Symbol Symbol Name -Meaning / definition= equals sign -equality≠ not equal sign- inequality≈ approximately equal- approximation strict inequality- greater than strict inequality- less than≥ inequality- greater than or equal to≤ inequality -less than or equal to parentheses -calculate expression inside first[ ] brackets -calculate expression inside first+ plus sign -addition− minus sign- subtraction± plus - minus -both plus and minus operations± minus - plus -both minus and plus operations* asterisk -multiplication× times sign -multiplication⋅ multiplication/dot- multiplication÷ division sign / obelus -division/ division slash -division— horizontal line -division / fractionmod modulo -remainder calculation. period -decimal point, decimal separatorab power -exponenta^b caret -exponent√a square root √a ⋅ √a = a3√a cube root 3√a ⋅ 3√a ⋅ 3√a = a4√a fourth root 4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a = an√a n-th root (radical)% percent 1% = 1/100‰ per-mille 1‰ = 1/1000 = .1%ppm per-million -1ppm = 1/1000000ppb per-billion -1ppb = 1/1000000000ppt per-trillion 1-ppt = 10-12Geometry symbolsSymbol Symbol Name -Meaning / definition∠ angle formed by two raysmeasured anglespherical angle∟ right angle = 90°° degree 1 turn = 360°deg degree 1 turn = 360deg′ prime arcminute, 1° = 60′″ double prime arcsecond, 1′ = 60″line infinite lineAB line segment line from point A to point Bray line that start from point Aarc arc from point A to point B⊥ perpendicular perpendicular lines (90° angle)∥ parallel parallel lines≅ congruent to equivalence of geometric shapes and size~ similarity same shapes, not same sizeΔ triangle triangle shape|x-y| distance distance between points x and yπ pi constant π = 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 to≜ equal by definition equal by definition:= equal by definition equal by definition~ approximately equal weak approximation≈ approximately equal approximation∝ proportional to proportional to∞ 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 set⌊x⌋ floor brackets rounds number to lower integer⌈x⌉ 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 ∘ g) function composition (f ∘ 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}∆ delta change / difference∆ discriminant Δ = b2 - 4ac∑ sigma summation - sum of all values in range of series∑∑ sigma double summation∏ capital pi product - product of all values in range of seriese e constant / Euler's number e = 2.718281828...γ Euler-Mascheroni constant γ = .5772156649...φ golden ratio golden ratio constantπ pi constant π = 3.141592654...is the ratio between the circumference and diameter of a circleLinear Algebra SymbolsSymbol Symbol Name Meaning / definition· dot scalar product× cross vector productA⊗B 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 transposeA† 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)μ 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 Xσ2 variance variance of population valuesstd(X) standard deviation standard deviation of random variable XσX 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 YρX,Y correlation correlation of random variables X and Y∑ summation summation - sum of all values in range of series∑∑ 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(μ,σ2) normal distribution gaussian distributionU(a,b) uniform distribution equal probability in range a,bexp(λ) exponential distribution f (x) = λe-λx , x≥0gamma(c, λ) gamma distribution f (x) = λ c xc-1e-λx / Γ(c), x≥0χ 2(k) chi-square distribution f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )F (k1, k2) F distributionBin(n,p) binomial distribution f (k) = nCk pk(1-p)n-kPoisson(λ) Poisson distribution f (k) = λke-λ / 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! = 1⋅2⋅3⋅...⋅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 ⊆ B subset A is a subset of B. set A is included in set B.A ⊂ B proper subset / strict subset A is a subset of B, but A is not equal to B.A ⊄ B not subset set A is not a subset of set BA ⊇ B superset A is a superset of B. set A includes set BA ⊃ B proper superset / strict superset A is a superset of B, but B is not equal to A.A ⊅ 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 ∆ B symmetric difference objects that belong to A or B but not to their intersectionA ⊖ B symmetric difference objects that belong to A or B but not to their intersectiona∈A element of,belongs to set membershipx∉A not element of no set membership(a,b) ordered pair collection of 2 elementsA×B 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 setØ empty set Ø = { }\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,b∈\mathbb{Z}}\mathbb{R} real numbers set \mathbb{R} = {x | -∞ x ∞}\mathbb{C} complex numbers set \mathbb{C} = {z | z=a+bi, -∞a∞, -∞b∞}Logic symbolsSymbol Symbol Name Meaning / definition⋅ and and^ caret / circumflex and& ampersand and+ plus or∨ recaret or| vertical line orx' single quote not - negationx bar not - negation¬ not not - negation! exclamation mark not - negation⊕ circled plus / oplus exclusive or - xor~ tilde negation⇒ implies⇔ equivalent if and only if (iff)↔ equivalent if and only if (iff)∀ for all∃ there exists∄ there does not exists∴ therefore∵ because / sinceCalculus & analysis symbolsSymbol Symbol Name Meaning / definition\lim_{x\to x0}f(x) limit limit value of a functionε 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 derivation∫∫ double integral integration of function of 2 variables∫∫∫ triple integral integration of function of 3 variables∮ closed contour / line integral∯ closed surface integral∰ 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 ≡ √-1z* complex conjugate z = a+bi → z*=a-biz complex conjugate z = a+bi → z = a-bi∇ nabla / del gradient / divergence operatorvectorunit vectorx * y convolution y(t) = x(t) * h(t)Laplace transform F(s) = {f (t)}Fourier transform X(ω) = {f (t)}δ delta function∞ lemniscate infinity symbolNumeral symbolsName European Roman Hebrewzero 0one 1 I אtwo 2 II בthree 3 III גfour 4 IV דfive 5 V הsix 6 VI וseven 7 VII זeight 8 VIII חnine 9 IX טten 10 X יeleven 11 XI יאtwelve 12 XII יבthirteen 13 XIII יגfourteen 14 XIV ידfifteen 15 XV טוsixteen 16 XVI טזseventeen 17 XVII יזeighteen 18 XVIII יחnineteen 19 XIX יטtwenty 20 XX כthirty 30 XXX לforty 40 XL מfifty 50 L נsixty 60 LX סseventy 70 LXX עeighty 80 LXXX פninety 90 XC צone hundred 100 C קGreek alphabet lettersUpper Case Letter Lower Case Letter Greek Letter Name Letter Name PronounceΑ α Alpha al-faΒ β Beta be-taΓ γ Gamma ga-maΔ δ Delta del-taΕ ε Epsilon ep-si-lonΖ ζ Zeta ze-taΗ η Eta eh-taΘ θ Theta te-taΙ ι Iota io-taΚ κ Kappa ka-paΛ λ Lambda lam-daΜ μ Mu m-yooΝ ν Nu nooΞ ξ Xi x-eeΟ ο Omicron o-mee-c-ronΠ π Pi pa-yeeΡ ρ Rho rowΣ σ Sigma sig-maΤ τ Tau ta-ooΥ υ Upsilon oo-psi-lonΦ φ Phi f-eeΧ χ Chi kh-eeΨ ψ Psi p-seeΩ ω 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!
