Mathematical structures, reasoning, modeling, and quantitative methods.
Guided learning
Build a connected foundation from functions and vectors to calculus, differential equations, transformations, and continuous probability models.
Mathematics · foundation
Concept library
Describing points in Cartesian space and deriving distances and angles from coordinates.
Accumulated signed quantity over an interval represented by a limiting sum.
Local rate of change represented as the limit of secant slopes and geometrically as tangent slope where differentiable.
Equations relating an unknown function to its first derivative and therefore to a local rate of change.
Rules that assign an output to each allowed input and can be represented symbolically, numerically, and graphically.
Structure-preserving mappings of vectors represented by matrices, including area scaling and orientation behavior.
Continuous probability models represented by nonnegative normalized density functions.
Second-degree polynomial functions and the linked meaning of coefficients, roots, discriminant, and vertex.
Quantities represented by components with magnitude and direction and combined through vector operations.