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1. Data Science (Python) > Math Notation > Flashcards

Math Notation Flashcards

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1
Q

≠

A

not equal sign
Inequality

5 ≠ 4
5 is not equal to 4

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2
Q

=

A

equals sign
Equality

5 = 2+3
5 is equal to 2+3

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3
Q

≈

A

approximately equal
approximation

x ≈ y means x is approximately equal to y

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4
Q

>

A

inequality
greater than

5 > 4
5 is greater than 4

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5
Q
A

inequality
less than

4 < 5
4 is less than 5

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6
Q

≥

A

inequality
greater than or equal to

5 ≥ 4,
x ≥ y means x is greater than or equal to y

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7
Q

≤

A

less than or equal to

4 ≤ 5,
x ≤ y means x is less than or equal to y

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8
Q

( )

A

parentheses
calculate expression inside first

2 × (3+5) = 16

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9
Q

[ ]

A

Brackets
calculate expression inside first

[(1+2)×(1+5)] = 18

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10
Q

+

A

plus sign
Addition

1 + 1 = 2

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11
Q

−

A

minus sign
Subtraction

2 − 1 = 1

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12
Q

±

A

plus - minus
both plus and minus operations

3 ± 5 = 8 or -2

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13
Q

*

A

Asterisk
Multiplication

2 * 3 = 6

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14
Q

×

A

times sign
Multiplication

2 × 3 = 6

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15
Q

⋅

A

multiplication dot
Multiplication

2 ⋅ 3 = 6

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16
Q

÷

A

division sign / obelus
Division

6 ÷ 2 = 3

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17
Q

/

A

division slash
Division

6 / 2 = 3

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18
Q

—

A

horizontal line

division / fraction

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19
Q

mod

A

Modulo
remainder calculation

7 mod 2 = 1

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20
Q

.

A

Period
decimal point, decimal separator

2.56 = 2+56/100

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21
Q

a^b

A

Caret
Exponent

2 ^ 3 = 8

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22
Q

√a

A

square root
√a ⋅ √a = a

√9 = ±3

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23
Q

3√a (3 superindex)

A

cube root
3√a ⋅ 3√a ⋅ 3√a = a

3√8 = 2

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24
Q

n√a (n superindex)

A

“n-th root (radical)

for n=3, n√8 = 2”

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25
Q

%

A

Percent
1% = 1/100

10% × 30 = 3

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26
Q

‰

A

Per-mille
1‰ = 1/1000 = 0.1%

10‰ × 30 = 0.3

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27
Q

ppm

A

Per-million
1ppm = 1/1000000

10ppm × 30 = 0.0003

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28
Q

ppb

A

Per-billion
1ppb = 1/1000000000

10ppb × 30 = 3×10-7

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29
Q

∠

A

Angle
formed by two rays

∠ABC = 30°

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30
Q

°

A

Degree
1 turn = 360°

α = 60°

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31
Q

deg

A

Degree
1 turn = 360deg

α = 60deg

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32
Q

≅

A

congruent to
equivalence of geometric shapes and size

∆ABC≅ ∆XYZ

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33
Q

~ (geometry)

A

Similarity
same shapes, not same size

∆ABC~ ∆XYZ

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34
Q

Δ

A

Triangle
triangle shape

ΔABC≅ ΔBCD

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35
Q

|x-y|

A

Distance
distance between points x and y

x-y | = 5

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36
Q

π

A

pi constant
π = 3.141592654…

c = π⋅d = 2⋅π⋅r

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37
Q

rad

A

Radians
radians angle unit

360° = 2π rad

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38
Q

c

A

Radians
radians angle unit

360° = 2π c

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39
Q

x

A

x variable
unknown value to find

when 2x = 4, then x = 2

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40
Q

≡

A

Equivalence

identical to

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41
Q

≜

A

equal by definition

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42
Q

:=

A

equal by definition

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43
Q

~

A

approximately equal
weak approximation

11 ~ 10

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44
Q

≈

A

approximately equal
Approximation

sin(0.01) ≈ 0.01

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45
Q

∝

A

proportional to

y ∝ x when y = kx, k constant

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46
Q

∞

A

Lemniscate

infinity symbol

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47
Q

≪

A

much less than

1 ≪ 1000000

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48
Q

≫

A

much greater than

1000000 ≫ 1

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49
Q

{ }

A

Braces

set

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50
Q

⌊x⌋

A

floor brackets
rounds number to lower integer

⌊4.3⌋ = 4

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51
Q

⌈x⌉

A

ceiling brackets
rounds number to upper integer

⌈4.3⌉ = 5

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52
Q

x!

A

exclamation mark
Factorial

4! = 123*4 = 24

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53
Q

x |

A

vertical bars
absolute value

-5 | = 5

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54
Q

f (x)

A 
function of x
maps values of x to f(x)

f (x) = 3x+5

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55
Q

(f ∘ g)

A 
function composition
(f ∘ g) (x) = f (g(x))

f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)

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56
Q

(a,b)

A 
open interval
(a,b) = {x | a < x < b}

x∈ (2,6)

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57
Q

[a,b]

A

closed interval
[a,b] = {x | a ≤ x ≤ b}

x ∈ [2,6]

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58
Q

∆

A

Delta
change / difference

∆t = t1 - t0

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59
Q

∑

A

Sigma
summation - sum of all values in range of series

∑ xi= x1+x2+…+xn

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60
Q

∑∑

A

Sigma
double summation

∑+∑

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61
Q

∏

A

capital pi
product - product of all values in range of series

∏ xi=x1∙x2∙…∙xn

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62
Q

e

A

Euler’s number
e = 2.718281828…

e = lim (1+1/x)x , x→∞

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63
Q

γ

A

Euler-Mascheroni constant

γ = 0.5772156649…

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64
Q

φ

A

golden ratio constant

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65
Q

·

A

Dot
scalar product

a · b

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66
Q

×

A

Cross
vector product

a × b

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67
Q

⊗

A

tensor product
tensor product of A and B
A ⊗ B

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68
Q

[ ]

A

Brackets

matrix of numbers

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69
Q

|| x ||

A

double vertical bars

norm

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70
Q

AT

A

Transpose
matrix transpose

(AT)ij = (A)ji

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71
Q

A -1

A

inverse matrix

72
Q

dim(U)

A

Dimension
dimension of matrix A
dim(U) = 3

73
Q

P(A)

A

probability function
probability of event A

P(A) = 0.5

74
Q

P(A ⋂ B)

A

probability of events intersection
probability that of events A and B

P(A⋂B) = 0.5

75
Q

P(A ⋃ B)

A

probability of events union
probability that of events A or B

P(A⋃B) = 0.5

76
Q

P(A | B)

A

conditional probability function
probability of event A given event B occured

P(A | B) = 0.3

77
Q

f (x) （probability)

A

probability density function (pdf)

P(a ≤ x ≤ b) = ∫ f (x) dx

78
Q

F(x)

A

cumulative distribution function (cdf)

F(x) = P(X≤ x)

79
Q

μ

A

Mu
population mean

μ = 10

80
Q

E(X)a

A

expectation value
expected value of random variable X

E(X) = 10

81
Q

E(X | Y)

A

conditional expectation
expected value of random variable X given Y

E(X | Y=2) = 5

82
Q

var(X)

A

Variance
variance of random variable X

var(X) = 4

83
Q

σ2

A

Sigma (variation)
Variance
variance of random variable X

σ2 = 4

84
Q

std(X)

A

standard deviation
standard deviation of random variable X

std(X) = 2

85
Q

σX

A

standard deviation
standard deviation value of random variable X

σX = 2

86
Q

x̃

A

Median

middle value of random variable x

87
Q

cov(X,Y)

A

Covariance
covariance of random variables X and Y

cov(X,Y) = 4

88
Q

corr(X,Y)

A

Correlation
correlation of random variables X and Y

corr(X,Y) = 0.6

89
Q

ρX,Y

A

Correlation
correlation of random variables X and Y

ρX,Y = 0.6

90
Q

MR

A

Mid-range

MR = (xmax+xmin)/2

91
Q

Md

A

sample median

half the population is below this value

92
Q

Q1

A

lower / first quartile

25% of population are below this value

93
Q

Q2

A

median / second quartile

50% of population are below this value = median of samples

94
Q

Q3

A

upper / third quartile

75% of population are below this value

95
Q

s 2

A

sample variance
population samples variance estimator

s 2 = 4

96
Q

x-bar

A

sample mean
average / arithmetic mean

x-bar = (2+5+9) / 3 = 5.333

97
Q

zx

A

standard score

zx = (x-xbar) / sx

98
Q

s

A

sample standard deviation
population samples standard deviation estimator

s = 2

99
Q

X ~

A

distribution of X
distribution of random variable X

X ~ N(0,3)

100
Q

N(μ,σ2)

A

normal distribution
gaussian distribution

X ~ N(0,3)

101
Q

U(a,b)

A

uniform distribution
equal probability in range a,b

X ~ U(0,3)

102
Q

exp(λ)

A

exponential distribution

f (x) = λe-λx , x≥0

103
Q

λ

A

Lambda

104
Q

gamma(c, λ)

A

gamma distribution

f (x) = λ c xc-1e-λx / Γ(c), x≥0

105
Q

χ 2(k)

A

chi-square distribution

f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) )

106
Q

F (k1, k2)

A

F distribution

107
Q

Bin(n,p)

A

binomial distribution

f (k) = nCk pk(1-p)n-k

108
Q

Poisson(λ)

A

Poisson distribution

f (k) = λke-λ / k!

109
Q

Geom(p)

A

geometric distribution

f (k) = p(1-p) k

110
Q

Bern(p)

A

Bernoulli distribution

111
Q

n!

A

Factorial
n! = 1⋅2⋅3⋅…⋅n

5! = 1⋅2⋅3⋅4⋅5 = 120

112
Q

nPk

A

Permutation
P(n,r)=n! (n−r)!

5P3 = 5! / (5-3)! = 60

113
Q

nCk

A

Combination

r! (n−r)!

114
Q

{ }

A

Set
a collection of elements

A = {3,7,9,14},
B = {9,14,28}
115
Q

A ∩ B

A

Intersection
objects that belong to set A and set B

A ∩ B = {9,14}

116
Q

A ∪ B

A

Union
objects that belong to set A or set B

A ∪ B = {3,7,9,14,28}

117
Q

A ⊆ B

A

Subset
A is a subset of B. set A is included in set B.

{9,14,28} ⊆ {9,14,28}

118
Q

A ⊂ B

A

proper subset / strict subset
A is a subset of B, but A is not equal to B.

{9,14} ⊂ {9,14,28}

119
Q

A ⊄ B

A

not subset
set A is not a subset of set B

{9,66} ⊄ {9,14,28}

120
Q

A ⊇ B

A

Superset
A is a superset of B. set A includes set B

{9,14,28} ⊇ {9,14,28}

121
Q

A ⊃ B

A

proper superset / strict superset
A is a superset of B, but B is not equal to A.

{9,14,28} ⊃ {9,14}

122
Q

A ⊅ B

A

not superset

set A is not a superset of set B
{9,14,28} ⊅ {9,66}

123
Q

A ⊅ B

A

not superset

set A is not a superset of set B
{9,14,28} ⊅ {9,66}

124
Q

A - B

A

relative complement
objects that belong to A and not to B

A = {3,9,14},
B = {1,2,3},
A-B = {9,14}
125
Q

A ∆ B

A

symmetric difference
objects that belong to A or B but not to their intersection

A = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}

126
Q

A ⊖ B

A

symmetric difference
objects that belong to A or B but not to their intersection

A = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}

127
Q

∈

A

element of,
belongs to
set membership

A={3,9,14}, 3 ∈ A

128
Q

∉

A

not element of
no set membership

A={3,9,14}, 1 ∉ A

129
Q

(a,b) (Set theory symbols)

A

ordered pair

collection of 2 elements

130
Q

A×B

A

cartesian product

set of all ordered pairs from A and B

131
Q 
|A|
#A
A

Cardinality
the number of elements of set A

A={3,9,14}, |A|=3

132
Q

|

Set theory symbols

A

vertical bar
such that
A={x|3

133
Q

Ø

A

empty set
Ø = { }

C = {Ø}

134
Q

∀

A

For All

∀x>1, x2>x

135
Q

∴

A

Therefore

a=b ∴ b=a

136
Q

⋅ (Logic)

A

And

x ⋅ y

137
Q

&

A

Ampersand
and

x & y

138
Q

(logic)+

A

Or

x + y

139
Q

(logic)

A

vertical line
Or

x | y

140
Q

⇒

A

implies

141
Q

¬

A

not - negation

¬ x

142
Q

⇔

A

Equivalent

if and only if (iff)

143
Q

∵

A

because / since

144
Q

y ‘

A

Derivative
derivative - Lagrange’s notation

(3x3)’ = 9x2

145
Q

y ‘’

A

second derivative
derivative of derivative

(3x3)’’ = 18x

146
Q

y(n)

A

nth derivative

(3x3)(3) = 18

147
Q

∫

A

Integral
opposite to derivation
∫ f(x)dx

148
Q

∫∫

A

double integral
integration of function of 2 variables

∫∫ f(x,y)dxdya

149
Q

i

A

imaginary unit
i ≡ √-1

z = 3 + 2i

150
Q

z*

A

complex conjugate
z = a+bi → z*=a-bi

z* = 3 - 2i

151
Q

Re(z)

A

real part of a complex number
z = a+bi → Re(z)=a

Re(3 - 2i) = 3

152
Q

Im(z)

A

imaginary part of a complex number
z = a+bi → Im(z)=b

Im(3 - 2i) = -2

153
Q

z |

A

absolute value/magnitude of a complex number
|z| = |a+bi| = √(a2+b2)

|3 - 2i| = √13

154
Q

Α α

A

Alpha

155
Q

Β β

A

Beta

156
Q

Γ γ

A

Gamma

157
Q

Δ δ

A

Delta

158
Q

Ε ε

A

Epsilon

159
Q

Ζ ζ

A

Zeta

160
Q

Η η

A

Eta

161
Q

Θ θ

A

Theta

162
Q

Ι ι

A

Iota

163
Q

Κ κ

A

Kappa

164
Q

Λ λ

A

Lambda

165
Q

Μ μ

A

Mu

166
Q

Ν ν

A

Nu

167
Q

Ξ ξ

A

Xi

168
Q

Π π

A

Pi

169
Q

Ρ ρ

A

Rho

170
Q

Σ σ

A

Sigma

171
Q

Τ τ

A

Tau

172
Q

Υ υ

A

Upsilon

173
Q

Φ φ

A

Phi

174
Q

Χ χ

A

Chi

175
Q

Ψ ψ

A

Psi

176
Q

Ω ω

A

Omega

1. Data Science (Python) (9 decks)

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