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Mathematics
From counting to topology — arithmetic, algebra, geometry, calculus, and the higher mathematics that follows. Written with worked examples, not definitions alone.
14 stages across 6 groups — topics in the same stage can be studied in any order.
Foundations of Numbers
The bedrock. Every equation starts here.
1.1
Numbers & Arithmetic5 subtopics
Stage 1Written1.2Fractions, Decimals & Percentages5 subtopicsAfter Numbers & Arithmetic
Stage 2Coming soon1.3Factors, Multiples & Divisibility5 subtopicsAfter Numbers & Arithmetic
Stage 2Coming soon1.4Exponents & Roots4 subtopicsAfter Numbers & Arithmetic · Factors, Multiples & Divisibility
Stage 3Coming soonAlgebra
Where numbers become variables and patterns become equations.
2.1
Introduction to Algebra4 subtopicsAfter Fractions, Decimals & Percentages
Stage 4Coming soon2.2Equations & Inequalities5 subtopicsAfter Introduction to Algebra
Stage 5Coming soon2.3Functions & Graphs5 subtopicsAfter Equations & Inequalities
Stage 6Coming soon2.4Polynomials5 subtopicsAfter Exponents & Roots · Introduction to Algebra
Stage 6Coming soon2.5Quadratics6 subtopicsAfter Polynomials · Equations & Inequalities
Stage 7Coming soon2.6Rational & Radical Expressions4 subtopicsAfter Polynomials · Exponents & Roots
Stage 7Coming soonGeometry
The study of shape, space, and the rules that govern them.
3.1
Plane Geometry6 subtopicsAfter Fractions, Decimals & Percentages
Stage 4Coming soon3.2Area, Perimeter & Volume5 subtopicsAfter Plane Geometry
Stage 5Coming soon3.3Congruence & Similarity4 subtopicsAfter Plane Geometry
Stage 5Coming soon3.4Transformations4 subtopicsAfter Plane Geometry
Stage 6Coming soon3.5Coordinate Geometry6 subtopicsAfter Functions & Graphs · Plane Geometry
Stage 7Coming soon3.6Vectors6 subtopicsAfter Coordinate Geometry
Stage 8WrittenHigher Mathematics
Where structure, abstraction, and beauty converge.
6.1
Set Theory5 subtopics
Stage 4Coming soon6.2Number Theory6 subtopicsAfter Factors, Multiples & Divisibility
Stage 5Coming soon6.4Combinatorics & Probability8 subtopicsAfter Fractions, Decimals & Percentages
Stage 6Coming soon6.5Statistics6 subtopicsAfter Combinatorics & Probability · Fractions, Decimals & Percentages
Stage 7Coming soon6.3Linear Algebra6 subtopicsAfter Vectors & Matrices · Equations & Inequalities
Stage 10Coming soon6.6Algebraic Geometry & Implicit Surfaces8 subtopicsAfter Polynomials · Linear Algebra
Stage 12Coming soon6.7Topology7 subtopicsAfter Set Theory · Linear Algebra
Stage 13Coming soonTrigonometry & Precalculus
The bridge between algebra and the mathematics of change.
4.1
Trigonometry7 subtopicsAfter Coordinate Geometry · Congruence & Similarity
Stage 8Coming soon4.2Complex Numbers5 subtopicsAfter Quadratics · Exponents & Roots
Stage 8Coming soon4.3Exponential & Logarithmic Functions6 subtopicsAfter Exponents & Roots · Functions & Graphs
Stage 8Coming soon4.4Sequences & Series5 subtopicsAfter Exponential & Logarithmic Functions · Functions & Graphs
Stage 9Coming soon4.5Conic Sections5 subtopicsAfter Coordinate Geometry · Quadratics
Stage 9Coming soon4.6Vectors & Matrices6 subtopicsAfter Trigonometry · Coordinate Geometry +1
Stage 9Coming soonCalculus
The mathematics of continuous change and accumulation.
5.1
Limits & Continuity6 subtopicsAfter Functions & Graphs · Sequences & Series
Stage 10Coming soon5.2Differential Calculus6 subtopicsAfter Limits & Continuity
Stage 11Coming soon5.3Applications of Derivatives6 subtopicsAfter Differential Calculus
Stage 12Coming soon5.4Integral Calculus6 subtopicsAfter Differential Calculus
Stage 12Coming soon5.5Applications of Integrals4 subtopicsAfter Integral Calculus
Stage 13Coming soon5.6Sequences, Series & Convergence5 subtopicsAfter Sequences & Series · Integral Calculus
Stage 13Coming soon5.7Multivariable Calculus6 subtopicsAfter Applications of Derivatives · Applications of Integrals +1
Stage 14Coming soon5.8Differential Equations4 subtopicsAfter Integral Calculus · Sequences, Series & Convergence
Stage 14Coming soon