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Math Fundamentals
Logarithms
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Arithmetic & Modulo
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Exponents & Roots
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Logarithms
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1
Intro
2
What Are Logarithms? (The inverse)
3
Logarithm Notation (Reading the symbols)
4
Quiz: Basic Logarithms (Knowledge check)
5
Binary Logarithm (Base 2)
6
Common Logarithm (Base 10)
7
Natural Logarithm (Base e)
8
Logarithm of 1 (Special case)
9
Logarithm of the Base (Another special case)
10
Product Rule (Multiplication becomes addition)
11
Quotient Rule (Division becomes subtraction)
12
Power Rule (Exponent comes out front)
13
Quiz: Logarithm Properties (Knowledge check)
14
Change of Base Formula (Converting bases)
15
Why Bases Don't Matter in Big-O (Constant factor)
16
The Halving Pattern (Where log n comes from)
17
Binary Search Example (Classic log n algorithm)
18
Tree Height Example (Another log n pattern)
19
Quiz: Logarithmic Growth (Knowledge check)
20
Problem - Power Function (Entry problem)
21
Power - The Insight (Squaring trick)
22
Power - Implementation (The code)
23
Power - Complexity Analysis (Why it's logarithmic)
24
Lessons from Power (Summary)
25
Problem - Search Insert Position (Second problem)
26
Search Insert - The Insight (Binary search variant)
27
Search Insert - Implementation (The code)
28
Search Insert - Walkthrough (Tracing execution)
29
Lessons from Search Insert (Summary)
30
Problem - Perfect Squares (Third problem)
31
Perfect Squares - The Insight (DP with square roots)
32
Perfect Squares - Implementation (The code)
33
Perfect Squares - Logarithm Connection (Square roots and logs)
34
Lessons from Perfect Squares (Summary)
35
Logarithms in Merge Sort (Divide and conquer)
36
Logarithms in Quicksort (Average case)
37
Logarithms in Heaps (Insert and extract)
38
Quiz: Logarithms in Algorithms (Knowledge check)
39
Problem - Find Kth Smallest (Fourth problem)
40
Kth Smallest - The Insight (Binary search on values)
41
Kth Smallest - Implementation (The code)
42
Lessons from Kth Smallest (Summary)
43
Logarithms and Bit Manipulation (Powers of 2)
44
Logarithms and Number of Digits (Base 10)
45
Quiz: Logarithms and Numbers (Knowledge check)
46
Logarithmic Growth vs Linear Growth (Scaling comparison)
47
Logarithmic Space Complexity (Recursion depth)
48
Common Logarithm Mistakes (Pitfalls to avoid)
49
Section Recap
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
Divisibility & Primes
0/44
GCD & LCM
0/47
Modular Arithmetic
0/46
Big O Notation
0/49
Geometry Basics
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3.1
Intro
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