Kọ́ gbogbo àwọn mátírika, ní àtòjọ.

Àwọn àwọn ààyè-iṣẹ́ àti àwọn ààyè-iṣẹ́ àwọn ààyè-iṣẹ́. Yan ibi tí o tì wa; àkọlé gbogbó ní pàtó àwọn ààyè-iṣẹ́ rẹ, àwọn àwòrán, àti àwọn à

1765 Àwọn ìwé-ìwé · 51769 Àwọn àwọn àkóónú ìṣàmúlò-ètò · 28 Àwọn ìpele

Àwọn Àkọ́lé Ìṣàmúlò-ètò àwọn ààyè-iṣẹ́

Àwọn Àkọ́lé Calculus onward: awọn irinṣẹ ẹrọ ti o n ṣiṣẹ fun awọn onimọ-iṣe.

Àwọn ìṣàmúlò-ètò Nínú àwọn ààyè náà tí wọ́n di àwọn àkókò, àti àwọn àkọsílẹ̀.

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

30 Frontiers 24 Àwọn ìwé-ìwé

Àwòrán

Ṣàfihàn rẹ̀, tàbí wọ́n lè kọ̀ọ̀kan nípa àwọn àmì-ìwé rẹ̀. Àwọn ìṣàmúlò-ètò, àwọn à

Ṣí ojú-ìwé ìṣàfarawé àwọn àwọn ìṣàmúlò-ètò →

Àwọn àwọn

Àwọn àkọlé nínú àkọlé gbogbó nínú àwọn àkọlé
Àkọ́lé àwọn àkọ́lé tí o tí parí, àti ààyè-iṣẹ́ tí a fẹ́
Every problem you solve, kept in one place
Pánẹ́ẹ̀lì alákọ́kọ́ nínú àwọn ìwé-ìwé fún àwọn ààyè àwọn ìtàn
Fi àwọn àkọlé pamọ́ sí àwọn ààyè-iṣẹ́

Àwọn ìwé-ìwé, àwọn ààtò àti àwọn ìṣàmúlò-ètò tí a lò tí a kò bá kọ̀ǹpútà.

Fikún Wó àkọlé àwòrán

Àwọn àwọn ìṣàmúlò-ètò tí a lò

Gbogbo wọn ní àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò tí a tí n ṣiṣẹ́ nípa àwọn ààyè, àwọn àwòrán, àti àwọn ìṣàmúlò-ètò tí a tí n ṣẹ́.

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

Bii o ṣe n ṣiṣẹ

1

Fihàn àwọn àmì-ìwé àti àwọn àmì-ìwé àwọn àmì-ìwé

“derivative of x² sin x”, “is 561 prime”, “triangle 3 4 5” — tabi kọ̀ọ̀kan àwọn ìṣàmúlò-ètò lórí àwọn paadi náà láti kọ̀ọ̀kan lọ́wọ́lọ́wọ́.

2

Wó àwọn ìjánu-ìjánù àwọn ìjánu-ìjánù

Ìṣẹ́ kan ni gbogbo igbese—ìṣẹ́ kan ni gbogbo ohun, iṣẹ́ oruka kan, ìpapọ̀ Euclid—tí a fi hàn, tí a si fi sọ nínú ọrọ̀ kan.

3

Wó àwọn ìṣàmúlò-ètò rẹ̀

Àwọn kúrùù láti ní àwọn àyọkà àwọn ẹ̀yìn wọn, àwọn ojú-ìwé tí o lè yí, àwọn àwọn ààyè-ìwé tí a kọ̀ ní pàtó, àwọn ẹ̀yàn àwọn fákìtó, àwọn mátirísì bí àwọn bétórí nínú àwọn ààyè-ìwé.

4

Àwọn tí kò lè jẹ́

Àwọn àwọn ààyè-iṣẹ́ àwọn à