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Mathematics > Notation > Flashcards

Notation Flashcards

1
Q

Is an element of

A

∈

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2
Q

Is not an element of

A

∉

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3
Q

Is a subset of

A

⊆

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4
Q

Is a proper subset of

A

⊂

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5
Q

The set with elements x1, x2…

A

{x1, x2…}

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6
Q

The set of all x such that

A

{x:…}

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7
Q

The number of elements in set a

A

n(A)

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8
Q

The empty set

A

∅ = { }

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9
Q

The universal set

A

ε

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10
Q

The complement of the set of A

A

A’

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11
Q

The set of natural numbers {1,2,3…} Positive integers

A

ℕ

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12
Q

The set of integers

A

Z

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13
Q

The set of positive integers

A

Z+

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14
Q

The set of non-negative integers

A

Z0+ (0 is subscript & + is superscript)

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15
Q

The set of real numbers

A

R

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16
Q

The set of rational numbers

A

Q

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17
Q

Union

A

U

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18
Q

Intersection

A

∩

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19
Q

The ordered pair x,y

A

(x,y)

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20
Q

The closed interval {x ∈ R: a=< x =< b}

A

[a,b]

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21
Q

The interval { x ∈ R: a=< x< b}

A

[a, b)

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22
Q

The interval {x ∈ R: a < x =< b}

A

(a,b]

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23
Q

The open interval {x ∈ R: a < x < b}

A

(a,b)

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24
Q

Because/since

A

∵

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25
Q

p implies q (if p then q)

A

p —> q

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26
Q

p is implied by q (if q then p)

A

p <— q

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27
Q

p implies & is implied by q (p is equivalent to q)

A

p ⇔ q

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28
Q

The first term of an arithmetic of geometric sequence

A

a

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29
Q

The last term of an arithmetic sequence

A

l

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30
Q

The common difference for an arithmetic sequence

A

d

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31
Q

The common ratio for a geometric sequence

A

r

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32
Q

Sum to n terms of a sequence

A

Sn

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33
Q

Sum to infinity of a sequence

A

S∞

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34
Q

a1 + a2 + a3… + an

A

n
Σ ai
i = 1

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35
Q

a1 x a2 x a3 x … x an

A

n
∏ ai
i = 1

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36
Q

n!

A

n factorial

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37
Q

0!

A

=1

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38
Q

Modulus of a

A

IaI

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39
Q

The binomial coefficient

A

n C r

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40
Q

Other way of writing the binomial coefficient

A

n! / r!(n - r)! Where r =< n & r is 0 or a positive integer

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41
Q

The other other binomial coefficient

A

n
r all in brackets

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42
Q

The function of f maps the element x to the element y

A

f : x —> y

43
Q

The inverse of the function f

A

f-1

44
Q

The composite function of f and g which is defined by gf(x)= g(f(x))

A

gf

45
Q

The limit of f(x) as x tends to a

A

lim f(x)
x—> a

46
Q

The increment of x

A

∆x, δx

47
Q

The derivative of y with respect to x

A

dy
—
dx

48
Q

The nth derivative of y with respect to x

A

d^ny
——
dx^n

49
Q

The first, second; nth derivatives of f(x) with respect to x

A

f’(x), f’’(x) ; f^(n) (x)

50
Q

The first and second derivatives of x with respect to t

A

. ..
x, x

51
Q

The indefinite integral of y with respect to x

A

∫y dx

52
Q

The definite integral of y with respect to x between the limits of x=a and x= b

A

a
∫ y dx
b

53
Q

The base of natural logarithms

A

e

54
Q

The exponential function of x

A

e^x, exp x

55
Q

log x
a

A

Logarithm to the base a of x

56
Q

Natural logarithm of x

A

ln x, log x
e

57
Q

The trig functions

A

sin, cos, tan, cosec, sec & cot

58
Q

Inverse trig functions

A

sin^-1, cos^-1, tan^-1, arcsin, arccos, arctan

59
Q

rad

A

Radians

60
Q

The vector a

A

a, a , a
— ~

61
Q

The vector represented in magnitude and direction by the line segment AB

A

—>
AB

62
Q

Unit vector in the direction of a

A

a

63
Q

The magnitude of a

A

|a|, a

64
Q

The magnitude of —>
AB

A

|—>|
|AB |, AB

65
Q

Column vector and corresponding unit vector notation

A

(a) , ai + bj
(b)

66
Q

Position vector

A

r

67
Q

Displacement vector

A

s

68
Q

Velocity vector

A

v

69
Q

Acceleration vector

A

a

70
Q

The union of events A & B

A

A ∪ B

71
Q

The intersection of events A and B

A

A ∩ B

72
Q

Complement if the event A

A

A’

73
Q

Probability of the event A conditional on the event B

A

P(A|B)

74
Q

Random variables

A

X, Y, R, etc.

75
Q

Values of the random variable X, Y, R, etc.

A

x, y, r, etc.

76
Q

Values of observations

A

x1, x2, …

77
Q

Frequencies with which the observations x1, x2, … occur

A

f1, f2

78
Q

Probability function of the discrete random variable x

A

p(x), P(X=x)

79
Q

Probabilities of the values x1, x2, … of the discrete random variable X

A

p1, p2, …

80
Q

Expectation of the random variable X

A

E(X)

81
Q

Variance of the random variable X

A

Var(X)

82
Q

~

A

Has the distribution

83
Q

Binomial distribution with the parameters n & p, where n is the number of trials & p is the probability of success in a trial

A

B(n,p)

84
Q

q

A

q= 1– p for binomial distribution

85
Q

Normal distribution with mean μ and variance σ^2

A

N(μ, σ^2)

86
Q

Standard Normal distribution

A

Z ~ N(0,1)

87
Q

The probability density function of the standardised normal variable with the distribution N(0,1)

A

φ

88
Q

Corresponding cumulative distribution function

A

Φ

89
Q

Population mean

A

μ

90
Q

Population variance

A

σ^2

91
Q

Population standard deviation

A

σ

92
Q

Sample mean

A

-
x

93
Q

Sample variance

A

s^2

94
Q

Sample standard deviation

A

s

95
Q

Null hypothesis

A

H
0

96
Q

Alternative hypothesis

A

H
1

97
Q

Product moment correlation coefficient for a sample

A

r

98
Q

Product moment correlation coefficient for a population

A

ρ

99
Q

Displacement

A

S

100
Q

Initial velocity

A

u

101
Q

Velocity or final velocity

A

v

102
Q

Acceleration due to gravity

A

a

103
Q

Coefficient of friction

A

μ

Mathematics (2 decks)

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