1000000
much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first2 * (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
{ }bracesset 
xfloor bracketsrounds number to lower integer⌊4.3⌋ = 4
xceiling bracketsrounds number to upper integer⌈4.3⌉ = 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
x |single vertical barabsolute value| -5 | = 5
f (x)function of xmaps values of x to f(x)f (x) = 3x+5
(f ∘ g)function composition(f ∘ g) (x) = f (g(x))f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)open interval(a,b) = {x | a < x < b}x∈ (2,6)
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}x ∈ [2,6]
deltachange / differencet = t t0
discriminantΔ = b2 – 4ac 
sigmasummation – sum of all values in range of series xi= x1+x2+…+xn
∑∑sigmadouble summation 
capital piproduct – product of all values in range of series xi=x1∙x2∙…∙xn
ee constant / Euler’s numbere = 2.718281828…e = lim (1+1/x)x , x→∞
γEuler-Mascheroni  constantγ = 0.527721566… 
φgolden ratiogolden ratio constant 
πpi constantπ = 3.141592654…

 

is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

Linear Algebra Symbols

SymbolSymbol NameMeaning / definitionExample
·dotscalar producta · b
×crossvector producta × b
ABtensor producttensor product of A and BA ⊗ B
 inner product  
[ ]bracketsmatrix of numbers 
( )parenthesesmatrix of numbers 
A |determinantdeterminant of matrix A 
det(A)determinantdeterminant of matrix A 
|| x ||double vertical barsnorm 
ATtransposematrix transpose(AT)ij = (A)ji
AHermitian matrixmatrix conjugate transpose(A)ij = (A)ji
A*Hermitian matrixmatrix conjugate transpose(A*)ij = (A)ji
A -1inverse matrixA A-1 = I 
rank(A)matrix rankrank of matrix Arank(A) = 3
dim(U)dimensiondimension of matrix Arank(U) = 3

Probability and statistics symbols

SymbolSymbol NameMeaning / definitionExample
P(A)probability functionprobability of event AP(A) = 0.5
P(A ∩ B)probability of events intersectionprobability that of events A and BP(AB) = 0.5
P(A ∪ B)probability of events unionprobability that of events A or BP(AB) = 0.5
P(A | B)conditional probability functionprobability of event A given event B occuredP(A | B) = 0.3
f (x)probability density function (pdf)P(a  x  b) = ∫ f (x) dx 
F(x)cumulative distribution function (cdf)F(x) = P(X x) 
μpopulation meanmean of population valuesμ = 10
E(X)expectation valueexpected value of random variable XE(X) = 10
E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5
var(X)variancevariance of random variable Xvar(X) = 4
σ2variancevariance of population valuesσ= 4
std(X)standard deviationstandard deviation of random variable Xstd(X) = 2
σXstandard deviationstandard deviation value of random variable XσX  = 2
 medianmiddle value of random variable x 
cov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4
corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6
ρX,Ycorrelationcorrelation of random variables X and YρX,Y = 0.6
summationsummation – sum of all values in range of series 
∑∑double summationdouble summation 
Momodevalue that occurs most frequently in population 
MRmid-rangeMR = (xmax+xmin)/2 
Mdsample medianhalf the population is below this value 
Q1lower / first quartile25% of population are below this value 
Q2median / second quartile50% of population are below this value = median of samples 
Q3upper / third quartile75% of population are below this value 
xsample meanaverage / arithmetic meanx = (2+5+9) / 3 = 5.333
s 2sample variancepopulation samples variance estimators 2 = 4
ssample standard deviationpopulation samples standard deviation estimators = 2
zxstandard scorezx = (xx) / sx 
X ~distribution of Xdistribution of random variable XX ~ N(0,3)
N(μ,σ2)normal distributiongaussian distributionX ~ N(0,3)
U(a,b)uniform distributionequal probability in range a,bX ~ U(0,3)
exp(λ)exponential distributionf (x) = λeλx , x≥0 
gamma(c, λ)gamma distributionf (x) = λ c xc-1eλx / Γ(c), x≥0 
χ 2(k)chi-square distributionf (x) = xk/2-1ex/2 / ( 2k/2 Γ(k/2) ) 
F (k1, k2)F distribution  
Bin(n,p)binomial distributionf (k) = nCk pk(1-p)n-k 
Poisson(λ)Poisson distributionf (k) = λkeλ / k! 
Geom(p)geometric distributionf (k) =  p(1-p) k 
HG(N,K,n)hyper-geometric distribution  
Bern(p)Bernoulli distribution  

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