Math Formulas Essay

1887 words - 8 pages

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Mathematical Symbols
List of all mathematical symbols and signs - meaning and examples.
Basic math symbols
Geometry symbols
Algebra symbols
Probability & statistics symbols
Set theory symbols
Logic symbols
Calculus & analysis symbols
Number symbols
Greek symbols
Roman numerals
Basic math symbols
Symbol Symbol Name Meaning / definition Example
= equals sign
equality 5 = 2+3
≠ not equal sign inequality 5 ≠ 4
> strict inequality greater than 5 > 4
< strict inequality less than 4 < 5
≥ inequality greater than or equal to 5 ≥ 4
≤ inequality less than or equal to 4 ≤ 5
( ) parentheses calculate expression inside ...view middle of the document...

is the ratio between the circumference and diameter of a circle c = π•d = 2•π•r
rad radians radians angle unit 360º = 2π rad
grad grads grads angle unit 360º = 400 grad
Algebra symbols
Symbol Symbol Name Meaning / definition Example
x x variable unknown value to find when 2x = 4, then x = 2
≡ equivalence identical to
≜ equal by definition equal by definition
:= equal by definition equal by definition
~ approximately equal weak approximation 11 ~ 10
≈ approximately equal approximation sin(0.01) ≈ 0.01
∝ proportional to proportional to f(x) ∝ g(x)
∞ lemniscate
infinity symbol

≪ much less than much less than 1 ≪ 1000000
≫ much greater than much greater than 1000000 ≫ 1
( ) parentheses calculate expression inside first 2 * (3+5) = 16
[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18
{ } braces set
⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋= 4
⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉= 5
x! exclamation mark factorial
4! = 1*2*3*4 = 24
| x | single vertical bar absolute value | -5 | = 5
f (x) function of x maps 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]
∆ delta change / difference ∆t = t1 - t0
∆ discriminant Δ = b2 - 4ac
∑ sigma summation - sum of all values in range of series ∑ xi= x1+x2+...+xn
∑∑ sigma double summation
∏ capital pi product - product of all values in range of series ∏ xi=x1∙x2∙...∙xn
e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞
γ Euler-Mascheroni constant
γ = 0.527721566...
φ golden ratio golden ratio constant
π pi constant π = 3.141592654...
is the ratio between the circumference and diameter of a circle c = π•d = 2•π•r
Linear Algebra Symbols
Symbol Symbol Name Meaning / definition Example
∙ dot scalar product a ∙ b
× cross vector product a × b
A⊗B tensor product tensor product of A and B A⊗ B
inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
| A | determinant determinant of matrix A
det(A) determinant determinant of matrix A
|| x || double vertical bars norm
AT transpose matrix transpose (AT)ij = (A)ji
A† Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji
A* Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji
A-1 inverse matrix A A-1 = I
rank(A) matrix rank rank of matrix A rank(A) = 3
dim(U) dimension dimension of matrix A rank(U) = 3
Probability and statistics symbols
Symbol Symbol Name Meaning / definition Example
P(A) probability function probability of event A P(A) = 0.5
P(A ∩ B) probability of events intersection probability that of events A and B P(A∩B) = 0.5
P(A∪ B) probability of events union probability that of events A or B P(A∪B) = 0.5
P(A | B) conditional probability function probability of event A given event B occured P(A...

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