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 {} #Outcome: 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! = 1*2*3*4 = 24

Question 64

#50.1 Code to get factorial : enter a number to compute its factorial:4 #Outcome: 24

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