Learn Number Theory
Properties of integers, primes, and modular arithmetic. A free, structured curriculum: 5 units · 20 lessons · self-paced.
Curriculum outline
Unit 1: Theory of Number Theory
Lesson 1.1: What Is Number Theory: Definitions and Scope
Lesson 1.2: Foundational Principles and Axioms
Lesson 1.3: Key Theorems and Laws
Lesson 1.4: How the Theory Was Developed
Unit 2: Core Methods and Approaches
Lesson 2.1: Standard Methods and When to Use Them
Lesson 2.2: Step-by-Step Problem-Solving Process
Lesson 2.3: Tools and Notation
Lesson 2.4: Choosing the Right Approach
Unit 3: Guided Practice
Lesson 3.1: Worked Examples: Simple Problems
Lesson 3.2: Worked Examples: Moderate Complexity
Lesson 3.3: Independent Practice Set
Lesson 3.4: Checking Your Work and Self-Assessment
Unit 4: Advanced Methods
Lesson 4.1: Advanced Techniques and Shortcuts
Lesson 4.2: Multi-Step and Compound Problems
Lesson 4.3: Proof-Based and Analytical Thinking
Lesson 4.4: Connecting Methods Across Topics
Unit 5: Applied Number Theory
Lesson 5.1: Number Theory in Real-World Contexts
Lesson 5.2: Modeling and Estimation
Lesson 5.3: Data Interpretation and Analysis
Lesson 5.4: Cross-Disciplinary Applications
Sample lesson preview
What Is Number Theory: Definitions and Scope
Understand what Number Theory is and why it matters.
Number Theory is best understood through its purpose: what problem does it solve, or what need does it address? Rather than starting with a textbook definition, think about when and why people encounter Number Theory in real life. Understanding the "why" first makes the technical details much easier to grasp. The simplest test of understanding: can you explain it in one sentence to someone who's never heard of it?