User:Y-S.Ko/Wikipedia course/Mathematics

Mathematics

Outline of mathematics

v t e Major mathematics areas
History Timeline Future Lists Glossary
Foundations	Category theory Information theory Mathematical logic Philosophy of mathematics Set theory Type theory
Algebra	Abstract Commutative Elementary Group theory Linear Multilinear Universal Homological
Analysis	Calculus Real analysis Complex analysis Hypercomplex analysis Differential equations Functional analysis Harmonic analysis Measure theory
Discrete	Combinatorics Graph theory Order theory
Geometry	Algebraic Analytic Arithmetic Differential Discrete Euclidean Finite
Number theory	Arithmetic Algebraic number theory Analytic number theory Diophantine geometry
Topology	General Algebraic Differential Geometric Homotopy theory
Applied	Engineering mathematics Mathematical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Probability Statistics Systems science Control theory Game theory Operations research
Computational	Computer science Theory of computation Computational complexity theory Numerical analysis Optimization Computer algebra
Related topics	Mathematicians lists Informal mathematics Films about mathematicians Recreational mathematics Mathematics and art Mathematics education
Mathematics portal Category Commons WikiProject

Common mathematical notation, symbols, and formulas

Lists of Unicode and LaTeX mathematical symbols
List of mathematical symbols by subject Glossary of mathematical symbols List of logic symbols

Lists of Unicode symbols

General	List of Unicode characters Unicode block
Alphanumeric	Mathematical Alphanumeric Symbols Blackboard bold Letterlike Symbols Symbols for zero
Arrows and Geometric Shapes	Arrows Miscellaneous Symbols and Arrows Geometric Shapes (Unicode block)
Operators	Mathematical operators and symbols Mathematical Operators (Unicode block)
Supplemental Math Operators	Supplemental Mathematical Operators Number Forms
Miscellaneous	A B Technical ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)

Typographical conventions and notations

Language	APL syntax and symbols
Letters	Diacritic Letters in STEM Greek letters in STEM Latin letters in STEM
Notation	Mathematical notation Abbreviations Notation in probability and statistics List of common physics notations

Meanings of symbols
Glossary of mathematical symbols List of mathematical constants Physical constants Table of mathematical symbols by introduction date List of typographical symbols and punctuation marks

Mathematics

Mathematics-related lists

History

edit

v t e Archimedes
Written works	Measurement of a Circle The Sand Reckoner On the Equilibrium of Planes Quadrature of the Parabola On the Sphere and Cylinder On Spirals On Conoids and Spheroids On Floating Bodies Ostomachion The Method of Mechanical Theorems Book of Lemmas (apocryphal)
Discoveries and inventions	Archimedean solid Archimedes's cattle problem Archimedes' principle Archimedes's screw Claw of Archimedes
Miscellaneous	Archimedes' heat ray Archimedes Palimpsest List of things named after Archimedes Pseudo-Archimedes
Related people	Euclid Eudoxus of Cnidus Apollonius of Perga Hero of Alexandria Eutocius of Ascalon
Category

v t e Pierre de Fermat
Work	Fermat's Last Theorem Fermat number Fermat's principle Fermat's little theorem Fermat polygonal number theorem Fermat pseudoprime Fermat point Fermat's theorem (stationary points) Fermat's theorem on sums of two squares Fermat's spiral Fermat's right triangle theorem
Related	List of things named after Pierre de Fermat Wiles's proof of Fermat's Last Theorem Fermat's Last Theorem in fiction Fermat Prize Fermat's Last Tango (2000 musical) Fermat's Last Theorem (popular science book)

Leonhard Euler

Category

v t e Carl Friedrich Gauss
Gauss composition law Gauss map Gauss notation Gauss's method Gaussian brackets Gaussian curvature Gaussian period Gaussian surface Gaussian units Gauss's law for gravity Gauss's law Gauss's law for magnetism
Category

Abel Prize laureates

- 2003 Jean-Pierre Serre
- 2004 Michael Atiyah
- Isadore Singer
- 2005 Peter Lax
- 2006 Lennart Carleson
- 2007 S. R. Srinivasa Varadhan
- 2008 John G. Thompson
- Jacques Tits
- 2009 Mikhail Gromov
- 2010 John Tate
- 2011 John Milnor
- 2012 Endre Szemerédi
- 2013 Pierre Deligne
- 2014 Yakov Sinai
- 2015 John Forbes Nash Jr.
- Louis Nirenberg
- 2016 Andrew Wiles
- 2017 Yves Meyer
- 2018 Robert Langlands
- 2019 Karen Uhlenbeck
- 2020 Hillel Furstenberg
- Grigory Margulis
- 2021 László Lovász
- Avi Wigderson
- 2022 Dennis Sullivan
- 2023 Luis Caffarelli
- 2024 Michel Talagrand

Fields Medalists

- 1936 Ahlfors
- Douglas
- 1950 Schwartz
- Selberg
- 1954 Kodaira
- Serre
- 1958 Roth
- Thom
- 1962 Hörmander
- Milnor
- 1966 Atiyah
- Cohen
- Grothendieck
- Smale
- 1970 Baker
- Hironaka
- Novikov
- Thompson
- 1974 Bombieri
- Mumford
- 1978 Deligne
- Fefferman
- Margulis
- Quillen
- 1982 Connes
- Thurston
- Yau
- 1986 Donaldson
- Faltings
- Freedman
- 1990 Drinfeld
- Jones
- Mori
- Witten
- 1994 Bourgain
- Lions
- Yoccoz
- Zelmanov
- 1998 Borcherds
- Gowers
- Kontsevich
- McMullen
- 2002 Lafforgue
- Voevodsky
- 2006 Okounkov
- Perelman
- Tao
- Werner
- 2010 Lindenstrauss
- Ngô
- Smirnov
- Villani
- 2014 Avila
- Bhargava
- Hairer
- Mirzakhani
- 2018 Birkar
- Figalli
- Scholze
- Venkatesh
- 2022 Duminil-Copin
- Huh
- Maynard
- Viazovska

Guy Medallists

Gold Medallists

Silver Medallists

John Glover (1893)
Augustus Sauerbeck (1894)
A. L. Bowley (1895)
F. J. Atkinson (1897)
C. S. Loch (1899)
Richard Crawford (1900)
Thomas A. Welton (1901)
R. H. Hooker (1902)
Yves Guyot (1903)
D. A. Thomas (1904)
R. H. Rew (1905)
W. H. Shaw (1906)
N. A. Humphreys (1907)
Edward Brabrook (1909)
G. H. Wood (1910)
R. Dudfield (1913)
S. Rowson (1914)
S. J. Chapman (1915)
J. S. Nicholson (1918)
J. C. Stamp (1919)
A. William Flux (1921)
H. W. Macrosty (1927)
Ethel Newbold (1928)
H. E. Soper (1930)
J. H. Jones (1934)
Ernest Charles Snow (1935)
R. G. Hawtrey (1936)
E. C. Ramsbottom (1938)
L. Isserlis (1939)
H. Leak (1940)
M. G. Kendall (1945)
Harry Campion (1950)
F. A. A. Menzler (1951)
M. S. Bartlett (1952)
J. O. Irwin (1953)
L. H. C. Tippett (1954)
D. G. Kendall (1955)
Henry Daniels (1957)
G. A. Barnard (1958)
E. C. Fieller (1960)
D. R. Cox (1961)
P. V. Sukhatme (1962)
George E. P. Box (1964)
C. R. Rao (1965)
Peter Whittle (1966)
Dennis Lindley (1968)
Robin Plackett (1973)
James Durbin (1976)
John Nelder (1977)
Peter Armitage (1978)
Michael Healy (1979)
M. Stone (1980)
John Kingman (1981)
Henry Wynn (1982)
Julian Besag (1983)
J. C. Gittins (1984)
A. Bissell (1985)
W. Pridmore (1985)
Richard Peto (1986)
John Copas (1987)
John Aitchison (1988)
F. P. Kelly (1989)
David Clayton (1990)
R. L. Smith (1991)
Robert Nicholas Curnow (1992)
A. F. M. Smith (1993)
David Spiegelhalter (1994)
B. W. Silverman (1995)
Steffen Lauritzen (1996)
Peter Diggle (1997)
Harvey Goldstein (1998)
Peter Green (1999)
Walter Gilks (2000)
Philip Dawid (2001)
David Hand (2002)
Kanti Mardia (2003)
Peter Donnelly (2004)
Peter McCullagh (2005)
Michael Titterington (2006)
Howell Tong (2007)
Gareth Roberts (2008)
Sylvia Richardson (2009)
Iain M. Johnstone (2010)
P. G. Hall (2011)
David Firth (2012)
Brian Ripley (2013)
Jianqing Fan (2014)
Anthony Davison (2015)
Nancy Reid (2016)
Neil Shephard (2017)
Peter Bühlmann (2018)
Susan Murphy (2019)
Arnaud Doucet (2020)
Håvard Rue (2021)
Paul Fearnhead (2022)

Bronze Medallists

v t e Kenneth O. May Prize laureates
Dirk Jan Struik and Adolph P. Yushkevich (1989) Christoph Scriba and Hans Wussing (1993) René Taton (1997) Ubiratàn D'Ambrosio and Lam Lay Yong (2001) Henk J. M. Bos (2005) Ivor Grattan-Guinness and Radha Charan Gupta (2009) Menso Folkerts and Jens Høyrup (2013) Eberhard Knobloch and Roshdi Rashed (2017)

v t e Awards of the London Mathematical Society
Anne Bennett Prize Berwick Prize De Morgan Medal Fröhlich Prize Hirst Prize and Lectureship Louis Bachelier Prize Naylor Prize and Lectureship Pólya Prize Senior Berwick Prize Senior Whitehead Prize Shephard Prize Whitehead Prize

v t e Nevanlinna Prize winners
1980s-1999	Tarjan (1982) Valiant (1986) Razborov (1990) Wigderson (1994) Shor (1998)
2000s-2019	Sudan (2002) Kleinberg (2006) Spielman (2010) Khot (2014) Daskalakis (2018)
2020s-present	Braverman (2022)

v t e Rolf Schock Prize laureates
Logic and philosophy	Willard Van Orman Quine (1993) Michael Dummett (1995) Dana Scott (1997) John Rawls (1999) Saul Kripke (2001) Solomon Feferman (2003) Jaakko Hintikka (2005) Thomas Nagel (2008) Hilary Putnam (2011) Derek Parfit (2014) Ruth Millikan (2017) Saharon Shelah (2018) Dag Prawitz / Per Martin-Löf (2020) David Kaplan (2022)
Mathematics	Elias M. Stein (1993) Andrew Wiles (1995) Mikio Sato (1997) Yuri I. Manin (1999) Elliott H. Lieb (2001) Richard P. Stanley (2003) Luis Caffarelli (2005) Endre Szemerédi (2008) Michael Aschbacher (2011) Yitang Zhang (2014) Richard Schoen (2017) Ronald Coifman (2018) Nikolai G. Makarov (2020) Jonathan Pila (2022)
Visual arts	Rafael Moneo (1993) Claes Oldenburg (1995) Torsten Andersson (1997) Herzog & de Meuron (1999) Giuseppe Penone (2001) Susan Rothenberg (2003) SANAA / Kazuyo Sejima + Ryue Nishizawa (2005) Mona Hatoum (2008) Marlene Dumas (2011) Anne Lacaton / Jean-Philippe Vassal (2014) Doris Salcedo (2017) Andrea Branzi (2018) Francis Alÿs (2020) Rem Koolhaas (2022)
Musical arts	Ingvar Lidholm (1993) György Ligeti (1995) Jorma Panula (1997) Kronos Quartet (1999) Kaija Saariaho (2001) Anne Sofie von Otter (2003) Mauricio Kagel (2005) Gidon Kremer (2008) Andrew Manze (2011) Herbert Blomstedt (2014) Wayne Shorter (2017) Barbara Hannigan (2018) György Kurtág (2020) Víkingur Ólafsson (2022)

Recipients of the Oswald Veblen Prize in Geometry

1964 Christos Papakyriakopoulos
1964 Raoul Bott
1966 Stephen Smale
1966 Morton Brown and Barry Mazur
1971 Robion Kirby
1971 Dennis Sullivan
1976 William Thurston
1976 James Harris Simons
1981 Mikhail Gromov
1981 Shing-Tung Yau
1986 Michael Freedman
1991 Andrew Casson and Clifford Taubes
1996 Richard S. Hamilton and Gang Tian
2001 Jeff Cheeger, Yakov Eliashberg and Michael J. Hopkins
2004 David Gabai
2007 Peter Kronheimer and Tomasz Mrowka; Peter Ozsváth and Zoltán Szabó
2010 Tobias Colding and William Minicozzi; Paul Seidel
2013 Ian Agol and Daniel Wise
2016 Fernando Codá Marques and André Neves
2019 Xiuxiong Chen, Simon Donaldson and Song Sun

v t e Laureates of the Wolf Prize in Mathematics
1970s	Israel Gelfand / Carl L. Siegel (1978) Jean Leray / André Weil (1979)
1980s	Henri Cartan / Andrey Kolmogorov (1980) Lars Ahlfors / Oscar Zariski (1981) Hassler Whitney / Mark Krein (1982) Shiing-Shen Chern / Paul Erdős (1983/84) Kunihiko Kodaira / Hans Lewy (1984/85) Samuel Eilenberg / Atle Selberg (1986) Kiyosi Itô / Peter Lax (1987) Friedrich Hirzebruch / Lars Hörmander (1988) Alberto Calderón / John Milnor (1989)
1990s	Ennio De Giorgi / Ilya Piatetski-Shapiro (1990) Lennart Carleson / John G. Thompson (1992) Mikhail Gromov / Jacques Tits (1993) Jürgen Moser (1994/95) Robert Langlands / Andrew Wiles (1995/96) Joseph Keller / Yakov G. Sinai (1996/97) László Lovász / Elias M. Stein (1999)
2000s	Raoul Bott / Jean-Pierre Serre (2000) Vladimir Arnold / Saharon Shelah (2001) Mikio Sato / John Tate (2002/03) Grigory Margulis / Sergei Novikov (2005) Stephen Smale / Hillel Furstenberg (2006/07) Pierre Deligne / Phillip A. Griffiths / David B. Mumford (2008)
2010s	Dennis Sullivan / Shing-Tung Yau (2010) Michael Aschbacher / Luis Caffarelli (2012) George Mostow / Michael Artin (2013) Peter Sarnak (2014) James G. Arthur (2015) Richard Schoen / Charles Fefferman (2017) Alexander Beilinson / Vladimir Drinfeld (2018) Jean-François Le Gall / Gregory Lawler (2019)
2020s	Simon K. Donaldson / Yakov Eliashberg (2020) George Lusztig (2022) Ingrid Daubechies (2023)
Mathematics portal

Philosophy of Mathematics

edit

v t e Metalogic and metamathematics
Cantor's theorem Entscheidungsproblem Church–Turing thesis Consistency Effective method Foundations of mathematics of geometry Gödel's completeness theorem Gödel's incompleteness theorems Soundness Completeness Decidability Interpretation Löwenheim–Skolem theorem Metatheorem Satisfiability Independence Type–token distinction Use–mention distinction

Mathematical logic

General

Theorems (list)
and paradoxes

Gödel's completeness and incompleteness theorems
Tarski's undefinability
Banach–Tarski paradox
Cantor's theorem, paradox and diagonal argument
Compactness
Halting problem
Lindström's
Löwenheim–Skolem
Russell's paradox

Logics

Traditional	Classical logic Logical truth Tautology Proposition Inference Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram
Propositional	Boolean algebra Boolean functions Logical connectives Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞
Predicate	First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus

Set theory

Set hereditary Class (Ur-)Element Ordinal number Extensionality Forcing Relation equivalence partition Set operations: intersection union complement Cartesian product power set identities
Types of sets	Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe constructible Grothendieck Von Neumann
Maps and cardinality	Function/Map domain codomain image In/Sur/Bi-jection Schröder–Bernstein theorem Isomorphism Gödel numbering Enumeration Large cardinal inaccessible Aleph number Operation binary
Set theories	Zermelo–Fraenkel axiom of choice continuum hypothesis General Kripke–Platek Morse–Kelley Naive New Foundations Tarski–Grothendieck Von Neumann–Bernays–Gödel Ackermann Constructive

Formal systems (list),
language and syntax

Alphabet
Arity
Automata
Axiom schema
Expression
- ground
Extension
- by definition
- conservative
Relation
Formation rule
Grammar
Formula
- atomic
- closed
- ground
- open
Free/bound variable
Language
Metalanguage
Logical connective
- ¬
- ∨
- ∧
- →
- ↔
- =
Predicate
- functional
- variable
- propositional variable
Proof
Quantifier
- ∃
- !
- ∀
- rank
Sentence
- atomic
- spectrum
Signature
String
Substitution
Symbol
- function
- logical/constant
- non-logical
- variable
Term
Theory
- list

Example axiomatic
systems (list)

of arithmetic:
of the real numbers
- Tarski's axiomatization
of Boolean algebras
- canonical
- minimal axioms
of geometry:
- Euclidean:
- non-Euclidean

Principia Mathematica

Proof theory

Model theory

Computability theory

Mathematics portal

Common logical symbols

∧ or &

and

∨

¬ or ~

not

→

implies

⊃

implies,
superset

↔ or ≡

iff

nand

∀

universal
quantification

∃

existential
quantification

⊤

true,
tautology

⊥

⊢

⊨

∴

∵

because

Philosophy portal

Mathematics portal

v t e Set theory
Overview	Set (mathematics)
Axioms	Adjunction Choice countable dependent global Constructibility (V=L) Determinacy Extensionality Infinity Limitation of size Pairing Power set Regularity Union Martin's axiom Axiom schema replacement specification
Operations	Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union
Concepts Methods	Almost Cardinality Cardinal number (large) Class Constructible universe Continuum hypothesis Diagonal argument Element ordered pair tuple Family Forcing One-to-one correspondence Ordinal number Set-builder notation Transfinite induction Venn diagram
Set types	Amorphous Countable Empty Finite (hereditarily) Filter base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal
Theories	Alternative Axiomatic Naive Cantor's theorem Zermelo General Principia Mathematica New Foundations Zermelo–Fraenkel von Neumann–Bernays–Gödel Morse–Kelley Kripke–Platek Tarski–Grothendieck
Paradoxes Problems	Russell's paradox Suslin's problem Burali-Forti paradox
Set theorists	Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

v t e Non-classical logic
Intuitionistic	Intuitionistic logic Constructive analysis Heyting arithmetic Intuitionistic type theory Constructive set theory
Fuzzy	Degree of truth Fuzzy rule Fuzzy set Fuzzy finite element Fuzzy set operations
Substructural	Structural rule Relevance logic Linear logic
Paraconsistent	Dialetheism
Description	Ontology (computer science) Ontology language
Many-valued	Three-valued Four-valued Łukasiewicz
Digital logic	Three-state logic Tri-state buffer Four-valued Verilog IEEE 1164 VHDL
Others	Dynamic semantics Inquisitive logic Intermediate logic Non-monotonic logic

Category theory

Key concepts

Universal constructions

Limits	Terminal objects Products Equalizers Kernels Pullbacks Inverse limit
Colimits	Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit

Algebraic categories

Constructions on categories

Higher category theory

Key concepts

Categorification

Enriched category

Higher-dimensional algebra

n-categories

Weak `n`-categories	Bicategory (pseudofunctor) Tricategory Tetracategory Kan complex ∞-groupoid ∞-topos
Strict `n`-categories	2-category (2-functor) 3-category

Categorified concepts

v t e Major topics in Foundations of Mathematics
Mathematical logic	Peano axioms Mathematical induction Formal system Axiomatic system Hilbert system Natural deduction Mathematical proof Model theory Mathematical constructivism Modal logic List of mathematical logic topics
Set theory	Set Naive set theory Axiomatic set theory Zermelo set theory Zermelo–Fraenkel set theory Constructive set theory Descriptive set theory Determinacy Russell's paradox List of set theory topics
Type theory	Axiom of reducibility Simple type theory Dependent type theory Intuitionistic type theory Homotopy type theory Univalent foundations Girard's paradox
Category theory	Category Topos theory Category of sets Higher category theory ∞-groupoid ∞-topos theory Mathematical structuralism Glossary of category theory List of category theory topics

Discrete, Algebra

edit

v t e Algebra
Outline History
Areas	Abstract algebra Algebraic geometry Algebraic number theory Category theory Commutative algebra Elementary algebra Homological algebra K-theory Linear algebra Multilinear algebra Noncommutative algebra Order theory Representation theory Universal algebra
Basic concepts	Algebraic expression Equation (Linear equation, Quadratic equation) Function (Polynomial function) Inequality (Linear inequality) Operation (Addition, Multiplication) Relation (Equivalence relation) Variable
Algebraic structures	Field (theory) Group (theory) Module (theory) Ring (theory) Vector space (Vector)
Linear and multilinear algebra	Basis Determinant Eigenvalues and eigenvectors Inner product space (Dot product) Hilbert space Linear map (Matrix) Linear subspace (Affine space) Norm (Euclidean norm) Orthogonality (Orthogonal complement) Rank Trace
Algebraic constructions	Composition algebra Exterior algebra Free object (Free group, ...) Geometric algebra (Multivector) Polynomial ring (Polynomial) Quotient object (Quotient group, ...) Symmetric algebra Tensor algebra
Topic lists	Algebraic structures
Glossaries	Field theory Linear algebra Order theory Ring theory
Category

Algebraic structures
Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory
Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division ring Lie ring Ring theory
Lattice-like Lattice Semilattice Complemented lattice Total order Heyting algebra Boolean algebra Map of lattices Lattice theory
Module-like Module Group with operators Vector space Linear algebra
Algebra-like Algebra Associative Non-associative Composition algebra Lie algebra Graded Bialgebra Hopf algebra
v t e

Basic notions

Finite groups

Dihedral group D_n
Quaternion group Q

Frobenius group

Schur multiplier

cyclic
alternating
Lie type
sporadic

v t e Groups
Basic notions	Subgroup Normal subgroup Commutator subgroup Quotient group Group homomorphism (Semi-) direct product direct sum
Types of groups	Finite groups Abelian groups Cyclic groups Infinite group Simple groups Solvable groups Symmetry group Space group Point group Wallpaper group Trivial group
Discrete groups	Classification of finite simple groups Cyclic group Z_n Alternating group A_n Sporadic groups Mathieu group M_11..12,M_22..24 Conway group Co_1..3 Janko groups J₁, J₂, J₃, J₄ Fischer group F_22..24 Baby monster group B Monster group M Other finite groups Symmetric group S_n Dihedral group D_n Rubik's Cube group
Lie groups	General linear group GL(n) Special linear group SL(n) Orthogonal group O(n) Special orthogonal group SO(n) Unitary group U(n) Special unitary group SU(n) Symplectic group Sp(n) Exceptional Lie groups G₂ F₄ E₆ E₇ E₈ Circle group Lorentz group Poincaré group Quaternion group
Infinite dimensional groups	Conformal group Diffeomorphism group Loop group Quantum group O(∞) SU(∞) Sp(∞)
History Applications Abstract algebra

v t e Linear algebra
Outline Glossary
Basic concepts	Scalar Vector Vector space Scalar multiplication Vector projection Linear span Linear map Linear projection Linear independence Linear combination Basis Change of basis Row and column vectors Row and column spaces Kernel Eigenvalues and eigenvectors Transpose Linear equations
Matrices	Block Decomposition Invertible Minor Multiplication Rank Transformation Cramer's rule Gaussian elimination
Bilinear	Orthogonality Dot product Hadamard product Inner product space Outer product Kronecker product Gram–Schmidt process
Multilinear algebra	Determinant Cross product Triple product Seven-dimensional cross product Geometric algebra Exterior algebra Bivector Multivector Tensor Outermorphism
Vector space constructions	Dual Direct sum Function space Quotient Subspace Tensor product
Numerical	Floating-point Numerical stability Basic Linear Algebra Subprograms Sparse matrix Comparison of linear algebra libraries
Category

Tensors

Glossary of tensor theory

Scope

Mathematics	Coordinate system Differential geometry Dyadic algebra Euclidean geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus
Physics Engineering	Computer vision Continuum mechanics Electromagnetism General relativity Transport phenomena

Notation

Tensor
definitions

Operations

Related
abstractions

Notable tensors

Mathematics	Kronecker delta Levi-Civita symbol Metric tensor Nonmetricity tensor Ricci curvature Riemann curvature tensor Torsion tensor Weyl tensor
Physics	Moment of inertia Angular momentum tensor Spin tensor Cauchy stress tensor stress–energy tensor Einstein tensor EM tensor Gluon field strength tensor Metric tensor (GR)

Mathematicians

Analysis

edit

v t e Major topics in mathematical analysis
Calculus: Integration Differentiation Differential equations ordinary partial stochastic Fundamental theorem of calculus Calculus of variations Vector calculus Tensor calculus Matrix calculus Lists of integrals Table of derivatives
Real analysis Complex analysis Hypercomplex analysis (quaternionic analysis) Functional analysis Fourier analysis Least-squares spectral analysis Harmonic analysis P-adic analysis (P-adic numbers) Measure theory Representation theory Functions Continuous function Special functions Limit Series Infinity
Mathematics portal

v t e Integrals
Types of integrals	Riemann integral Lebesgue integral Burkill integral Bochner integral Daniell integral Darboux integral Henstock–Kurzweil integral Haar integral Hellinger integral Khinchin integral Kolmogorov integral Lebesgue–Stieltjes integral Pettis integral Pfeffer integral Riemann–Stieltjes integral Regulated integral
Integration techniques	Substitution Trigonometric Euler Weierstrass By parts Partial fractions Euler's formula Inverse functions Changing order Reduction formulas Parametric derivatives Differentiation under the integral sign Laplace transform Contour integration Laplace's method Numerical integration Simpson's rule Trapezoidal rule Risch algorithm
Improper integrals	Gaussian integral Dirichlet integral Fermi–Dirac integral complete incomplete Bose–Einstein integral Frullani integral Common integrals in quantum field theory
Stochastic integrals	Itô integral Russo–Vallois integral Stratonovich integral Skorokhod integral
Miscellaneous	Basel problem Euler–Maclaurin formula Gabriel's horn Integration Bee Proof that 22/7 exceeds π Volumes Washers Shells

v t e Infinitesimals
History	Adequality Leibniz's notation Integral symbol Criticism of nonstandard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle
Related branches	Nonstandard analysis Nonstandard calculus Internal set theory Synthetic differential geometry Smooth infinitesimal analysis Constructive nonstandard analysis Infinitesimal strain theory (physics)
Formalizations	Differentials Hyperreal numbers Dual numbers Surreal numbers
Individual concepts	Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of continuity Overspill Microcontinuity Transcendental law of homogeneity
Mathematicians	Gottfried Wilhelm Leibniz Abraham Robinson Pierre de Fermat Augustin-Louis Cauchy Leonhard Euler
Textbooks	Analyse des Infiniment Petits Elementary Calculus Cours d'Analyse

v t e Calculus
Precalculus	Binomial theorem Concave function Continuous function Factorial Finite difference Free variables and bound variables Graph of a function Linear function Radian Rolle's theorem Secant Slope Tangent
Limits	Indeterminate form Limit of a function One-sided limit Limit of a sequence Order of approximation (ε, δ)-definition of limit
Differential calculus	Derivative Second derivative Partial derivative Differential Differential operator Mean value theorem Notation Leibniz's notation Newton's notation Rules of differentiation linearity Power Sum Chain L'Hôpital's Product General Leibniz's rule Quotient Other techniques Implicit differentiation Inverse functions and differentiation Logarithmic derivative Related rates Stationary points First derivative test Second derivative test Extreme value theorem Maximum and minimum Further applications Newton's method Taylor's theorem Differential equation Ordinary differential equation Partial differential equation Stochastic differential equation
Integral calculus	Antiderivative Arc length Riemann integral Basic properties Constant of integration Fundamental theorem of calculus Differentiating under the integral sign Integration by parts Integration by substitution trigonometric Euler Tangent half-angle substitution Partial fractions in integration Quadratic integral Trapezoidal rule Volumes Washer method Shell method Integral equation Integro-differential equation
Vector calculus	Derivatives Curl Directional derivative Divergence Gradient Laplacian Basic theorems Line integrals Green's Stokes' Gauss'
Multivariable calculus	Divergence theorem Geometric Hessian matrix Jacobian matrix and determinant Lagrange multiplier Line integral Matrix Multiple integral Partial derivative Surface integral Volume integral Advanced topics Differential forms Exterior derivative Generalized Stokes' theorem Tensor calculus
Sequences and series	Arithmetico-geometric sequence Types of series Alternating Binomial Fourier Geometric Harmonic Infinite Power Maclaurin Taylor Telescoping Tests of convergence Abel's Alternating series Cauchy condensation Direct comparison Dirichlet's Integral Limit comparison Ratio Root Term
Special functions and numbers	Bernoulli numbers e (mathematical constant) Exponential function Natural logarithm Stirling's approximation
History of calculus	Adequality Brook Taylor Colin Maclaurin Generality of algebra Gottfried Wilhelm Leibniz Infinitesimal Infinitesimal calculus Isaac Newton Fluxion Law of Continuity Leonhard Euler Method of Fluxions The Method of Mechanical Theorems
Lists	Differentiation rules List of integrals of exponential functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of inverse trigonometric functions List of integrals of irrational functions List of integrals of logarithmic functions List of integrals of rational functions List of integrals of trigonometric functions Secant Secant cubed List of limits Lists of integrals
Miscellaneous topics	Complex calculus Contour integral Differential geometry Manifold Curvature of curves of surfaces Tensor Euler–Maclaurin formula Gabriel's horn Integration Bee Proof that 22/7 exceeds π Regiomontanus' angle maximization problem Steinmetz solid

v t e Convex analysis and variational analysis
Basic concepts	Convex combination Convex function Convex set
Topics (list)	Choquet theory Convex geometry Convex metric space Convex optimization Duality Lagrange multiplier Legendre transformation Locally convex topological vector space Simplex
Maps	Convex conjugate Concave (Closed K- Logarithmically Proper Pseudo- Quasi-) Convex function Invex function Legendre transformation Semi-continuity Subderivative
Main results (list)	Carathéodory's theorem Ekeland's variational principle Fenchel–Moreau theorem Fenchel-Young inequality Jensen's inequality Hermite–Hadamard inequality Krein–Milman theorem Mazur's lemma Shapley–Folkman lemma Robinson–Ursescu Simons Ursescu
Sets	Convex hull (Orthogonally, Pseudo-) Convex set Effective domain Epigraph Hypograph John ellipsoid Lens Radial set/Algebraic interior Zonotope
Series	Convex series related ((cs, lcs)-closed, (cs, bcs)-complete, (lower) ideally convex, (Hx), and (Hwx))
Duality	Dual system Duality gap Strong duality Weak duality
Applications and related	Convexity in economics

Differential equations

Classification

Operations	Differential operator Notation for differentiation Ordinary Partial Differential-algebraic Integro-differential Fractional Linear Non-linear Holonomic
Attributes of variables	Dependent and independent variables Homogeneous Nonhomogeneous Coupled Decoupled Order Degree Autonomous Exact differential equation On jet bundles
Relation to processes	Difference (discrete analogue) Stochastic Stochastic partial Delay

Solutions

Existence/uniqueness	Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kowalevski theorem
Solution topics	Wronskian Phase portrait Phase space Lyapunov stability Asymptotic stability Exponential stability Rate of convergence Series solutions Integral solutions Numerical integration Dirac delta function
Solution methods	Inspection Substitution Separation of variables Method of undetermined coefficients Variation of parameters Integrating factor Integral transforms Euler method Finite difference method Crank–Nicolson method Runge–Kutta methods Finite element method Finite volume method Galerkin method Perturbation theory

Examples

Mathematicians

Functional analysis (topics – glossary)

Spaces

Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev Topological vector
Properties	Barrelled Complete Dual (Algebraic/Topological) Locally convex Reflexive Separable

Theorems

Operators

Algebras

Open problems

Applications

Advanced topics

Category

v t e Lists of integrals
Rational functions Irrational functions Trigonometric functions Inverse trigonometric functions Hyperbolic functions Inverse hyperbolic functions Exponential functions Logarithmic functions Gaussian functions Definite integrals

Number

edit

v t e Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory (analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, P-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers P-adic numbers (P-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Continued fractions
Category List of topics List of recreational topics Wikibook Wikiversity

Classes of natural numbers

Powers and related numbers
Achilles Power of 2 Power of 3 Power of 10 Square Cube Fourth power Fifth power Sixth power Seventh power Eighth power Perfect power Powerful Prime power

Of the form a × 2^b ± 1
Cullen Double Mersenne Fermat Mersenne Proth Thabit Woodall

Other polynomial numbers
Hilbert Idoneal Leyland Loeschian Lucky numbers of Euler

Recursively defined numbers
Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin

Possessing a specific set of other numbers
Amenable Congruent Knödel Riesel Sierpiński

Expressible via specific sums
Nonhypotenuse Polite Practical Primary pseudoperfect Ulam Wolstenholme

Figurate numbers

2-dimensional

centered	Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star
non-centered	Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal Dodecagonal

3-dimensional

centered	Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral
non-centered	Tetrahedral Cubic Octahedral Dodecahedral Icosahedral Stella octangula
pyramidal	Square pyramidal

4-dimensional

non-centered	Pentatope Squared triangular Tesseractic

Combinatorial numbers
Bell Cake Catalan Dedekind Delannoy Euler Eulerian Fuss–Catalan Lah Lazy caterer's sequence Lobb Motzkin Narayana Ordered Bell Schröder Schröder–Hipparchus Stirling first Stirling second Telephone number Wedderburn–Etherington

Primes
Wieferich Wall–Sun–Sun Wolstenholme prime Wilson

Pseudoprimes
Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime

Arithmetic functions and dynamics

Divisor functions	Abundant Almost perfect Arithmetic Betrothed Colossally abundant Deficient Descartes Hemiperfect Highly abundant Highly composite Hyperperfect Multiply perfect Perfect Practical Primitive abundant Quasiperfect Refactorable Semiperfect Sublime Superabundant Superior highly composite Superperfect
Prime omega functions	Almost prime Semiprime
Euler's totient function	Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient
Aliquot sequences	Amicable Perfect Sociable Untouchable
Primorial	Euclid Fortunate

Other prime factor or divisor related numbers
Blum Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet Zeisel

Numeral system-dependent numbers

Arithmetic functions
and dynamics

Persistence
- Additive
- Multiplicative

Digit sum	Digit sum Digital root Self Sum-product
Digit product	Multiplicative digital root Sum-product
Coding-related	Meertens
Other	Dudeney Factorion Kaprekar Kaprekar's constant Keith Lychrel Narcissistic Perfect digit-to-digit invariant Perfect digital invariant Happy

P-adic numbers-related

Automorphic
- Trimorphic

Digit-composition related

Digit-permutation related

Divisor-related

Other

Friedman

Binary numbers
Evil Odious Pernicious

Generated via a sieve
Lucky Prime

Sorting related
Pancake number Sorting number

Natural language related
Aronson's sequence Ban

Graphemics related
Strobogrammatic

Mathematics portal

Figurate numbers

2-dimensional

centered	Centered triangular numbers Centered square numbers Centered pentagonal numbers Centered hexagonal numbers Centered heptagonal numbers Centered octagonal numbers Centered nonagonal numbers Centered decagonal numbers Star numbers
non-centered	Triangular numbers Square numbers Pentagonal numbers Hexagonal numbers Heptagonal numbers Octagonal numbers Nonagonal numbers Decagonal numbers Dodecagonal numbers

3-dimensional

centered	Centered tetrahedral numbers Centered cube numbers Centered octahedral numbers Centered dodecahedral numbers Centered icosahedral numbers
non-centered	Cube numbers Octahedral numbers Dodecahedral numbers Icosahedral numbers Stella octangula numbers
pyramidal	Tetrahedral numbers Square pyramidal numbers

4-dimensional

non-centered	Pentatope numbers Squared triangular numbers Tesseractic numbers

Higher dimensional

non-centered	5-hypercube numbers 6-hypercube numbers 7-hypercube numbers 8-hypercube numbers

Geometry, Topology

edit

Two-dimensional

by period

BCE
Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius
1–1400s
Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara
1400s–1700s
Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida
1700s–1900s
Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter
Present day
Atiyah Gromov

Trigonometry

Outline History Usage Functions (sin, cos, tan, inverse) Generalized trigonometry
Reference
Identities Exact constants Tables Unit circle
Laws and theorems
Sines Cosines Tangents Cotangents Pythagorean theorem
Calculus
Trigonometric substitution Integrals (inverse functions) Derivatives Trigonometric series
Mathematicians
Hipparchus Ptolemy Brahmagupta al-Hasib al-Battani Regiomontanus Viète de Moivre Euler Fourier
v t e

v t e Dimension
Dimensional spaces	Vector space Euclidean space Affine space Projective space Free module Manifold Algebraic variety Spacetime
Other dimensions	Krull Lebesgue covering Inductive Hausdorff Minkowski Fractal Degrees of freedom
Polytopes and shapes	Hyperplane Hypersurface Hypercube Hyperrectangle Demihypercube Hypersphere Cross-polytope Simplex Hyperpyramid
Dimensions by number	Zero One Two Three Four Five Six Seven Eight n-dimensions
See also	Hyperspace Codimension
Category

v t e Banach space topics
Types of Banach spaces	Asplund Banach list Banach lattice Grothendieck Hilbert Inner product space Polarization identity (Polynomially) Reflexive Riesz L-semi-inner product (B Strictly Uniformly) convex Uniformly smooth (Injective Projective) Tensor product (of Hilbert spaces)
Banach spaces are:	Barrelled Complete F-space Fréchet tame Locally convex Seminorms/Minkowski functionals Mackey Metrizable Normed norm Quasinormed Stereotype
Function space Topologies	Banach–Mazur compactum Dual Dual space Dual norm Operator Ultraweak Weak polar operator Strong polar operator Ultrastrong Uniform convergence
Linear operators	Adjoint Bilinear form operator sesquilinear (Un)Bounded Closed Compact on Hilbert spaces (Dis)Continuous Densely defined Fredholm kernel operator Hilbert–Schmidt Functionals positive Pseudo-monotone Normal Nuclear Self-adjoint Strictly singular Trace class Transpose Unitary
Operator theory	Banach algebras C-algebras Operator space Spectrum C-algebra radius Spectral theory of ODEs Spectral theorem Polar decomposition Singular value decomposition
Theorems	Anderson–Kadec Banach–Alaoglu Banach–Mazur Banach–Saks Banach–Schauder (open mapping) Banach–Steinhaus (Uniform boundedness) Bessel's inequality Cauchy–Schwarz inequality Closed graph Closed range Eberlein–Šmulian Freudenthal spectral Gelfand–Mazur Gelfand–Naimark Goldstine Hahn–Banach hyperplane separation Kakutani fixed-point Krein–Milman Lomonosov's invariant subspace Mackey–Arens Mazur's lemma M. Riesz extension Parseval's identity Riesz's lemma Riesz representation Robinson-Ursescu Schauder fixed-point
Analysis	Abstract Wiener space Banach manifold bundle Bochner space Convex series Differentiation in Fréchet spaces Derivatives Fréchet Gateaux functional holomorphic quasi Integrals Bochner Dunford Gelfand–Pettis regulated Paley–Wiener weak Functional calculus Borel continuous holomorphic Measures Lebesgue Projection-valued Vector Weakly / Strongly measurable function
Types of sets	Absolutely convex Absorbing Affine Balanced/Circled Bounded Convex Convex cone (subset) Convex series related ((cs, lcs)-closed, (cs, bcs)-complete, (lower) ideally convex, (Hx), and (Hwx)) Linear cone (subset) Radial Radially convex/Star-shaped Symmetric Zonotope
Subsets / set operations	Affine hull (Relative) Algebraic interior (core) Bounding points Convex hull Extreme point Interior Linear span Minkowski addition Polar (Quasi) Relative interior
Examples	Absolute continuity AC $ba(\Sigma )$ c space Banach coordinate BK Besov $B_{p,q}^{s}(\mathbb {R} )$ Birnbaum–Orlicz Bounded variation BV Bs space Continuous C(K) with K compact Hausdorff Hardy H^p Hilbert H Morrey–Campanato $L^{\lambda ,p}(\Omega )$ ℓ^p $\ell ^{\infty }$ L^p $L^{\infty }$ weighted Schwartz $S\left(\mathbb {R} ^{n}\right)$ Segal–Bargmann F Sequence space Sobolev W^k,p Sobolev inequality Triebel–Lizorkin Wiener amalgam $W(X,L^{p})$
Applications	Differential operator Finite element method Mathematical formulation of quantum mechanics Ordinary Differential Equations (ODEs) Validated numerics

v t e Boundedness and bornology
Basic concepts	Barrelled space Bounded set Bornological space (Vector) Bornology
Operators	(Un)Bounded operator Uniform boundedness principle
Subsets	Barrelled set Bornivorous set Saturated family
Related spaces	(Countably) Barrelled space (Countably) Quasi-barrelled space Infrabarrelled space (Quasi-) Ultrabarrelled space Ultrabornological space

Compact topological surfaces and their immersions in 3D

Without boundary

Orientable	Sphere (genus 0) Torus (genus 1) Number 8 (genus 2) Pretzel (genus 3) ...
Non-orientable	Real projective plane genus 1; Boy's surface Roman surface Klein bottle (genus 2) Dyck's surface (genus 3) ...

With boundary

Related
notions

Properties	Connectedness Compactness Triangulatedness or smoothness Orientability
Characteristics	Number of boundary components Genus Euler characteristic
Operations	Connected sum Making a hole Gluing a handle Gluing a cross-cap Immersion

v t e Various notions of curvature defined in differential geometry
Differential geometry of curves	Curvature Torsion of a curve Frenet–Serret formulas Radius of curvature (applications) Affine curvature Total curvature Total absolute curvature
Differential geometry of surfaces	Principal curvatures Gaussian curvature Mean curvature Darboux frame Gauss–Codazzi equations First fundamental form Second fundamental form Third fundamental form
Riemannian geometry	Curvature of Riemannian manifolds Riemann curvature tensor Ricci curvature Scalar curvature Sectional curvature
Curvature of connections	Curvature form Torsion tensor Cocurvature Holonomy

v t e Fractals
Characteristics	Fractal dimensions Assouad Box-counting Higuchi Correlation Hausdorff Packing Topological Recursion Self-similarity
Iterated function system	Barnsley fern Cantor set Koch snowflake Menger sponge Sierpinski carpet Sierpinski triangle Apollonian gasket Fibonacci word Space-filling curve Blancmange curve De Rham curve Minkowski Dragon curve Hilbert curve Koch curve Lévy C curve Moore curve Peano curve Sierpiński curve Z-order curve String T-square n-flake Vicsek fractal Hexaflake Gosper curve Pythagoras tree Weierstrass function
Strange attractor	Multifractal system
L-system	Fractal canopy Space-filling curve H tree
Escape-time fractals	Burning Ship fractal Julia set Filled Newton fractal Douady rabbit Lyapunov fractal Mandelbrot set Misiurewicz point Multibrot set Newton fractal Tricorn Mandelbox Mandelbulb
Rendering techniques	Buddhabrot Orbit trap Pickover stalk
Random fractals	Brownian motion Brownian tree Brownian motor Fractal landscape Lévy flight Percolation theory Self-avoiding walk
People	Michael Barnsley Georg Cantor Bill Gosper Felix Hausdorff Desmond Paul Henry Gaston Julia Helge von Koch Paul Lévy Aleksandr Lyapunov Benoit Mandelbrot Hamid Naderi Yeganeh Lewis Fry Richardson Wacław Sierpiński
Other	"How Long Is the Coast of Britain?" Coastline paradox Fractal art List of fractals by Hausdorff dimension The Fractal Geometry of Nature (1982 book) The Beauty of Fractals (1986 book) Chaos: Making a New Science (1987 book) Kaleidoscope Chaos theory

Polygons (List)

Triangles

Quadrilaterals

By number
of sides

1–10 sides	Monogon (1) Digon (2) Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6) Heptagon (7) Octagon (8) Nonagon/Enneagon (9) Decagon (10)
11–20 sides	Hendecagon (11) Dodecagon (12) Tridecagon (13) Tetradecagon (14) Pentadecagon (15) Hexadecagon (16) Heptadecagon (17) Octadecagon (18) Icosagon (20)
>20 sides	Icositrigon (23) Icositetragon (24) Triacontagon (30) 257-gon Chiliagon (1000) Myriagon (10,000) 65537-gon Megagon (1,000,000) Apeirogon (∞)

Star polygons

Classes

v t e Polyhedra
Listed by number of faces and type
1–10 faces	Monohedron Dihedron Trihedron Tetrahedron Pentahedron Hexahedron Heptahedron Octahedron Enneahedron Decahedron
11–20 faces	Hendecahedron Dodecahedron Tridecahedron Tetradecahedron Pentadecahedron Hexadecahedron Heptadecahedron Octadecahedron Enneadecahedron Icosahedron
>20 faces	Icositetrahedron (24) Triacontahedron (30) Icosidodecahedron (32) Hexoctahedron (48) Hexecontahedron (60) Enneacontahedron (90) Hectotriadiohedron (132) Apeirohedron (∞)
elemental things	face edge vertex uniform polyhedron (two infinite groups and 75) regular polyhedron (9) quasiregular polyhedron (16) semiregular polyhedron (two infinite groups and 50)
convex polyhedron	Platonic solid (5) Archimedean solid (13) Catalan solid (13) Johnson solid (92)
non-convex polyhedron	Kepler–Poinsot polyhedron (4) Star polyhedron (infinite) Uniform star polyhedron (57)
prismatoid‌s	prism antiprism frustum cupola wedge pyramid parallelepiped

v t e Topological tensor products and nuclear spaces
Basic concepts	Auxiliary normed spaces Nuclear space Tensor product Topological tensor product of Hilbert spaces
Topologies	Inductive tensor product Injective tensor product Projective tensor product
Operators/Maps	Fredholm determinant Fredholm kernel Hilbert–Schmidt operator Hypocontinuity Integral Nuclear between Banach spaces Trace class
Theorems	Grothendieck trace theorem Schwartz kernel theorem

v t e Topological vector spaces (TVSs)
Basic concepts	Banach space Completeness Continuous linear operator Linear functional Fréchet space Linear map Locally convex space Metrizability Operator topologies Topological vector space Vector space
Main results	Anderson–Kadec Banach–Alaoglu Closed graph theorem F. Riesz's Hahn–Banach (hyperplane separation Vector-valued Hahn–Banach) Open mapping (Banach–Schauder) Bounded inverse Uniform boundedness (Banach–Steinhaus)
Maps	Bilinear operator form Linear map Almost open Bounded Continuous Closed Compact Densely defined Discontinuous Topological homomorphism Functional Linear Bilinear Sesquilinear Norm Seminorm Sublinear function Transpose
Types of sets	Absolutely convex/disk Absorbing/Radial Affine Balanced/Circled Banach disks Bounding points Bounded Complemented subspace Convex Convex cone (subset) Linear cone (subset) Extreme point Pre-compact/Totally bounded Prevalent/Shy Radial Radially convex/Star-shaped Symmetric
Set operations	Affine hull (Relative) Algebraic interior (core) Convex hull Linear span Minkowski addition Polar (Quasi) Relative interior
Types of TVSs	Asplund B-complete/Ptak Banach (Countably) Barrelled BK-space (Ultra-) Bornological Brauner Complete Convenient (DF)-space Distinguished F-space FK-AK space FK-space Fréchet tame Fréchet Grothendieck Hilbert Infrabarreled Interpolation space K-space LB-space LF-space Locally convex space Mackey (Pseudo)Metrizable Montel Quasibarrelled Quasi-complete Quasinormed (Polynomially Semi-) Reflexive Riesz Schwartz Semi-complete Smith Stereotype (B Strictly Uniformly) convex (Quasi-) Ultrabarrelled Uniformly smooth Webbed With the approximation property
Category

v t e Topology
Fields	General (point-set) Algebraic Combinatorial Continuum Differential Geometric low-dimensional Homology cohomology Set-theoretic Digital
Key concepts	Open set / Closed set Interior Continuity Space compact connected Hausdorff metric uniform Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold Bundle (mathematics) Second-countable space Cobordism
Metrics and properties	Euler characteristic Betti number Winding number Chern number Orientability
Key results	Banach fixed-point theorem De Rham cohomology Invariance of domain Poincaré conjecture Tychonoff's theorem Urysohn's lemma
Category Mathematics portal Wikibook Wikiversity Topics general algebraic geometric Publications

Applied mathematics

edit

Probability theory
Part of a series on statistics

Probability Axioms Determinism System Indeterminism Randomness
Probability space Sample space Event Collectively exhaustive events Elementary event Mutual exclusivity Outcome Singleton Experiment Bernoulli trial Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution Probability measure Random variable Bernoulli process Continuous or discrete Expected value Variance Markov chain Observed value Random walk Stochastic process
Complementary event Joint probability Marginal probability Conditional probability
Independence Conditional independence Law of total probability Law of large numbers Bayes' theorem Boole's inequality
Venn diagram Tree diagram
v t e

Industrial and applied mathematics

Computational

Mathematical software	Arbitrary-precision arithmetic Finite element analysis Tensor software Interactive geometry software Optimization software Statistical software Numerical-analysis software Numerical libraries Solvers

Algebraic structures	Algebra of physical space Feynman integral Poisson algebra Quantum group Renormalization group Representation theory Spacetime algebra Superalgebra Supersymmetry algebra

Decision sciences

Other applications

Mathematics

Organizations

Category
Mathematics portal / outline / topics list

Statistics

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in
Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons
Parametric tests	Likelihood-ratio Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC
Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis	Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)
Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression
Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity
Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality
Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey
Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)
Frequency domain	Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time
Hazard function	Nelson–Aalen estimator
Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

v t e Computer science
Note: This template roughly follows the 2012 ACM Computing Classification System.
Hardware	Printed circuit board Peripheral Integrated circuit Very Large Scale Integration Systems on Chip (SoCs) Energy consumption (Green computing) Electronic design automation Hardware acceleration
Computer systems organization	Computer architecture Computational complexity Dependability Embedded system Real-time computing
Networks	Network architecture Network protocol Network components Network scheduler Network performance evaluation Network service
Software organization	Interpreter Middleware Virtual machine Operating system Software quality
Software notations and tools	Programming paradigm Programming language Compiler Domain-specific language Modeling language Software framework Integrated development environment Software configuration management Software library Software repository
Software development	Control variable Software development process Requirements analysis Software design Software construction Software deployment Software engineering Software maintenance Programming team Open-source model
Theory of computation	Model of computation Formal language Automata theory Computability theory Computational complexity theory Logic Semantics
Algorithms	Algorithm design Analysis of algorithms Algorithmic efficiency Randomized algorithm Computational geometry
Mathematics of computing	Discrete mathematics Probability Statistics Mathematical software Information theory Mathematical analysis Numerical analysis Theoretical computer science
Information systems	Database management system Information storage systems Enterprise information system Social information systems Geographic information system Decision support system Process control system Multimedia information system Data mining Digital library Computing platform Digital marketing World Wide Web Information retrieval
Security	Cryptography Formal methods Security hacker Security services Intrusion detection system Hardware security Network security Information security Application security
Human–computer interaction	Interaction design Social computing Ubiquitous computing Visualization Accessibility
Concurrency	Concurrent computing Parallel computing Distributed computing Multithreading Multiprocessing
Artificial intelligence	Natural language processing Knowledge representation and reasoning Computer vision Automated planning and scheduling Search methodology Control method Philosophy of artificial intelligence Distributed artificial intelligence
Machine learning	Supervised learning Unsupervised learning Reinforcement learning Multi-task learning Cross-validation
Graphics	Animation Rendering Photograph manipulation Graphics processing unit Mixed reality Virtual reality Image compression Solid modeling
Applied computing	Quantum Computing E-commerce Enterprise software Computational mathematics Computational physics Computational chemistry Computational biology Computational social science Computational engineering Differentiable computing Computational healthcare Digital art Electronic publishing Cyberwarfare Electronic voting Video games Word processing Operations research Educational technology Document management
Category Outline WikiProject Commons

v t e Complexity classes
Considered feasible	DLOGTIME AC⁰ ACC⁰ TC⁰ L SL RL FL NL NL-complete NC SC CC P P-complete ZPP RP BPP BQP APX FP
Suspected infeasible	UP NP NP-complete NP-hard co-NP co-NP-complete TFNP FNP AM QMA PH ⊕P PP #P #P-complete IP PSPACE PSPACE-complete
Considered infeasible	EXPTIME NEXPTIME EXPSPACE 2-EXPTIME ELEMENTARY PR R RE ALL
Class hierarchies	Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy
Families of classes	DTIME NTIME DSPACE NSPACE Probabilistically checkable proof Interactive proof system
List of complexity classes

v t e Conway's Game of Life and related cellular automata
Structures	Breeder Garden of Eden Glider Gun Methuselah Oscillator Puffer train Rake Reflector Replicator Sawtooth Spacefiller Spaceship Spark Still life
Life variants	Day and Night Highlife Lenia Life without Death Seeds
Concepts	Moore neighborhood Speed of light Von Neumann neighborhood
Implementations	Golly Life Genesis Video Life Anonymous;Code
Key people	John Conway Martin Gardner Bill Gosper Richard Guy
Websites	LifeWiki
Popular culture	Bloom Wake

v t e Terms in graph theory
Types of graphs	Directed Undirected Acyclic Bipartite Connected Complete Labeled Hypergraph Multigraph Planar Pseudograph Regular Tree Weighted Wheel
Graph elements	Bridge Edge Directed edge Loop Node Strongly connected component Subgraph (graph theory) Vertex Weighted edge
Graph attributes	Edge-connectedness Dominator (graph theory) Girth (graph theory) Multiplicity (graph theory) Order (graph theory) Size (graph theory) Vertex-connectedness
Category Outline Glossary Wikibook Wikiversity

User:Y-S.Ko/Wikipedia course/Mathematics

Mathematics

History

Philosophy of Mathematics

Discrete, Algebra

Analysis

Number

Geometry, Topology

Applied mathematics

See also