Learn all of maths, in order.
From counting to the open problems. Pick where you are; every lesson shows its steps, draws the picture, and hides the answer until you ask.
1749 lessons · 51769 practice problems · 26 stages
Or bring your own problem
Type it, or draw it with your mouse or finger. Equations, derivatives, matrices, triangles, primes, or a word problem the tutor breaks into parts.
What each stage covers
Each one is a set of lessons with a live worked example, a visual, and a solver tuned for it.
Stage 1 · school Arithmetic Numbers, fractions, percentages and the order of operations. Stage 2 · school Algebra Equations, inequalities, factoring, functions and systems. Stage 3 · school Geometry Triangles, circles, polygons, solids and coordinates. Stage 4 · school Trigonometry Angles, the unit circle, identities and trig equations. Stage 5 · school Precalculus Functions in depth, complex numbers, sequences, conics and vectors. Stage 6 · school Statistics & Probability Averages, spread, counting and probability. Stage 7 · school Discrete Math & Logic Counting, logic, truth tables, sets and proof. Stage 8 · college Calculus Limits, derivatives, integrals, series and optimisation. Stage 9 · college Linear Algebra Matrices, determinants, inverses, row reduction and eigenvalues. Stage 10 · college Number Theory Primes, divisibility, gcd, modular arithmetic and sequences. Stage 11 · college Differential Equations Equations whose unknown is a function: growth, oscillation, and how physics is written. Stage 12 · college Multivariable Calculus Partial derivatives, gradients, multiple integrals, vector fields. Stage 13 · college Real Analysis Limits made rigorous: sequences, series, convergence, improper integrals, complex numbers as functions. Stage 14 · college Combinatorics & Graph Theory Counting, generating functions, graphs, trees, colourings and networks. Stage 15 · college Set Theory & Logic Sets, relations, functions, cardinality, proof and the foundations of mathematics. Stage 16 · college Abstract Algebra Groups, rings, fields: symmetry made into structure. Stage 17 · college Probability Theory Random variables, distributions, expectation, limit theorems. Stage 18 · college Numerical Methods Root finding, approximation, numerical integration and error. Stage 19 · college Complex Analysis Holomorphic functions, contour integrals, residues, the rigidity of the complex plane. Stage 20 · graduate Topology Open sets, continuity, compactness, connectedness: geometry without distance. Stage 21 · graduate Measure Theory Lebesgue measure and integral, σ-algebras, convergence theorems. Stage 22 · graduate Functional Analysis Banach and Hilbert spaces, operators, spectral theory. Stage 23 · graduate Differential Geometry Curves, surfaces, curvature, manifolds: the language of general relativity. Stage 24 · graduate Algebraic Topology Fundamental groups, homology: counting holes with algebra. Stage 25 · graduate Category Theory Objects, arrows, functors, universal properties: mathematics about mathematics. Stage 30 · research Frontiers The open problems (Riemann, Navier-Stokes, P vs NP) broken into what you need to even read them.
How it works
1
Type it or draw it
“derivative of x² sin x”, “is 561 prime”, “triangle 3 4 5”, or sketch the equation on the pad and it is read for you.
2
Watch every move
One rule per step (the product rule, a row operation, a Euclid division) animated, and explained in a sentence.
3
See the shape of it
Curves with their roots marked, surfaces you can rotate, triangles drawn to scale, factor trees, matrices as vectors in space.
4
The impossible ones too
A word problem, a proof, an open question: the tutor breaks it into parts you can attack, tells you what is known, and hides the solution until you want it.