Mathematics Portal
1How to Use This Portal
This portal is the top-level guide from mathematics lectures to portals for individual fields. The top-level math/_order.json specifies the display order for field navigation, not a recommended learning order. Each field portal and that field's _order.json govern its recommended internal order, while each lecture's prerequisites govern dependencies both within and across fields. The sections below follow learning stages and therefore differ from the top-level display order.
2Main Path through High-School Foundations
Use algebra as the foundation for computation and symbolic manipulation, then proceed to coordinate geometry, trigonometric functions, vectors, and sequences. Discrete mathematics organizes logic, sets, and maps. Probability, statistics, and number theory each begin at their field portal. Because trigonometry has no separate portal, its two lectures appear in their _order.json order.
3Representative High-School Lectures
These examples help select an entry point. For continued study, proceed to the corresponding field portal.
data/lecture/math/algebra/polynomials.lecture.n.md data/lecture/math/geometry/coordinate-geometry-basics.lecture.n.md data/lecture/math/vector/introduction-to-vectors.lecture.n.md data/lecture/math/sequence/arithmetic-and-geometric-sequences.lecture.n.md data/lecture/math/probability/counting-permutations-and-combinations.lecture.n.md4Connections to First-Year University Mathematics
Linear algebra and calculus form the core. Linear operators develop linear algebra from the perspective of equations and transformations. Multivariable calculus and ordinary differential equations follow single-variable calculus.
data/lecture/math/linear-algebra/linear-algebra-portal.lecture.n.md data/lecture/math/linear-operator/linear-operators-portal.lecture.n.md data/lecture/math/calculus/calculus-portal.lecture.n.md data/lecture/math/multivariable-calculus/multivariable-calculus-portal.lecture.n.md data/lecture/math/differential-equations/differential-equations-portal.lecture.n.md5Advanced Fields
From first-year foundations, proceed to vector calculus, partial differential equations, exterior algebra and differential forms, abstract algebra, and analysis. Consult each lecture's prerequisites before beginning.