Week 1: Data Science Math Skills

What is Set?

Cardinality

Intersections

Unions

Medical Testing Example (test and cardinality)

Venn Diagrams

Inclusion-Exclusion Formula

Set

Cardinality

Intersections

A ∩ C = ∅ (∅, is known as the empty set)

Unions

Medical Testing Example

S ∩ H = ∅ (No one person is both S and H)
S ∪ H = X ( either person have VBS or not)
P ∩ N = ∅ (No one tests is both P and N)
P ∪ N = X (Either test is P or N)
|S|
─── = proportion of people who have VBS
|X|
|H|
─── = proportion of people who do not have VBS
|X|
|S∩P|
───── = true positive rate
|X|
|H∩N|
───── = true negative rate
|X|
|H∩P|
───── = false positive rate
|X|
|S∩N|
───── = false negative rate
|X|

Venn Diagrams

Fig 1.1 Single Set
Fig 1.2 Multiple Sets

Inclusion-Exclusion Formula

|A ⋃ B| = |A| + |B|- |A ∩ B|
|A ⋃ B| = 8, {1,9,6,3,4,8} |A| = 5, {1,9,6,5,7}|B| = 5, {3,4,8,5,7}|A ∩ B| = 2, {5,7}|A ⋃ B| = |A| + |B|- |A ∩ B|8 = 5 + 5–28 = 10 -28 = 8

Real Numbers : Integers and rational numbers

Absolute value

Intervals and Interval Notation

Fig 2.1 : Real Numbers

Absolute Value

|x| = x, if x is non-negative|x| = -x, if x is negative

Inequalities

a < b “ a is less than b”a > b “a is greater than b”a ≤ b “a is less than or equal to b”a ≥ b “a is greater than or equal to b”a << b “a is much much lesser than b”

Closed intervals

Open intervals

Half-open intervals

Sigma Notation

Distributive and Commutative property

Summation of constants

Mean and Variance

Sigma Notation

i is just an “dummy indices”, that is used as a counter.

Distributive Property

Commutative Property

Summation of constants

Mean and Variance

The mean μz is also denoted by μ(z)
Formula for calculating mean
Formula for calculating variance

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Programming , Ethical Hacking and Cyber Security

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Nishant Tiwari

Nishant Tiwari

Programming , Ethical Hacking and Cyber Security

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