Vital articles is a list of subjects for which Wikipedia should have corresponding high-quality articles. It serves as a centralized watchlist to track the status of Wikipedia's most essential articles. This is one of the sub-lists of the fifty thousand article Vital articles/Level 5 and is currently under construction.
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Total articles: 1,129/1,100
- See also: People: Mathematicians
Basics (114 articles)
- Mathematics (Level 1)
- Arithmetic (Level 2)
- Number (Level 2)
- Positional notation (Level 4)
- Scientific notation (Level 4)
Functions (88 articles)
General (41 articles)
- Function (Level 3)
- Algebraic function
- Function of a real variable
- Arithmetic function
- Inverse function (Level 4)
- Implicit function (Level 4)
- Function composition (Level 4)
- Graph of a function (Level 4)
- Parametric equation (Level 4)
- Even and odd functions
- Piecewise
- Bijection, injection and surjection
- Domain of a function
- Range of a function
- Zero of a function
- Fixed point
- Critical point
- Limit of a function (Level 4)
- Multivalued function
- Partial function
- Reflection
- Rotation
- Scaling
- Bounded function
- Vector-valued function
- Real-valued function
- Analytic function
- Elliptic function
- Periodic function
- Curvature
Specific functions (47 articles)
- Elementary function
- Rational function
- Exponentiation (Level 3)
- Logarithm (Level 3)
- nth root (Level 3)
- Trigonometric functions (Level 4)
- Hyperbolic functions (Level 4)
- Bessel function
- Floor and ceiling functions
- Gamma function (Level 4)
- Prime-counting function
- Weierstrass function
- Error function
- Step function
- Dirac delta function
- Kronecker delta
- Absolute value
- Lambert W function
- Exponential integral
Geometry (139 articles)
General (14 articles)
- Geometry (Level 2)
- Coordinate system (Level 4)
- Dimension (Level 4)
- Zero-dimensional space
- One-dimensional space
- Congruence (geometry)
- Similarity
Two-dimensional space (40 articles)
- Two-dimensional Euclidean space (Level 4)
- Plane (Level 4)
- Angle (Level 3)
- Polygon (Level 3)
- Conic section (Level 3)
- Cardioid
- Cycloid
- Lemniscate
- Elliptic curve
- Catenary
- Parallel
- Perpendicular
- Line–line intersection
Three-dimensional space (22 articles)
- Three-dimensional space (Level 3)
- Solid geometry
- Cone
- Cylinder
- Sphere (Level 4)
- Polyhedron (Level 4)
- Solid angle
- Skew lines
Four-dimensional space (8 articles)
- Four-dimensional space
- Rotations in 4-dimensional Euclidean space
- 5-cell
- Tesseract
- 16-cell
- 24-cell
- 120-cell
- 600-cell
Trigonometry (4 articles)
Topology (12 articles)
- Topology (Level 3)
- General topology (Level 4)
- Topological space (Level 4)
- Compact space (Level 4)
- Manifold (Level 4)
- Open set (Level 4)
- Homology (Level 4)
- Homotopy (Level 4)
- Euler characteristic (Level 4)
- Knot theory (Level 4)
- Poincaré conjecture (Level 4)
- Winding number
Measurement (8 articles)
Euclidean geometry (5 articles)
Non-Euclidean geometry (6 articles)
Other (20 articles)
Algebra (74 articles)
General (2 articles)
Elementary algebra (5 articles)
Linear algebra (24 articles)
- Linear algebra (Level 3)
- Linear map
- Linear equation (Level 4)
- System of linear equations
- Gaussian elimination (Level 4)
- Jacobi method
- Gauss–Seidel method
- Cramer's rule
- Successive over-relaxation
- LU decomposition
- Matrix (Level 4)
- Vector space (Level 4)
Abstract algebra (31 articles)
- Abstract algebra (Level 3)
- Algebraic topology (Level 4)
- Associative property (Level 4)
- Commutative algebra (Level 4)
- Commutative property (Level 4)
- Distributive property (Level 4)
- Field (Level 4)
- Fundamental theorem of algebra (Level 4)
- Galois theory (Level 4)
- Group (Level 4)
- Homological algebra (Level 4)
- Isomorphism (Level 4)
- Module (Level 4)
- Multiplicative inverse
- Representation theory (Level 4)
- Ring theory (Level 4)
Other algebra topics (12 articles)
Statistics and probability (85 articles)
Statistics (48 articles)
- Statistics (Level 2)
- Bayesian inference (Level 4)
- Bayesian statistics
- Confidence interval
- Correlation (Level 4)
- Data and information visualization (Level 4)
- Design of experiments (Level 4)
- Frequentist statistics
- Mean (Level 4)
- Maximum likelihood estimation
- Median (Level 4)
- Meta-analysis (Level 4)
- Mode (Level 4)
- Observational study (Level 4)
- Principal component analysis
- Sample mean and covariance (Level 4)
- Standard deviation (Level 4)
- Standard error (Level 4)
- Statistical hypothesis testing (Level 4)
- Survey methodology (Level 4)
- Type I and type II errors
- Analysis of variance
Probability (37 articles)
- Probability (Level 3)
- Probability theory (Level 4)
- Probability space
- Bayes' theorem (Level 4)
- Central limit theorem (Level 4)
- Covariance
- Law of large numbers (Level 4)
- Moment
- Probability distribution (Level 4)
- Random variable (Level 4)
- Stochastic process (Level 4)
- Monty Hall problem
Foundations (161 articles)
Mathematical logic (32 articles)
- Mathematical logic (Level 4)
- Propositional calculus (Level 4)
- First-order logic (Level 4)
- Higher-order logic
- Intuitionistic logic
- Type theory
Set theory (36 articles)
Axiomatic systems (19 articles)
- Axiomatic system
- Zermelo–Fraenkel set theory
- Axiom of choice (Level 4)
- New Foundations
- Peano axioms
- Hilbert's axioms
- Tarski's axioms
Computability theory (26 articles)
- Computability theory (Level 4)
- Model of computation
- Computable function (Level 4)
- Decision problem
- Oracle machine
Model theory (19 articles)
Category theory (28 articles)
Discrete mathematics (140 articles)
Combinatorics (24 articles)
- Combinatorics (Level 3)
- Combinatorial principles
- Double counting (proof technique)
- Method of distinguished element
- Twelvefold way
- Latin square
Graph theory (89 articles)
- Graph theory (Level 4)
- Clique (graph theory)
- Connectivity (graph theory)
- Flow network
- Graph homomorphism
- Matching (graph theory)
- Edge cover
- Path (graph theory)
- Planar graph
- Snark (graph theory)
- Spectral graph theory
Order theory (26 articles)
Calculus and analysis (178 articles)
Basics (11 articles)
- Calculus (Level 3)
- Limit (Level 3)
- Fundamental theorem of calculus (Level 4)
- Continuous function (Level 4)
- Infinitesimal
- Series expansion
- Linear approximation
Differential calculus (13 articles)
- Differential calculus (Level 4)
- Differentiable function
- Differential operator
- Derivative (Level 4)
- Differentiation rules
- L'Hôpital's rule
- Taylor's theorem
- Related rates
Integral calculus (11 articles)
- Integral (Level 4)
- Antiderivative
- Lebesgue integration
- Numerical integration (Level 4)
- Riemann integral
- Constant of integration
- Improper integral
- Integration by parts
- Integration by substitution
- Limits of integration
- Riemann sum
Multivariable and vector calculus (29 articles)
- Multivariable calculus (Level 4)
- Vector calculus (Level 4)
- Multiple integral (Level 4)
- Iterated integral
- Partial derivative (Level 4)
- Total derivative
- Directional derivative
- Differential form
- Vector field
- Del (Level 4)
- Poisson's equation
- Line integral
- Surface integral
- Volume integral
- Stokes' theorem
- Jacobian matrix and determinant
- Lagrange multiplier
- Helmholtz decomposition
Differential equations (44 articles)
- Differential equation (Level 4)
- Boundary value problem
- Separation of variables
- Integrating factor
- Power series solution of differential equations
- Change of variables
- Numerical methods for ordinary differential equations
- Numerical methods for partial differential equations
- Dirichlet problem
- Elliptic operator
- System of differential equations
Dynamical systems (20 articles)
- Dynamical systems theory (Level 4)
- Dynamical system (Level 4)
- Phase space
- Stability theory
- Control theory (Level 4)
- Chaos theory (Level 4)
- Multibody system
- Initial condition
- Conserved quantity
- Dynamic simulation
- Flow
- Lyapunov exponent
- Attractor
Sequences and series (18 articles)
- Sequence (Level 4)
- Series (Level 3)
- Taylor series (Level 4)
- Laurent series
- Convergent series
- Divergent series
- Geometric series
- Power series
- Dirichlet series
- Binomial series
- Harmonic series
- Multipole expansion
Mathematical analysis (52 articles)
- Mathematical analysis (Level 3)
- Approximation theory (Level 4)
- Numerical analysis (Level 4)
- Functional analysis (Level 4)
- Measure
- Calculus of variations (Level 4)
- Asymptotic analysis
- Interpolation
Real analysis (12 articles)
- Real analysis (Level 4)
- Real line
- Extreme value theorem
- Intermediate value theorem
- Mean value theorem
- Squeeze theorem
Complex analysis (20 articles)
- Complex analysis (Level 4)
- Complex plane
- Contour integration
- Euler's formula (Level 4)
- Euler's identity (Level 4)
- Holomorphic function (Level 4)
- Riemann surface (Level 4)
- Liouville's theorem
- Cauchy–Riemann equations
- Cauchy principal value
- Conformal map
- Singularity
- Picard theorem
- Residue
- Branch point
- Root of unity
Harmonic analysis (10 articles)
Number theory (50 articles)
Prime numbers (12 articles)
- Prime number (Level 3)
- Primality test
- Coprime integers
- Euclid's theorem (Level 4)
- Prime number theorem (Level 4)
Sums and products (8 articles)
Modular arithmetic (8 articles)
- Chinese remainder theorem
- Discrete logarithm
- Fermat's little theorem
- Quadratic residue
- Wilson's theorem
Sequences (8 articles)
Diophantine equations (6 articles)
Subdisciplines (7 articles)
Applied mathematics (37 articles)
Game theory (17 articles)
Information theory (7 articles)
Optimization (13 articles)
Theoretical computer science (63 articles)
For topics in applied computer science, see Technology: Computing and information technology
Algorithms (23 articles)
- Algorithm (Level 3)
Automata theory (3 articles)
Complexity theory (17 articles)
Data structures and types (16 articles)