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mathematicskit.abstract_algebra
Group actions
Error-correcting codes
Finite fields
Groups
Homomorphisms
Polynomial ring arithmetic
Group structure
Subgroups and cosets
mathematicskit.calculus
Reverse-mode autodiff
Dual numbers
Method of exhaustion
Finite differences
Newton and Leibniz
Quadrature
Taylor series
mathematicskit.combinatorics
Counting
Combinatorial designs
Extremal combinatorics
Inclusion-exclusion
Matchings
Necklaces
Integer partitions
Pascal’s triangle
Integer sequences
Special numbers
Labeled trees
mathematicskit.fractals_chaos
Box-counting dimension
Cellular automata
Fractal curves
Aggregation
Iterated function systems
Lindenmayer systems
Lyapunov exponents
Mandelbrot and Julia sets
Discrete maps
mathematicskit.geometry
Bézier curves
Convex hull
Curves and the Frenet-Serret frame
Distances between shapes
Enclosing circles
Point-in-polygon
Polygon area
Polyhedra
Proximity
Line simplification
Surfaces
Voronoi diagrams and Delaunay triangulation
mathematicskit.graph_theory
Assignment
Graph coloring
Connected components
Eulerian paths
Extremal graph theory
Hamiltonian cycles
Bipartite matching
Maximum flow
Ranking
Heuristic search
Shortest paths
Minimum spanning tree
Spectral graph theory
mathematicskit.linalg
Cholesky decomposition
Classical matrix theory
Eigenvalue algorithms
Iterative solvers
LU decomposition
QR decomposition
Numerical stability
Singular value decomposition
mathematicskit.number_theory
Continued fractions
Chinese Remainder Theorem
Diophantine equations
Integer factorization
Modular arithmetic
Primality
Distribution of primes
Quadratic residues
Sums of squares
Multiplicative functions
The zeta function
mathematicskit.numerical_analysis
Function approximation
Runge’s phenomenon and Chebyshev nodes
Floating-point arithmetic
Interpolation
Polynomials
Least-squares regression
Root finding
Cubic splines
mathematicskit.ode_dynamics
Bifurcation normal forms
Chaotic flows
Epidemic models
Excitable systems
Limit cycles
The logistic map
Phase portraits
Poincare sections
Population models
Fixed-point stability
Synchronization
mathematicskit.optimization
Nonlinear conjugate gradient
Constrained optimization
Direct search
Dynamic programming
Game theory
Gradient descent
Nonlinear least squares
Linear programming
Momentum methods
Newton’s method and BFGS
One-dimensional search
Stochastic approximation
Benchmark functions
mathematicskit.probability
Kolmogorov’s axioms
Bayesian inference
Branching processes
Classical problems
Continuous distributions
Discrete distributions
Limit theorems and inequalities
Markov chains
Monte Carlo integration
Queueing theory
Random walks and Brownian motion
mathematicskit.special_functions
Airy functions
Bessel functions
Elliptic functions
Error function and Fresnel integrals
Discrete Fourier transform
Gamma and beta functions
Hypergeometric functions
Lambert W function
Mathieu functions
Orthogonal polynomials
Riemann zeta function
mathematicskit.statistics
Bootstrap resampling
Confidence intervals
Correlation
Descriptive statistics
Hypothesis tests
Likelihood
Multiple testing
Nonparametric tests
Linear regression
Shrinkage estimation
Examples
Examples
Shrinkage estimation
Shrinkage estimation
#
The James-Stein estimator and Stein’s paradox.
Stein’s paradox
Stein's paradox
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