Symbol | Symbol Meaning |
---|---|

= | equality |

≠ | inequality |

≈ | approximation |

> | greater than |

< | less than |

≥ | greater than or equal to |

≤ | greater than or equal to |

( ) | calculate expression inside first |

+ | addition |

− | subtraction |

± | both plus and minus operations |

± | both minus and plus operations |

*|×|⋅ | multiplication |

÷|/|— | division/fraction |

. | decimal point, decimal separator |

ab|a^b | exponent |

√a | square root |

3√a | cube root |

n√a | n-th root (radical) |

% | percent |

‰ | per-mille |

Symbol | Symbol Meaning |
---|---|

∠ | angle, formed by two rays |

∟ | *= 90° |

° | 1 turn = 360° |

deg | 1 turn = 360 deg |

′ | arcminute, 1° = 60′ |

″ | arcsecond, 1′ = 60″ |

AB | line from point A to point B |

⊥ | perpendicular lines (90° angle) |

∥ | parallel lines |

≅ | equivalence of geometric shapes and size |

~ | same shapes, not same size |

Δ | triangle shape |

|x-y| | distance between points x and y |

π | Ratio between the circumference and diameter of a circle |

rad | radians angle unit |

c | radians angle unit |

grad | grads angle unit |

g | grads angle unit |

Symbol | Symbol Meaning |
---|---|

x | unknown value to find |

≡ | identical to |

≜ | equal by definition |

:= | equal by definition |

~ | weak approximation |

≈ | approximation |

∝ | proportional to |

∞ | infinity symbol |

≪ | much less than |

≫ | much greater than |

( ) | calculate expression inside first |

[ ] | calculate expression inside first |

{ } | set |

⌊x⌋ | rounds number to lower integer |

⌈x⌉ | rounds number to upper integer |

x! | factorial |

| x | | absolute value |

f (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} |

∆ | change / difference |

∆ | discriminant, Δ = b2 - 4ac |

∑ | summation - sum of all values in range of series |

∑∑ | double summation |

∏ | product - product of all values in range of series |

e | Euler's number, e = 2.718281828... |

γ | Euler-Mascheroni constant, γ = 0.5772156649... |

φ | golden ratio constant |

π | π = 3.141592654... |

Symbol | Symbol Meaning |
---|---|

· | scalar product |

× | vector product |

A⊗B | tensor product of A and B |

[ ] | matrix of numbers |

( ) | matrix of numbers |

| A | | determinant of matrix A |

det(A) | determinant of matrix A |

|| x || | norm |

AT | matrix transpose |

A† | matrix conjugate transpose |

A* | matrix conjugate transpose |

A -1 | inverse matrix, A A-1 = I |

rank(A) | rank of matrix A |

dim(U) | dimension of matrix A |

Symbol | Symbol Meaning |
---|---|

P(A) | probability function |

P(A ⋂ B) | probability of events intersection |

P(A ⋃ B) | probability of events union |

P(A | B) | conditional probability function |

f (x) | probability density function (pdf) |

F(x) | cumulative distribution function (cdf) |

μ | population mean |

E(X) | expectation value |

E(X | Y) | conditional expectation |

var(X) | variance |

σ2 | variance |

std(X) | standard deviation |

σX | standard deviation |

cov(X,Y) | covariance |

corr(X,Y) | correlation |

ρX,Y | correlation |

∑ | summation |

∑∑ | double summation |

Mo | mode |

MR | mid-range |

Md | sample median |

Q1 | lower / first quartile |

Q2 | median / second quartile |

Q3 | upper / third quartile |

x | sample mean |

s 2 | sample variance |

s | sample standard deviation |

zx | standard score |

X ~ | distribution of X |

N(μ,σ2) | normal distribution |

U(a,b) | uniform distribution |

exp(λ) | exponential distribution |

gamma(c, λ) | gamma distribution |

χ 2(k) | chi-square distribution |

F (k1, k2) | F distribution |

Bin(n,p) | binomial distribution |

Poisson(λ) | Poisson distribution |

Geom(p) | geometric distribution |

HG(N,K,n) | hyper-geometric distribution |

Bern(p) | Bernoulli distribution |

Symbol | Symbol Meaning |
---|---|

n! | factorial |

nPk | permutation |

nCk | combination |

Symbol | Symbol Meaning |
---|---|

{ } | set |

A ∩ B | intersection |

A ∪ B | union |

A ⊆ B | subset |

A ⊂ B | proper subset / strict subset |

A ⊄ B | not subset |

A ⊇ B | superset |

A ⊃ B | proper superset / strict superset |

A ⊅ B | not superset |

2A | power set |

A = B | equality |

Ac | complement |

A \ B | relative complement |

A - B | relative complement |

A ∆ B | symmetric difference |

A ⊖ B | symmetric difference |

a∈A | element of, belongs to |

Symbol | Symbol Meaning |
---|---|

⋅ | and |

^ | caret / circumflex (and) |

& | ampersand (and) |

+ | plus (or) |

∨ | reversed caret (or) |

| | vertical line (or) |

x' | single quote (not - negation) |

x | 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 / since |

Symbol | Symbol Meaning |
---|---|

ε | epsilon |

e | e constant / Euler's number |

y ' | derivative |

y '' | second derivative |

y(n) | nth derivative |

Dx y | derivative |

Dx2y | second derivative |

∫ | integral |

∫∫ | double integral |

∫∫∫ | triple integral |

∮ | closed contour / line integral |

∯ | closed surface integral |

∰ | closed volume integral |

[a,b] | closed interval |

(a,b) | open interval |

i | imaginary unit |

z* | complex conjugate |

z | complex conjugate |

Re(z) | real part of a complex number |

Im(z) | imaginary part of a complex number |

| z | | absolute value/magnitude of a complex number |

arg(z) | argument of a complex number |

∇ | nabla / del |

x * y | convolution |

δ | delta function |

∞ | lemniscate |