# 3 Symbols in Data Science (part 1) (Math & Python) Flashcards

1
Q

1 Name, use and example of =

A

Equality

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

2
Q

2 Name, use example and equivalent in Python of ≠

A

Inequality

5 ≠ 4
5 is not equal to 4

In Python:
!= 3!=4

3
Q

2.1 Outcome of:

print(5!=4)

A

True

4
Q

3 Name, use and example of ≈

A

approximation

x ≈ y
x is approximately equal to y

5
Q

4 What does the /= operator mean in Python?

A

It’s an assignment operator shorthand for / and =

x /= 3 # equivalent to x = x / 3

6
Q

4.1 Outcome of:

x = 1
x/=4
x

A

0.25

7
Q

5 Name, use and example of >

A

greater than

5 > 4
5 is greater than 4

8
Q

5.1 Outcome of:

5>4

A

True

9
Q

6 Name, how to read and example of

A

less than

4 < 5
4 is less than 5

10
Q

6.1 Outcome of:

5<4

A

False

11
Q

7 Name, how to read, example, and equivalent in Python of≥

A

greater than or equal to

5 ≥ 4,
x ≥ y means x is greater than or equal to y
Python: 5>=4

12
Q

Outcome of:

a =[0,0]
b=[0,1]
a>=b

A

False

13
Q

8 Name, how to read, example, and equivalent in Python of ≤

A

less than or equal to

4 ≤ 5,
x ≤ y x is less than or equal to y
Python: 4<=4

14
Q

8.1 Outcome of:

A

a =[0,0]
b=[0,1]
a<=b

15
Q

9 Name, use in Maths and Python and examples of: ( )

A

Parentheses
Maths:order of operation. calculate expression inside first
Python: order of operation, tuples, generator expressions, function calls and other syntax

2 × (3+5) = 16
a=(1,4,5) #tuple (unchangeable)

16
Q

9.1 Outcome of:

print(2* (3+5) )
print(2*3+5)

A

16

11

17
Q

10 Name, use in Maths and Python and examples of:[ ]

A

Brackets
Maths: order of operations.calculates expression inside first
Python: order of operation, to define mutable data types - lists, list comprehensions and for indexing/lookup/slicing

18
Q

10.1 Outcome of:

print[2* [3+5] ]

A

TypeError: ‘builtin_function_or_method’ object is not subscriptable

19
Q

11 Name and read: +

1 + 1 = 2

A

One plus one equals two
1 + 1 = 2

20
Q

12 Name and read: −

A

Subtraction

2 − 1 = 1
Two minus one equals one

21
Q

13 Name and example of: ±

A

plus and minus

3 ± 5 = 8 or -2

22
Q

14 Name and example of: ±

±

A

minus - plus
both minus and plus operations

3 ∓ 5 = -2 or 8

23
Q

15 Name,use,read and Python uses of *

2 * 3 = 6

A

Asterisk
Multiplication
2 * 3 = 6

Two multiplied by three is equal to six

Python: Multiplication and unpacking

24
Q

16 Name,use of ⋅

A

Multiplication dot

2 ⋅ 3 = 6

25
Q

6 ÷ 2 = 3

A

Division sign

Six divided by 2 equals three

26
Q

18 Name and use in Maths and Python of /

A

Slash

Maths: Division
Python: Division, for file paths

6 / 2 = 3
p = PurePath(‘/etc’)

27
Q

18 Name and use of —

A

horizontal line

division / fraction

28
Q

19 Name and use of % in Maths and Python

A

Maths: Percentage
Python:Modulo
Python: remainder calculation

Python: 7%2 = 1

Maths: 1% = 1/100
10% × 30 = 3

29
Q

20 Name and use of .

A

Period, decimal point, decimal separator

2.56 = 2+56/100

30
Q

21 Name and use of a^b

A

Power Exponent

2^3 = 8

31
Q

22 Name and use of a^b

A

Caret
Exponent

2 ^ 3 = 8

32
Q

22 Name and use of √a

A

square root
√a ⋅ √a = a
√9 = ±3

33
Q

22 Name and use of 3√a

A

cube root
3√a ⋅ 3√a ⋅ 3√a = a

3√8 = 2

34
Q

23 Name and use of n√a

A

for n=3, n√8 = 2

35
Q

23.1 Calculate for n=7, n√8 = 2

A
```#Answer:
n = 7
8**(1/n)```
36
Q

24 Name and use of ‰

A

Per-mille
1‰ = 1/1000 = 0.1%

10‰ × 30 = 0.3

37
Q

25 Name and use of ppm

A

Per-million

38
Q

26 Name and use of ppb

A

Per-billion
1ppb = 1/1000000000

10ppb × 30 = 3×10^-7

39
Q

27 Name and use of ∠

A

Angle
formed by two rays

∠ABC = 30°

40
Q

28 Name and use of °

A

Degree
1 turn = 360°

α = 60°

41
Q

29 Name and use of deg

A

Degree
1 turn = 360deg

α = 60deg

42
Q

30 Name and use of ≅

A

congruent to
equivalence of geometric shapes and size

∆ABC≅ ∆XYZ

43
Q

31 Name and use of ~ (geometry)

A

Similarity
same shapes, not same size

∆ABC~ ∆XYZ

44
Q

32 Name and use of Δ

A

Triangle
triangle shape

ΔABC≅ ΔBCD

45
Q

33 Name and use of |x-y|

A

Distance
distance between points x and y

x-y | = 5

46
Q

34 Name and use of π

A

pi constant
π = 3.141592654…

c = π⋅d = 2⋅π⋅r

47
Q

35 Name and use of rad

A

360° = 2π rad

48
Q

36 Name and use of c

A

360° = 2π c

49
Q

37 Name and use of x

A

x variable
unknown value to find

when 2x = 4, then x = 2

50
Q

38 Name of ≡

A

Equivalence

identical to

51
Q

39 Use of ≜

A

equal by definition

52
Q

40 Name of:=

A

equal by definition

Python: walrus operator

53
Q

41 Name and use of ~

A

approximately equal

11 ~ 10

54
Q

42 Name and use of ≈

A

approximately equal
Approximation

sin(0.01) ≈ 0.01

55
Q

43 Name and use of ∝

A

proportional to

y ∝ x when y = kx, k constant

56
Q

44 Name of ∞

A

Lemniscate

infinity symbol

57
Q

45 Name and use of ≪

A

much less than

1 ≪ 1000000

58
Q

46 Name and use of ≫

A

much greater than

1000000 ≫ 1

59
Q

47 Name and use of {}

name: Braces
{1, 3, 4}

A

Braces
Python: use for sets

e.g.
print(‘name: Braces’)
_set={1,3,4,4,4}
_set

60
Q

47.1 What is a set?

A

Set is an unordered collection data type that is iterable, mutable and has no duplicate elements

61
Q

48 Name and use of ⌊x⌋

A

Floor brackets
rounds number to lower integer

⌊4.3⌋ = 4

62
Q

49 Name and use of ⌈x⌉

A

Ceiling brackets
rounds number to upper integer

⌈4.3⌉ = 5

63
Q

50 Name and use of x!

A

Exclamation mark
Factorial

4! = 123*4 = 24

64
Q

50.1 Code to get factorial :

enter a number to compute its factorial:4

A

num =int(input (‘enter a number to compute its factorial:’))
factorial = 1

for i in range(1,num + 1):
factorial = factorial*i

print(factorial)

65
Q

51 Name and use of | x |

A

vertical bars
absolute value

-5 | = 5

66
Q

52 Name and use of f(x)

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

f (x) = 3x+5

67
Q

53 Name and use of (f ∘ g)

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

f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)

68
Q

54 Name and use of(a,b)

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

x∈ (2,6)

69
Q

55 Name and use of[a,b]

A

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

x ∈ [2,6]

70
Q

56 Name and use of ∆

A

Delta
change / difference

∆t = t1 - t0

71
Q

57 Name and use of ∑

A

Sigma
summation - sum of all values in range of series

∑ xi= x1+x2+…+xn

72
Q

58 Name and use of ∑∑

A

Sigma
double summation

∑+∑

73
Q

59 Name and use of ∏

A

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

∏ xi=x1∙x2∙…∙xn

74
Q

60 Name and use of e

A

Euler’s number
e = 2.718281828…

e = lim (1+1/x)x , x→∞

75
Q

61 Name of γ

A

Euler-Mascheroni constant

γ = 0.5772156649…

76
Q

62 Name and use of ·

A

Dot
scalar product

a · b

77
Q

63 Name and use of ×

A

Cross
vector product

a × b

78
Q

64 Name and use of ⊗

A

tensor product
tensor product of A and B
A ⊗ B

79
Q

65 Name and use in Maths and Python of [ ]

A

Brackets

• Maths: Matrix of numbers
• Python: Used to define mutable data types - lists, list comprehensions and for indexing/lookup/slicing
80
Q

65 Name and use in Maths and Python of ( )

A

Parentheses

matrix of numbers

81
Q

66 Name of | A |

A

Determinant

82
Q

67 Name of det(A)

A

Determinant

determinant of matrix A

83
Q

68 Name of || x ||

A

double vertical bars
norm of that vector
(Norm or Magnitude of denoted is defined as the length or magnitude of the vector)

84
Q

69 Name and use of A^T

A

Transpose
matrix transpose

(A^T)ij = (A)ji

85
Q

70 Name of A -1

A

inverse matrix

86
Q

71 Name and use of dim(U)

A

Dimension
dimension of matrix A
dim(U) = 3

87
Q

72 Name and use of P(A)

A

probability function
probability of event A

P(A) = 0.5

88
Q

73 Name and use of P(A ⋂ B)

A

probability of events intersection
probability that of events A and B

P(A⋂B) = 0.5

89
Q

74 Name and use of P(A ⋃ B)

A

probability of events union
probability that of events A or B

P(A⋃B) = 0.5

90
Q

75 Name of φ

A

golden ratio constant