Symbol Symbol Name -Meaning / definition= equals sign -equalityâ not equal sign- inequalityâ approximately equal- approximation strict inequality- greater than strict inequality- less than⼠inequality- greater than or equal to⤠inequality -less than or equal to parentheses -calculate expression inside first[ ] brackets -calculate expression inside first+ plus sign -additionâ minus sign- subtractionÂą plus - minus -both plus and minus operationsÂą minus - plus -both minus and plus operations* asterisk -multiplicationĂ times sign -multiplicationâ
multiplication/dot- multiplicationá division sign / obelus -division/ division slash -divisionâ horizontal line -division / fractionmod modulo -remainder calculation. period -decimal point, decimal separatorab power -exponenta^b caret -exponentâa square root âa â
âa = a3âa cube root 3âa â
3âa â
3âa = a4âa fourth root 4âa â
4âa â
4âa â
4âa = anâa n-th root (radical)% percent 1% = 1/100â° per-mille 1â° = 1/1000 = .1%ppm per-million -1ppm = 1/1000000ppb per-billion -1ppb = 1/1000000000ppt per-trillion 1-ppt = 10-12Geometry symbolsSymbol Symbol Name -Meaning / definitionâ angle formed by two raysmeasured anglespherical angleâ right angle = 90°° degree 1 turn = 360°deg degree 1 turn = 360degⲠprime arcminute, 1° = 60â˛âł double prime arcsecond, 1Ⲡ= 60âłline infinite lineAB line segment line from point A to point Bray line that start from point Aarc arc from point A to point B⼠perpendicular perpendicular lines (90° angle)⼠parallel parallel linesâ
congruent to equivalence of geometric shapes and size~ similarity same shapes, not same sizeÎ triangle triangle shape|x-y| distance distance between points x and yĎ pi constant Ď = 3.141592654...is the ratio between the circumference and diameter of a circlerad radians radians angle unitc radians radians angle unitgrad gradians / gons grads angle unitg gradians / gons grads angle unitAlgebra symbolsSymbol Symbol Name Meaning / definitionx x variable unknown value to find⥠equivalence identical toâ equal by definition equal by definition:= equal by definition equal by definition~ approximately equal weak approximationâ approximately equal approximationâ proportional to proportional toâ lemniscate infinity symbol⪠much less than much less than⍠much greater than much greater than parentheses calculate expression inside first[ ] brackets calculate expression inside first{ } braces setâxâ floor brackets rounds number to lower integerâxâ ceiling brackets rounds number to upper integerx! exclamation mark factorial| x | single vertical bar absolute valuef (x) function of x maps values of x to f(x)(f â g) function composition (f â g) (x) = f (g(x))(a,b) open interval (a,b) = {x | a x b}[a,b] closed interval [a,b] = {x | a ⤠x ⤠b}â delta change / differenceâ discriminant Î = b2 - 4acâ sigma summation - sum of all values in range of seriesââ sigma double summationâ capital pi product - product of all values in range of seriese e constant / Euler's number e = 2.718281828...Îł Euler-Mascheroni constant Îł = .5772156649...Ď golden ratio golden ratio constantĎ pi constant Ď = 3.141592654...is the ratio between the circumference and diameter of a circleLinear Algebra SymbolsSymbol Symbol Name Meaning / definition¡ dot scalar productĂ cross vector productAâB tensor product tensor product of A and B\langle x,y \rangle inner 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 normAT transpose matrix transposeAâ Hermitian matrix matrix conjugate transposeA* Hermitian matrix matrix conjugate transposeA -1 inverse matrix A A-1 = Irank(A) matrix rank rank of matrix Adim(U) dimension dimension of matrix AProbability and statistics symbolsSymbol Symbol Name Meaning / definitionP(A) probability function probability of event AP(A ⊠B) probability of events intersection probability that of events A and BP(A ⪠B) probability of events union probability that of events A or BP(A | B) conditional probability function probability of event A given event B occuredf (x) probability density function (pdf) P(a ⤠x ⤠b) = ⍠f (x) dxF(x) cumulative distribution function (cdf) F(x) = P(X⤠x)Îź population mean mean of population valuesE(X) expectation value expected value of random variable XE(X | Y) conditional expectation expected value of random variable X given Yvar(X) variance variance of random variable XĎ2 variance variance of population valuesstd(X) standard deviation standard deviation of random variable XĎX standard deviation standard deviation value of random variable Xmedian middle value of random variable xcov(X,Y) covariance covariance of random variables X and Ycorr(X,Y) correlation correlation of random variables X and YĎX,Y correlation correlation of random variables X and Yâ summation summation - sum of all values in range of seriesââ double summation double summationMo mode value that occurs most frequently in populationMR mid-range MR = (xmax+xmin)/2Md sample median half the population is below this valueQ1 lower / first quartile 25% of population are below this valueQ2 median / second quartile 50% of population are below this value = median of samplesQ3 upper / third quartile 75% of population are below this valuex sample mean average / arithmetic means 2 sample variance population samples variance estimators sample standard deviation population samples standard deviation estimatorzx standard score zx = (x-x) / sxX ~ distribution of X distribution of random variable XN(Îź,Ď2) normal distribution gaussian distributionU(a,b) uniform distribution equal probability in range a,bexp(Îť) exponential distribution f (x) = Îťe-Îťx , xâĽ0gamma(c, Îť) gamma distribution f (x) = Îť c xc-1e-Îťx / Î(c), xâĽ0Ď 2(k) chi-square distribution f (x) = xk/2-1e-x/2 / ( 2k/2 Î(k/2) )F (k1, k2) F distributionBin(n,p) binomial distribution f (k) = nCk pk(1-p)n-kPoisson(Îť) Poisson distribution f (k) = Îťke-Îť / k!Geom(p) geometric distribution f (k) = p(1-p) kHG(N,K,n) hyper-geometric distributionBern(p) Bernoulli distributionCombinatorics SymbolsSymbol Symbol Name Meaning / definitionn! factorial n! = 1â
2â
3â
...â
nnPk permutation _{n}P_{k}=\frac{n!}{(n-k)!}nCkcombination _{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}Set theory symbolsSymbol Symbol Name Meaning / definition{ } set a collection of elementsA ⊠B intersection objects that belong to set A and set BA ⪠B union objects that belong to set A or set BA â B subset A is a subset of B. set A is included in set B.A â B proper subset / strict subset A is a subset of B, but A is not equal to B.A â B not subset set A is not a subset of set BA â B superset A is a superset of B. set A includes set BA â B proper superset / strict superset A is a superset of B, but B is not equal to A.A â
B not superset set A is not a superset of set B2A power set all subsets of A\mathcal{P}(A) power set all subsets of AA = B equality both sets have the same membersAc complement all the objects that do not belong to set AA \ B relative complement objects that belong to A and not to BA - B relative complement objects that belong to A and not to BA â B symmetric difference objects that belong to A or B but not to their intersectionA â B symmetric difference objects that belong to A or B but not to their intersectionaâA element of,belongs to set membershipxâA not element of no set membership(a,b) ordered pair collection of 2 elementsAĂB cartesian product set of all ordered pairs from A and B|A| cardinality the number of elements of set A#A cardinality the number of elements of set Aaleph-null infinite cardinality of natural numbers setaleph-one cardinality of countable ordinal numbers setĂ empty set Ă = { }\mathbb{U} universal set set of all possible values\mathbb{N}0 natural numbers / whole numbers set (with zero) \mathbb{N}0 = {0,1,2,3,4,...}\mathbb{N}1 natural numbers / whole numbers set (without zero) \mathbb{N}1 = {1,2,3,4,5,...}\mathbb{Z} integer numbers set \mathbb{Z} = {...-3,-2,-1,0,1,2,3,...}\mathbb{Q} rational numbers set \mathbb{Q} = {x | x=a/b, a,bâ\mathbb{Z}}\mathbb{R} real numbers set \mathbb{R} = {x | -â x â}\mathbb{C} complex numbers set \mathbb{C} = {z | z=a+bi, -âaâ, -âbâ}Logic symbolsSymbol Symbol Name Meaning / definitionâ
and and^ caret / circumflex and& ampersand and+ plus or⨠reversed caret or| vertical line orx' single quote not - negationx bar not - negationÂŹ not not - negation! exclamation mark not - negationâ circled plus / oplus exclusive or - xor~ tilde negationâ impliesâ equivalent if and only if (iff)â equivalent if and only if (iff)â for allâ there existsâ there does not existsâ´ thereforeâľ because / sinceCalculus & analysis symbolsSymbol Symbol Name Meaning / definition\lim_{x\to x0}f(x) limit limit value of a functionÎľ epsilon represents a very small number, near zeroe e constant / Euler's number e = 2.718281828...y ' derivative derivative - Lagrange's notationy '' second derivative derivative of derivativey(n) nth derivative n times derivation\frac{dy}{dx} derivative derivative - Leibniz's notation\frac{d^2y}{dx^2} second derivative derivative of derivative\frac{d^ny}{dx^n} nth derivative n times derivation\dot{y} time derivative derivative by time - Newton's notationtime second derivative derivative of derivativeDx y derivative derivative - Euler's notationDx2y second derivative derivative of derivative\frac{\partial f(x,y)}{\partial x} partial derivative⍠integral opposite to derivationâŤâŤ double integral integration of function of 2 variablesâŤâŤâŤ triple integral integration of function of 3 variables⎠closed contour / line integral⯠closed surface integralâ° 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 ⥠â-1z* complex conjugate z = a+bi â z*=a-biz complex conjugate z = a+bi â z = a-biâ nabla / del gradient / divergence operatorvectorunit vectorx * y convolution y(t) = x(t) * h(t)Laplace transform F(s) = {f (t)}Fourier transform X(Ď) = {f (t)}δ delta functionâ lemniscate infinity symbolNumeral symbolsName European Roman Hebrewzero 0one 1 I ×two 2 II ×three 3 III ×four 4 IV ×five 5 V ×six 6 VI ×seven 7 VII ×eight 8 VIII ×nine 9 IX ×ten 10 X ×eleven 11 XI ××twelve 12 XII ××thirteen 13 XIII ××fourteen 14 XIV ××fifteen 15 XV ××sixteen 16 XVI ××seventeen 17 XVII ××eighteen 18 XVIII ××nineteen 19 XIX ××twenty 20 XX ×thirty 30 XXX ×forty 40 XL ×fifty 50 L × sixty 60 LX ץseventy 70 LXX עeighty 80 LXXX פninety 90 XC ׌one hundred 100 C קGreek alphabet lettersUpper Case Letter Lower Case Letter Greek Letter Name Letter Name PronounceÎ Îą Alpha al-faΠβ Beta be-taÎ Îł Gamma ga-maΠδ Delta del-taÎ Îľ Epsilon ep-si-lonÎ Îś Zeta ze-taΠΡ Eta eh-taΠθ Theta te-taΠΚ Iota io-taÎ Îş Kappa ka-paÎ Îť Lambda lam-daÎ Îź Mu m-yooΠν Nu nooΠΞ Xi x-eeÎ Îż Omicron o-mee-c-ronÎ Ď Pi pa-yeeÎĄ Ď Rho rowÎŁ Ď Sigma sig-maΤ Ď Tau ta-ooÎĽ Ď
Upsilon oo-psi-lonÎŚ Ď Phi f-eeΧ Ď Chi kh-eeΨ Ď Psi p-seeΊ Ď Omega o-me-gaRoman numeralsNumber Roman numeral0 not defined1 I2 II3 III4 IV5 V6 VI7 VII8 VIII9 IX10 X11 XI12 XII13 XIII14 XIV15 XV16 XVI17 XVII18 XVIII19 XIX20 XX30 XXX40 XL50 L60 LX70 LXX80 LXXX90 XC100 C200 CC300 CCC400 CD500 D600 DC700 DCC800 DCCC900 CM1000 M5000 V10000 X50000 L100000 C500000 D1000000 MFor more information Mathematical symbols list (+,-,x,/,=,,,...)Hoep this helps.Do upvote!
