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

Question 1

1 Name, use and example of =

Answer 1

Equality

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

Question 2

2 Name, use example and equivalent in Python of ≠

Answer 2

Inequality

5 ≠ 4
5 is not equal to 4

In Python:
!= 3!=4

Question 3

2.1 Outcome of:

print(5!=4)

Answer 3

True

Question 4

3 Name, use and example of ≈

Answer 4

approximation

x ≈ y
x is approximately equal to y

Question 5

4 What does the /= operator mean in Python?

Answer 5

It’s an assignment operator shorthand for / and =

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

Question 6

4.1 Outcome of:

x = 1
x/=4
x

Answer 6

0.25

Question 7

5 Name, use and example of >

Answer 7

greater than

5 > 4
5 is greater than 4

Question 8

5.1 Outcome of:

5>4

Answer 8

True

Question 9

6 Name, how to read and example of

Answer 9

less than

4 < 5
4 is less than 5

Question 10

6.1 Outcome of:

5<4

Answer 10

False

Question 11

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

Answer 11

greater than or equal to

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

Question 12

Outcome of:

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

Answer 12

False

Question 13

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

Answer 13

less than or equal to

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

Question 14

8.1 Outcome of:

Answer 14

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

Question 15

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

Answer 15

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)

Question 16

9.1 Outcome of:

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

Answer 16

16

11

Question 17

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

Answer 17

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

Question 18

10.1 Outcome of:

print[2* [3+5] ]

Answer 18

TypeError: ‘builtin_function_or_method’ object is not subscriptable

Question 19

11 Name and read: +

1 + 1 = 2

Answer 19

Addition
One plus one equals two
1 + 1 = 2

Question 20

12 Name and read: −

Answer 20

Subtraction

2 − 1 = 1
Two minus one equals one

Question 21

13 Name and example of: ±

Answer 21

plus and minus

3 ± 5 = 8 or -2

Question 22

14 Name and example of: ±

±

Answer 22

minus - plus
both minus and plus operations

3 ∓ 5 = -2 or 8

Question 23

15 Name,use,read and Python uses of *

2 * 3 = 6

Answer 23

Asterisk
Multiplication
2 * 3 = 6

Two multiplied by three is equal to six

Python: Multiplication and unpacking

Question 24

16 Name,use of ⋅

Answer 24

Multiplication dot

2 ⋅ 3 = 6

Question 25

17 Name,use,read of:÷

6 ÷ 2 = 3

Answer 25

Division sign

Six divided by 2 equals three

Question 26

18 Name and use in Maths and Python of /

Answer 26

Slash

Maths: Division
Python: Division, for file paths

6 / 2 = 3
p = PurePath(‘/etc’)

Question 27

18 Name and use of —

Answer 27

horizontal line

division / fraction

Question 28

19 Name and use of % in Maths and Python

Answer 28

Maths: Percentage
Python:Modulo
Python: remainder calculation

Python: 7%2 = 1

Maths: 1% = 1/100
10% × 30 = 3

Question 29

20 Name and use of .

Answer 29

Period, decimal point, decimal separator

2.56 = 2+56/100

Question 30

21 Name and use of a^b

Answer 30

Power Exponent

2^3 = 8

Question 31

22 Name and use of a^b

Answer 31

Caret
Exponent

2 ^ 3 = 8

Question 32

22 Name and use of √a

Answer 32

square root
√a ⋅ √a = a
√9 = ±3

Question 33

22 Name and use of 3√a

Answer 33

cube root
3√a ⋅ 3√a ⋅ 3√a = a

3√8 = 2

Question 34

23 Name and use of n√a

Answer 34

n-th root (radical)

for n=3, n√8 = 2

Question 35

23.1 Calculate for n=7, n√8 = 2

Answer 35

#Answer:
n = 7
8**(1/n)

Question 36

24 Name and use of ‰

Answer 36

Per-mille
1‰ = 1/1000 = 0.1%

10‰ × 30 = 0.3

Question 37

25 Name and use of ppm

Answer 37

Per-million

Question 38

26 Name and use of ppb

Answer 38

Per-billion
1ppb = 1/1000000000

10ppb × 30 = 3×10^-7

Question 39

27 Name and use of ∠

Answer 39

Angle
formed by two rays

∠ABC = 30°

Question 40

28 Name and use of °

Answer 40

Degree
1 turn = 360°

α = 60°

Question 41

29 Name and use of deg

Answer 41

Degree
1 turn = 360deg

α = 60deg

Question 42

30 Name and use of ≅

Answer 42

congruent to
equivalence of geometric shapes and size

∆ABC≅ ∆XYZ

Question 43

31 Name and use of ~ (geometry)

Answer 43

Similarity
same shapes, not same size

∆ABC~ ∆XYZ

Question 44

32 Name and use of Δ

Answer 44

Triangle
triangle shape

ΔABC≅ ΔBCD

Question 45

33 Name and use of |x-y|

Answer 45

Distance
distance between points x and y

x-y | = 5

Question 46

34 Name and use of π

Answer 46

pi constant
π = 3.141592654…

c = π⋅d = 2⋅π⋅r

Question 47

35 Name and use of rad

Answer 47

Radians
radians angle unit

360° = 2π rad

Question 48

36 Name and use of c

Answer 48

Radians
radians angle unit

360° = 2π c

Question 49

37 Name and use of x

Answer 49

x variable
unknown value to find

when 2x = 4, then x = 2

Question 50

38 Name of ≡

Answer 50

Equivalence

identical to

Question 51

39 Use of ≜

Answer 51

equal by definition

Question 52

40 Name of:=

Answer 52

equal by definition

Python: walrus operator

Question 53

41 Name and use of ~

Answer 53

approximately equal

11 ~ 10

Question 54

42 Name and use of ≈

Answer 54

approximately equal
Approximation

sin(0.01) ≈ 0.01

Question 55

43 Name and use of ∝

Answer 55

proportional to

y ∝ x when y = kx, k constant

Question 56

44 Name of ∞

Answer 56

Lemniscate

infinity symbol

Question 57

45 Name and use of ≪

Answer 57

much less than

1 ≪ 1000000

Question 58

46 Name and use of ≫

Answer 58

much greater than

1000000 ≫ 1

Question 59

47 Name and use of {}

name: Braces
{1, 3, 4}

Answer 59

Braces
Python: use for sets

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

Question 60

47.1 What is a set?

Answer 60

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

Question 61

48 Name and use of ⌊x⌋

Answer 61

Floor brackets
rounds number to lower integer

⌊4.3⌋ = 4

Question 62

49 Name and use of ⌈x⌉

Answer 62

Ceiling brackets
rounds number to upper integer

⌈4.3⌉ = 5

Question 63

50 Name and use of x!

Answer 63

Exclamation mark
Factorial

4! = 123*4 = 24

Question 64

50.1 Code to get factorial :

enter a number to compute its factorial:4

Answer 64

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

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

print(factorial)

Question 65

51 Name and use of | x |

Answer 65

vertical bars
absolute value

-5 | = 5

Question 66

52 Name and use of f(x)

Answer 66

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

f (x) = 3x+5

Question 67

53 Name and use of (f ∘ g)

Answer 67

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

f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)

Question 68

54 Name and use of(a,b)

Answer 68

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

x∈ (2,6)

Question 69

55 Name and use of[a,b]

Answer 69

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

x ∈ [2,6]

Question 70

56 Name and use of ∆

Answer 70

Delta
change / difference

∆t = t1 - t0

Question 71

57 Name and use of ∑

Answer 71

Sigma
summation - sum of all values in range of series

∑ xi= x1+x2+…+xn

Question 72

58 Name and use of ∑∑

Answer 72

Sigma
double summation

∑+∑

Question 73

59 Name and use of ∏

Answer 73

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

∏ xi=x1∙x2∙…∙xn

Question 74

60 Name and use of e

Answer 74

Euler’s number
e = 2.718281828…

e = lim (1+1/x)x , x→∞

Question 75

61 Name of γ

Answer 75

Euler-Mascheroni constant

γ = 0.5772156649…

Question 76

62 Name and use of ·

Answer 76

Dot
scalar product

a · b

Question 77

63 Name and use of ×

Answer 77

Cross
vector product

a × b

Question 78

64 Name and use of ⊗

Answer 78

tensor product
tensor product of A and B
A ⊗ B

Question 79

65 Name and use in Maths and Python of [ ]

Answer 79

Brackets

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

Question 80

65 Name and use in Maths and Python of ( )

Answer 80

Parentheses

matrix of numbers

Question 81

66 Name of | A |

Answer 81

Determinant

Question 82

67 Name of det(A)

Answer 82

Determinant

determinant of matrix A

Question 83

68 Name of || x ||

Answer 83

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

Question 84

69 Name and use of A^T

Answer 84

Transpose
matrix transpose

(A^T)ij = (A)ji

Question 85

70 Name of A -1

Answer 85

inverse matrix

Question 86

71 Name and use of dim(U)

Answer 86

Dimension
dimension of matrix A
dim(U) = 3

Question 87

72 Name and use of P(A)

Answer 87

probability function
probability of event A

P(A) = 0.5

Question 88

73 Name and use of P(A ⋂ B)

Answer 88

probability of events intersection
probability that of events A and B

P(A⋂B) = 0.5

Question 89

74 Name and use of P(A ⋃ B)

Answer 89

probability of events union
probability that of events A or B

P(A⋃B) = 0.5

Question 90

75 Name of φ

Answer 90

golden ratio constant