Curriculum graph

Learning paths

Choose a coherent route through connected ideas. Paths branch where understanding does.

Mathematics · Algebra

Algebra Foundations

Build symbolic fluency, equations, graphs, functions, polynomials, and the notation used in higher mathematics.

10 articles
OrientationFoundationsCore ConceptsMethodsApplications
  1. 1Algebraic Expressions Preserve Structure
  2. 2Linear Equations Express Balance
  3. 3Graphs Turn Relationships into Geometry
  4. 4Functions Organize Input and Output

Mathematics · Calculus

Calculus Foundations

Build the language of change and accumulation from functions through integration.

5 articles
OrientationFoundationsCore Concepts
  1. 1Functions: Machines, Maps, and Relationships
  2. 2Why Limits Matter
  3. 3Continuity: When Nearby Inputs Stay Nearby
  4. 4Derivatives Measure Local Change

Mathematics · Statistics

Curve Fitting Foundations

Move from fitting a model to diagnosing error and solving nonlinear estimation problems.

11 articles
OrientationFoundationsCore ConceptsMethodsApplications
  1. 1Curve Fitting: From Data to Model
  2. 2Least Squares Finds the Closest Model
  3. 3Residual Plots Reveal How a Model Fails
  4. 4RMSE Expresses Typical Error in Response Units

Mathematics · Differential Equations

Ordinary Differential Equations

Understand evolving systems, solve foundational equations, then study oscillation and coupled dynamics.

14 articles
OrientationFoundationsCore ConceptsMethodsApplications
  1. 1Ordinary Differential Equations Describe Evolving Systems
  2. 2First-Order ODEs Model Growth, Decay, and Balance
  3. 3Second-Order ODEs Govern Oscillation and Motion
  4. 4Systems of ODEs Track Interacting Quantities

Physics · Mechanics

Mechanics Foundations

Connect position, velocity, force, and energy into a coherent account of motion.

3 articles
OrientationFoundationsCore Concepts
  1. 1Velocity Is Change with Direction
  2. 2Newton’s Second Law Connects Force to Motion
  3. 3Energy Is Nature’s Accounting System