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Never end, continue writing infinitely. https://twitter.com/burny_tech/status/1768461544801616019 Gigantic map of as much of applied mathematics as possible Algebra - Linear algebra - Matrices and matrix operations - Eigenvalues and eigenvectors - Vector spaces - Linear transformations - Abstract algebra - Group theory - Ring theory - Field theory - Galois theory - Boolean algebra - Algebraic geometry - Algebraic topology Analysis - Real analysis - Limits and continuity - Differentiation - Integration - Measure theory - Complex analysis - Complex numbers - Analytic functions - Cauchy's theorem - Residue theorem - Functional analysis - Banach spaces - Hilbert spaces - Operator theory - Harmonic analysis - Fourier analysis - Wavelet analysis Geometry and Topology - Euclidean geometry - Non-Euclidean geometry - Hyperbolic geometry - Elliptic geometry - Differential geometry - Manifolds - Riemannian geometry - Lie groups - Algebraic topology - Homotopy theory - Homology and cohomology - Knot theory - 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Graph theory - Planar graphs - Coloring problems - Network flows - Random graphs - Ramsey theory - Coding theory Optimization - Linear programming - Integer programming - Nonlinear programming - Convex optimization - Stochastic optimization - Optimal control theory - Game theory Dynamical Systems and Chaos Theory - Discrete dynamical systems - Continuous dynamical systems - Bifurcation theory - Chaos theory - Ergodic theory - Fractals Mathematical Physics - Classical mechanics - Quantum mechanics - Relativity theory - Statistical mechanics - Thermodynamics - Fluid dynamics - Electromagnetism - Quantum field theory Financial Mathematics - Stochastic calculus - Option pricing theory - Portfolio optimization - Risk management - Interest rate modeling - Credit risk modeling - Algorithmic trading Cryptography and Coding Theory - Public-key cryptography - Symmetric-key cryptography - Cryptanalysis - Error-correcting codes - Data compression - Information theory Computational Biology and Bioinformatics - 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20th-century mathematics - Contemporary mathematics - Foundations of mathematics - Mathematical logic Mathematics Education - Curriculum development - Instructional design - Assessment and evaluation - Technology in mathematics education - Cognitive science of mathematics learning - Equity and diversity in mathematics education - Teacher education and professional development Algebra - Linear algebra - Matrices and matrix operations - Matrix addition and subtraction - Matrix multiplication - Matrix inversion - Determinants - Rank and nullity - Eigenvalues and eigenvectors - Characteristic polynomial - Diagonalization - Spectral theorem - Singular value decomposition - Vector spaces - Subspaces - Basis and dimension - Inner product spaces - Orthogonality - Linear transformations - Kernel and image - Isomorphisms - Change of basis - Matrix representation - Abstract algebra - Group theory - Subgroups - Cosets and Lagrange's theorem - Normal subgroups - Quotient groups - Homomorphisms and isomorphisms - 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Poisson distribution - Gaussian (normal) distribution - Exponential and gamma distributions - Beta and Dirichlet distributions - Stochastic processes - Markov chains - Transition matrices - Stationary distributions - Ergodicity - Hidden Markov models - Poisson processes - Brownian motion - Martingales - Stochastic calculus - Mathematical statistics - Estimation theory - Point estimation - Interval estimation - Maximum likelihood estimation - Method of moments - Bayesian estimation - Hypothesis testing - Null and alternative hypotheses - Type I and Type II errors - p-values and significance levels - Likelihood ratio tests - Bayesian hypothesis testing - Regression analysis - Linear regression - Logistic regression - Polynomial regression - Nonparametric regression - Generalized linear models - Bayesian inference - Prior and posterior distributions - Bayes' theorem - Conjugate priors - Markov chain Monte Carlo (MCMC) methods - Variational inference - Stochastic calculus - Stochastic integrals - Itô calculus - Stratonovich calculus - Stochastic differential equations - Feynman-Kac formula - Girsanov's theorem - Machine learning - Supervised learning - Classification - Regression - Support vector machines - Decision trees and random forests - Neural networks - Unsupervised learning - Clustering - Dimensionality reduction - Principal component analysis - Independent component analysis - Autoencoders - Reinforcement learning - Markov decision processes - Q-learning - Policy gradients - Actor-critic methods - Deep reinforcement learning - Deep learning - Convolutional neural networks - Recurrent neural networks - Long short-term memory (LSTM) - Generative adversarial networks (GANs) - Transfer learning Differential Equations - Ordinary differential equations (ODEs) - First-order ODEs - Separable equations - Linear equations - Exact equations - Bernoulli equations - Riccati equations - Second-order ODEs - Homogeneous equations - Nonhomogeneous equations - Variation of parameters - Cauchy-Euler equations - Legendre equations - Systems of ODEs - Linear systems - Nonlinear systems - Phase plane analysis - Linearization and stability - Stability theory - Equilibrium points - Lyapunov stability - Asymptotic stability - Lyapunov functions - Poincaré-Bendixson theorem - Partial differential equations (PDEs) - Elliptic PDEs - Laplace's equation - Poisson's equation - Harmonic functions - Green's functions - Variational methods - Parabolic PDEs - Heat equation - Diffusion equation - Reaction-diffusion equations - Maximum principles - Fundamental solutions - Hyperbolic PDEs - Wave equation - Transport equation - Conservation laws - Characteristics - Shock waves - Numerical methods for PDEs - Finite difference methods - Finite element methods - Spectral methods - Boundary element methods - Multigrid methods - Stochastic differential equations - Itô diffusions - Stratonovich diffusions - Fokker-Planck equation - Kolmogorov equations - Feynman-Kac formula - Integral equations - Fredholm equations - Volterra equations - Singular integral equations - Wiener-Hopf equations - Nonlinear integral equations Numerical Analysis - Numerical linear algebra - Matrix factorizations (LU, QR, SVD) - Iterative methods (Jacobi, Gauss-Seidel, SOR) - Eigenvalue problems - Least squares problems - Sparse matrix methods - Numerical optimization - Unconstrained optimization - Constrained optimization - Linear programming - Quadratic programming - Nonlinear programming - Numerical integration - Newton-Cotes formulas - Gaussian quadrature - Romberg integration - Adaptive quadrature - Multidimensional integration - Finite difference methods - Explicit and implicit methods - Stability and convergence - Upwind and central differencing - Crank-Nicolson method - Alternating direction implicit (ADI) methods - Finite element methods - Weak formulation - Galerkin method - Triangular and quadrilateral elements - Isoparametric elements - Adaptive mesh refinement - Spectral methods - Fourier spectral methods - Chebyshev spectral methods - Legendre spectral methods - Spectral element methods - Pseudospectral methods - Monte Carlo methods - Random number generation - Importance sampling - Markov chain Monte Carlo (MCMC) - Quasi-Monte Carlo methods - Multilevel Monte Carlo methods Combinatorics and Graph Theory - Enumerative combinatorics - Permutations and combinations - Generating functions - Recurrence relations - Inclusion-exclusion principle - Polya enumeration theorem - Algebraic combinatorics - Symmetric functions - Young tableaux - Schur functions - Representation theory of the symmetric group - Macdonald polynomials - Extremal combinatorics - Ramsey theory - Turán's theorem - Szemerédi's theorem - Erdős-Ko-Rado theorem - Combinatorial nullstellensatz - Graph theory - Planar graphs - Euler's formula - Kuratowski's theorem - Graph minors - Planar separator theorem - Coloring problems - Chromatic number - Chromatic polynomial - Brooks' theorem - Hadwiger's conjecture - Network flows - Max-flow min-cut theorem - Ford-Fulkerson algorithm - Edmonds-Karp algorithm - Dinic's algorithm - Push-relabel algorithm - Random graphs - Erdős-Rényi model - Preferential attachment model - Small-world networks - Percolation theory - Threshold phenomena - Ramsey theory - Ramsey's theorem - Van der Waerden's theorem - Hales-Jewett theorem - Graham-Rothschild theorem - Shelah's theorem - Coding theory - Linear codes - Cyclic codes - BCH codes - Reed-Solomon codes - Convolutional codes - Turbo codes - Low-density parity-check (LDPC) codes