User:Mgkrupa/Articles

ML, Data Science
Probability Theory


 * Cumulative distribution function
 * Random variable

Stats


 * Bias–variance tradeoff
 * Pearson correlation coefficient

Statistical Learning


 * Statistical learning theory
 * Vapnik–Chervonenkis theory

Words/Terminology
Useful terminology or words with special symbols


 * Fréchet
 * Kuratowski closure axioms has useful terminology.


 * : Category:en:Mathematics and Glossary of areas of mathematics
 * : Thesaurus:Mathematics


 * Figure of merit
 * A facultative point is a point at which a given function is positive.
 * Proof by intimidation


 * Mathematical analysis
 * Functional analysis
 * Linear algebra and Glossary of linear algebra
 * Complex analysis
 * Calculus
 * Measure theory


 * Probability theory and Probability and Glossary of probability and statistics
 * Statistics
 * Combinatorics


 * Geometry
 * Differential geometry
 * Non-Euclidean geometry
 * Shapes


 * Topology and Glossary of topology
 * Set theory and Glossary of set theory
 * Category theory
 * Glossary of order theory
 * Graph theory


 * Algebra and Glossary of abstract algebra
 * Algebraic geometry
 * Group theory and Glossary of group theory
 * Ring theory
 * Number theory
 * Arithmetic

Math articles
Algebra, Number theory/systems

Algebra/Number theory/Number systems


 * Chebyshev polynomials
 * Grothendieck group
 * Legendre polynomials
 * Representation theory
 * Group representation
 * Tensor product

(Non-)Elementary functions


 * Elementary function
 * Liouvillian function
 * Liouvillian function
 * Liouvillian function

Number theory and number systems


 * Hyperreal number
 * Quaternion
 * Quaternionic analysis
 * Gamma function

$\pi$ and related


 * Turn (angle)


 * Tau manifesto
 * Tau Before It Was Cool

Polynomials

Roots of polynomials

Polynomial Root Finding


 * Root-finding algorithm
 * See also lists some algorithms for finding roots.
 * Splitting circle method - "uses FFT-based polynomial transformations to find large-degree factors corresponding to clusters of roots. The precision of the factorization is maximized using a Newton-type iteration. This method is useful for finding the roots of polynomials of high degree to arbitrary precision; it has almost optimal complexity in this setting."
 * Laguerre's method - Known for almost always converging to some root.
 * Jenkins–Traub algorithm - Frequently used, globally convergent algorithm.
 * Graeffe's method

Root Counting and Bounds on Location of Roots


 * Real-root isolation
 * Sturm's theorem - Gives a computable algorithm for the exact number of roots between two reals.
 * Descartes' rule of signs - Gives a computable algorithm for incomplete information about the number of positive and negative roots. Sturm's theorem's generalizes this.
 * Rouché's theorem - Bounds on roots in the complex plane.
 * Other Bounds
 * Bound based on Samuelson's inequality - For polynomials whose roots are all real.

Polynomial Root Properties
 * Properties of polynomial roots
 * Vieta's formulas - Relates coefficients to sums and products of roots.
 * Rational root theorem - Theoretically important for rational roots of polynomials with integer coefficients.
 * Gauss–Lucas theorem - Roots of a polynomial's derivative lie within the convex hull of the polynomial's roots.
 * Newton's identities

Category theory

Category theory


 * Adjoint functors
 * Forgetful functor
 * Natural transformation
 * Universal property


 * Outline of category theory

Set theory/Foundations

Set theory/Foundations


 * Cantor's first set theory article

Misc math

Misc math


 * List of unsolved problems in mathematics
 * User:Charles Matthews/New - mathematics

Geometry, Topology, Functional
Functional analysis

Functional analysis


 * Differential calculus over commutative algebras


 * List of functional analysis topics
 * L-semi-inner product - Every normed space is an L-semi-inner product space.
 * Kolmogorov–Arnold representation theorem

Topology

Point-set topology


 * Totally disconnected space

Theorems


 * Alexander subbase theorem
 * Krylov–Bogolyubov theorem

Example spaces


 * Knaster–Kuratowski fan
 * Particular point topology

Uniform spaces


 * Uniform space
 * Uniform spaces at wikibooks

Geometry

Geometry


 * Angle
 * Brunn–Minkowski theorem
 * Projective geometry


 * Jacobi identity
 * Adjoint representation
 * Lie group


 * Differential form
 * Exterior derivative
 * Interior product
 * Stokes' theorem
 * De Rham cohomology
 * Exterior algebra


 * Vector bundle
 * Jet bundle
 * Fiber bundle


 * Diffiety
 * Secondary calculus and cohomological physics
 * Differential calculus over commutative algebras


 * Volume of an n-ball - Nice intuitive explanation of why surface area is the derivative of volume: "The $(n + 1)$-ball is a union of concentric spheres, and consequently the surface area and the volume are related by: $$A_n(R) = \frac{d}{dR}V_{n+1}(R)$$."

Applied
Quantum mechanics

Quantum mechanics


 * Boson
 * Event (particle physics)
 * Mathematical formulation of quantum mechanics
 * Quantum state
 * Quantum field theory
 * Topological quantum field theory
 * Quantum gravity

Table taken from: Visible spectrum. See also: Color vision.

Physics

Physics related/Relativity


 * Angular momentum
 * Torque
 * Entropy
 * Renormalization
 * Renormalization group

Relativity/Black holes


 * Gravitational singularity
 * Naked singularity - Singularity not hidden by an event horizon
 * Ring singularity - Inside a spinning black hole
 * Rapidity − "used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates."

Astronomy


 * Comoving and proper distances

Misc
Biology

Biology


 * Calcium carbonate
 * Evolutionary history of life
 * Harlequin-type ichthyosis

Geology

Geology


 * Geological period

Geography


 * Template:Clickable world map

Misc


 * Affirming the consequent - AKA converse error, fallacy of the converse, or confusion of necessity and sufficiency
 * List of common misconceptions
 * List of natural disasters by death_toll