User:Mgkrupa/Articles

Elementary function
Nonelementary integral – Integrals not expressible in closed-form from elementary functions
Liouville's theorem (differential algebra) – Says when antiderivatives of elementary functions can be expressed as elementary functions
Liouvillian function
Richardson's theorem – Undecidability of equality of real numbers
Tarski's high school algebra problem – Mathematical problem

Number theory and number systems

π

and related

Turn (angle)

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

Outline of category theory

Set theory/Foundations

Set theory/Foundations

Cantor's first set theory article

Misc math

Misc math

Geometry, Topology, Functional edit

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

Example spaces

Uniform spaces

Geometry

Geometry

Jacobi identity
- Adjoint representation
- Lie group#Representations

Differential form

Volume of an n-ball#Relation with surface area - 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 edit

Quantum mechanics

Quantum mechanics

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

sRGB rendering of the spectrum of visible light
Color	Wavelength	Frequency	Photon energy
Violet	380–450 nm	680–790 THz	2.95–3.10 eV
Blue	450–485 nm	620–680 THz	2.64–2.75 eV
Cyan	485–500 nm	600–620 THz	2.48–2.52 eV
Green	500–565 nm	530–600 THz	2.25–2.34 eV
Yellow	565–590 nm	510–530 THz	2.10–2.17 eV
Orange	590–625 nm	480–510 THz	2.00–2.10 eV
Red	625–740 nm	405–480 THz	1.65–2.00 eV

Physics

Physics related/Relativity

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 edit

Biology

Biology

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#Ten deadliest pandemics / epidemics