What topics does this roadmap cover?

Arithmetic & Modulo, Exponents & Roots, Logarithms, Basic Algebra, Sequences & Summations, Number Bases, Bit Manipulation, Boolean Logic, Sets, Counting Principles, Factorials & Permutations, Combinations, Probability Basics, Divisibility & Primes, GCD & LCM, Modular Arithmetic, Big O Notation, Geometry Basics

How many units are in this roadmap?

This roadmap contains 814 units across 18 sections.

Is this roadmap free?

Yes, this roadmap is completely free.

Math Fundamentals - Roadmaps

Logarithms

800 → 1200

1200 → 1500

What logarithms are, key properties, common vs natural log, and why O(log n) appears everywhere in CS. The inverse of exponentiation.

Intro

The Goal

What Are Logarithms? (The inverse)

Undoing exponentiation

Logarithm Notation (Reading the symbols)

Base and argument explained

Quiz: Basic Logarithms (Knowledge check)

Test your understanding

Binary Logarithm (Base 2)

Most common in CS

Common Logarithm (Base 10)

Scientific notation base

Natural Logarithm (Base e)

Calculus and growth rates

Logarithm of 1 (Special case)

Any base equals zero

Logarithm of the Base (Another special case)

Always equals one

Product Rule (Multiplication becomes addition)

First logarithm property

Quotient Rule (Division becomes subtraction)

Second logarithm property

Power Rule (Exponent comes out front)

Third logarithm property

Quiz: Logarithm Properties (Knowledge check)

Test your understanding

Change of Base Formula (Converting bases)

Switch between any bases

Why Bases Don't Matter in Big-O (Constant factor)

All logarithms are equivalent

The Halving Pattern (Where log n comes from)

Divide and conquer

Binary Search Example (Classic log n algorithm)

Halving the search space

Tree Height Example (Another log n pattern)

Balanced binary trees

Quiz: Logarithmic Growth (Knowledge check)

Test your understanding

Problem - Power Function (Entry problem)

LeetCode 50

Power - The Insight (Squaring trick)

Halve the exponent

Power - Implementation (The code)

Recursive solution

Power - Complexity Analysis (Why it's logarithmic)

Time and space breakdown

Lessons from Power (Summary)

What you learned

Problem - Search Insert Position (Second problem)

LeetCode 35

Search Insert - The Insight (Binary search variant)

Find or insert position

Search Insert - Implementation (The code)

Binary search solution

Search Insert - Walkthrough (Tracing execution)

Step-by-step example

Lessons from Search Insert (Summary)

What you learned

Problem - Perfect Squares (Third problem)

LeetCode 279

Perfect Squares - The Insight (DP with square roots)

Building from smaller values

Perfect Squares - Implementation (The code)

DP solution

Perfect Squares - Logarithm Connection (Square roots and logs)

Why logs appear

Lessons from Perfect Squares (Summary)

What you learned

Logarithms in Merge Sort (Divide and conquer)

Tree height analysis

Logarithms in Quicksort (Average case)

Balanced partitions

Logarithms in Heaps (Insert and extract)

Heap operations

Quiz: Logarithms in Algorithms (Knowledge check)

Test your understanding

Problem - Find Kth Smallest (Fourth problem)

LeetCode 378

Kth Smallest - The Insight (Binary search on values)

Count elements below threshold

Kth Smallest - Implementation (The code)

Binary search solution

Lessons from Kth Smallest (Summary)

What you learned

Logarithms and Bit Manipulation (Powers of 2)

Binary representation

Logarithms and Number of Digits (Base 10)

Counting digits

Quiz: Logarithms and Numbers (Knowledge check)

Test your understanding

Logarithmic Growth vs Linear Growth (Scaling comparison)

Why log n is fast

Logarithmic Space Complexity (Recursion depth)

Call stack usage

Common Logarithm Mistakes (Pitfalls to avoid)

What to watch out for

Section Recap

What we learned

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