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1765 lekcije · 51769 vježbajte probleme · 28 stadija

Škola Counting to precalculus: the path everyone walks.

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

Univerzitet Calculus onward: the working mathematician's toolkit.

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

Diplomirao Gdje su subjekti postali apstraktni i povezani.

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

Istraživanje Otvoreni problemi, razbijeni na ono što trebate da ih pročitate.

  1. 30 Frontiers 24 lekcije

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Šta svaki stadij pokriva

Svaki od njih je skup lekcija sa živim rađenim primjerom, vizualnim i rješavačem podešenim za to.

Faza 1 · school Arithmetic Numbers, fractions, percentages and the order of operations. Faza 2 · school Algebra Equations, inequalities, factoring, functions and systems. Faza 3 · school Geometry Triangles, circles, polygons, solids and coordinates. Faza 4 · school Trigonometry Angles, the unit circle, identities and trig equations. Faza 5 · school Precalculus Functions in depth, complex numbers, sequences, conics and vectors. Faza 6 · school Statistics & Probability Averages, spread, counting and probability. Faza 7 · school Discrete Math & Logic Counting, logic, truth tables, sets and proof. Faza 8 · college Calculus Limits, derivatives, integrals, series and optimisation. Faza 9 · college Linear Algebra Matrices, determinants, inverses, row reduction and eigenvalues. Faza 10 · college Number Theory Primes, divisibility, gcd, modular arithmetic and sequences. Faza 11 · college Differential Equations Equations whose unknown is a function: growth, oscillation, and how physics is written. Faza 12 · college Multivariable Calculus Partial derivatives, gradients, multiple integrals, vector fields. Faza 13 · college Real Analysis Limits made rigorous: sequences, series, convergence, improper integrals, complex numbers as functions. Faza 14 · college Combinatorics & Graph Theory Counting, generating functions, graphs, trees, colourings and networks. Faza 15 · college Set Theory & Logic Sets, relations, functions, cardinality, proof and the foundations of mathematics. Faza 16 · college Abstract Algebra Groups, rings, fields: symmetry made into structure. Faza 17 · college Probability Theory Random variables, distributions, expectation, limit theorems. Faza 18 · college Numerical Methods Root finding, approximation, numerical integration and error. Faza 19 · college Complex Analysis Holomorphic functions, contour integrals, residues, the rigidity of the complex plane. Faza 20 · graduate Topology Open sets, continuity, compactness, connectedness: geometry without distance. Faza 21 · graduate Measure Theory Lebesgue measure and integral, σ-algebras, convergence theorems. Faza 22 · graduate Functional Analysis Banach and Hilbert spaces, operators, spectral theory. Faza 23 · graduate Differential Geometry Curves, surfaces, curvature, manifolds: the language of general relativity. Faza 24 · graduate Algebraic Topology Fundamental groups, homology: counting holes with algebra. Faza 25 · graduate Category Theory Objects, arrows, functors, universal properties: mathematics about mathematics. Faza 26 · graduate Partial Differential Equations Heat, waves, potentials and transport: Fourier methods, energy estimates, Sobolev spaces and scaling. Faza 27 · graduate Fluid Dynamics Continuity, vorticity, the Euler and Navier-Stokes equations, and what is proved about them. Faza 30 · research Frontiers The open problems (Riemann, Navier-Stokes, P vs NP) broken into what you need to even read them.

Kako to funkcioniše

1

Napiši ili nacrtaj.

"derivacija x² sin x", "je 561 prost broj", "trokuta 3 4 5" - ili skiciraj jednačinu na papiru i ona će ti se pročitati.

2

Gledaj svaki potez

Jedno pravilo po koraku (pravilo proizvoda, operacija reda, Euklidova podjela) animirano, i objašnjeno u rečenici.

3

Vidiš li oblik?

Krivulje sa označenim korijenom, površine koje se mogu rotirati, trouglovi nacrtani u mjerilu, stabla faktora, matrice kao vektori u prostoru.

4

I nemoguce.

Problem sa riječima, dokaz, otvoreno pitanje: tutor ga razbija na dijelove koje možete napadati, kaže vam što je poznato i skriva rješenje dok ga ne želite.