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Math Fundamentals
Probability Basics
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Arithmetic & Modulo
0/41
Exponents & Roots
0/49
Logarithms
0/49
Basic Algebra
0/46
Sequences & Summations
0/41
Number Bases
0/41
Bit Manipulation
0/41
Boolean Logic
0/40
Sets
0/41
Counting Principles
0/43
Factorials & Permutations
0/45
Combinations
0/44
Probability Basics
0/62
1
Intro
2
Sample Space
3
Outcomes
4
Events
5
Probability Formula
6
Example - Rolling a Die
7
Probability Bounds
8
Complement Rule
9
Example - Complement
10
Union of Events
11
Addition Rule
12
Intersection of Events
13
Example - Union and Intersection
14
Mutually Exclusive Events
15
Example - Mutually Exclusive
16
Independent Events - Intro
17
Multiplication Rule
18
Example - Independent Events
19
Dependent Events - Intro
20
Conditional Probability
21
Example - Conditional Probability
22
General Multiplication Rule
23
Quiz: Basic Probability
24
Expected Value - Intro
25
Expected Value Formula
26
Example - Expected Die Roll
27
Expected Value - Unfair Outcomes
28
Applications in CS
29
Randomized Algorithms
30
Hash Collisions
31
Problem - Two Dice Sum
32
Two Dice - Sample Space
33
Two Dice - Event
34
Two Dice - Answer
35
Problem - Birthday Paradox
36
Birthday - Complement Approach
37
Birthday - Calculation
38
Birthday - Insight
39
Problem - Weighted Random
40
Weighted Random - Idea
41
Weighted Random - Prefix Sum
42
Weighted Random - Binary Search
43
Weighted Random - Implementation
44
Quiz: Independence and Expected Value
45
Practice Problems
46
Problem - Linked List Random Node
47
Linked List Random Node - Insight
48
Linked List Random Node - Implementation
49
Problem - Shuffle an Array
50
Shuffle - Fisher-Yates Algorithm
51
Shuffle - Implementation
52
Lessons from Shuffle
53
Problem - Random Pick with Weight
54
Weighted Pick - Prefix Sum
55
Weighted Pick - Binary Search
56
Weighted Pick - Implementation
57
Lessons from Weighted Pick
58
Problem - Random Pick Index
59
Pick Index - Reservoir Sampling
60
Pick Index - Implementation
61
Lessons from Pick Index
62
Section Recap
Divisibility & Primes
0/44
GCD & LCM
0/47
Modular Arithmetic
0/46
Big O Notation
0/49
Geometry Basics
0/45
13.1
Intro
2 minutes
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Tasks
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