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.

1765 lessons · 51769 practice problems · 28 stages

School Counting to precalculus: the path everyone walks.

  1. 1 Arithmetic 62 lessons
  2. 2 Algebra 190 lessons
  3. 3 Geometry 60 lessons
  4. 4 Trigonometry 48 lessons
  5. 5 Precalculus 83 lessons
  6. 6 Statistics & Probability 59 lessons
  7. 7 Discrete Math & Logic 68 lessons

University Calculus onward: the working mathematician's toolkit.

  1. 8 Calculus 133 lessons
  2. 9 Linear Algebra 85 lessons
  3. 10 Number Theory 57 lessons
  4. 11 Differential Equations 47 lessons
  5. 12 Multivariable Calculus 107 lessons
  6. 13 Real Analysis 43 lessons
  7. 14 Combinatorics & Graph Theory 166 lessons
  8. 15 Set Theory & Logic 70 lessons
  9. 16 Abstract Algebra 126 lessons
  10. 17 Probability Theory 48 lessons
  11. 18 Numerical Methods 34 lessons
  12. 19 Complex Analysis 32 lessons

Graduate Where the subjects become abstract, and connected.

  1. 20 Topology 39 lessons
  2. 21 Measure Theory 27 lessons
  3. 22 Functional Analysis 32 lessons
  4. 23 Differential Geometry 32 lessons
  5. 24 Algebraic Topology 26 lessons
  6. 25 Category Theory 26 lessons
  7. 26 Partial Differential Equations 19 lessons
  8. 27 Fluid Dynamics 22 lessons

Research The open problems, broken into what you need to read them.

  1. 30 Frontiers 24 lessons

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.

Open the full solver page →

What a free account adds: your workbook

  • Notes on every lesson, saved as you type
  • A record of the lessons you have finished, and where to pick up
  • Every problem you solve, kept in one place
  • A tutor panel on each lesson for questions about that page
  • Posting and replying on the help board

Every lesson, worked example and the solver stay open without an account.

Sign Up See the workbook

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 26 · graduate Partial Differential Equations Heat, waves, potentials and transport: Fourier methods, energy estimates, Sobolev spaces and scaling. Stage 27 · graduate Fluid Dynamics Continuity, vorticity, the Euler and Navier-Stokes equations, and what is proved about them. 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.