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{{Short description|none}}
{{Short description|none}}
This is a list of [[Mathematical object|mathematical objects]], organized by branch.
This is a list of [[mathematical object]]s, organized by branch.


== List of mathematical objects by branch ==
== List of mathematical objects by branch ==
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* [[Linear span]]
* [[Linear span]]
* [[Basis (linear algebra)|Bases]]
* [[Basis (linear algebra)|Bases]]
* [[Linear map|Linear maps]]
* [[Linear map]]s
* [[Parallelepiped]]
* [[Parallelepiped]]


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* [[Group (mathematics)|Groups]]
* [[Group (mathematics)|Groups]]
* [[Ring (mathematics)|Rings]], [[Module (mathematics)|Modules]]
* [[Ring (mathematics)|Rings]], [[Module (mathematics)|Modules]]
* [[Monoid|monoids]]
* [[monoid]]s
* [[Field (mathematics)|Fields]], [[Vector space|Vector spaces]]
* [[Field (mathematics)|Fields]], [[Vector space]]s
* [[Algebra over a field|Algebras]]
* [[Algebra over a field|Algebras]]
* [[Chain complex|Chain complexes]]
* [[Chain complex]]es
* [[Operation (mathematics)|Operations]]
* [[Operation (mathematics)|Operations]]
* [[Lattice (group)|group-theoretic lattices]], [[Lattice (order)|Order-theoretic lattices]]
* [[Lattice (group)|group-theoretic lattices]], [[Lattice (order)|Order-theoretic lattices]]
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==== [[Nonstandard analysis]] ====
==== [[Nonstandard analysis]] ====


* [[Infinitesimal|Infinitesimals]]
* [[Infinitesimal]]s
* [[Fluxion]]
* [[Fluxion]]


==== [[Differential equation|Differential equations]] ====
==== [[Differential equation]]s ====


* [[Dirac delta function]]
* [[Dirac delta function]]
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* [[Category (mathematics)|Categories]]
* [[Category (mathematics)|Categories]]
* [[Functor|Functors]]
* [[Functor]]s
* [[Morphism|Morphisms]]
* [[Morphism]]s
* objects
* objects
* [[Natural transformation|Natural transformations]]
* [[Natural transformation]]s


[[Category (mathematics)|Categories]] are simultaneously homes to mathematical objects and mathematical objects in their own right. In [[proof theory]], proofs and [[Theorem|theorems]] are also mathematical objects
[[Category (mathematics)|Categories]] are simultaneously homes to mathematical objects and mathematical objects in their own right. In [[proof theory]], proofs and [[theorem]]s are also mathematical objects


=== [[Combinatorics]] ===
=== [[Combinatorics]] ===


* [[permutation]]s, [[derangement]]s, [[combination]]s
* [[Permutation|permutations]], [[Derangement|derangements]], [[Combination|combinations]]


=== [[Computer science]] and [[Theoretical computer science]] ===
=== [[Computer science]] and [[Theoretical computer science]] ===


* [[Data structure|Data structures]]
* [[Data structure]]s
** [[Array (data structure)|Arrays]]
** [[Array (data structure)|Arrays]]
** [[Linked list|Linked lists]]
** [[Linked list]]s
** [[Hash table|Hash tables]]
** [[Hash table]]s
** [[Stack (abstract data type)|Stacks]] and [[Queue (abstract data type)|Queues]]
** [[Stack (abstract data type)|Stacks]] and [[Queue (abstract data type)|Queues]]
** [[Heap (data structure)|Heap]]
** [[Heap (data structure)|Heap]]
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==== [[Euclidean geometry|Euclidian geometry]] ====
==== [[Euclidean geometry|Euclidian geometry]] ====


* [[Point (geometry)|Points]], [[Line (geometry)|Lines]], [[Line segment|Line segments]],
* [[Point (geometry)|Points]], [[Line (geometry)|Lines]], [[Line segment]]s,
* [[Polytope|Polytopes]], [[Regular polytope|Regular polytopes]]
* [[Polytope]]s, [[Regular polytope]]s
** [[Polygon|Polygons]] - 2-dimensional polytope
** [[Polygon]]s - 2-dimensional polytope
*** [[Convex polygon]]
*** [[Convex polygon]]
**** [[Triangle|Triangles]]
**** [[Triangle]]s
**** [[Square|Squares]]
**** [[Square]]s
**** [[Pentagon|Pentagons]]
**** [[Pentagon]]s
**** [[Hexagon|Hexagons]]
**** [[Hexagon]]s
** [[Polyhedron|Polyhedra]] 3-dimensional polytope
** [[Polyhedron|Polyhedra]] 3-dimensional polytope
*** [[Platonic solid|Platonic solids]]
*** [[Platonic solid]]s
**** [[Tetrahedron]]
**** [[Tetrahedron]]
**** [[Cube]]
**** [[Cube]]
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**** [[Dodecahedron]]
**** [[Dodecahedron]]
**** [[Icosahedron]]
**** [[Icosahedron]]
* [[Conic section|Conic sections]]
* [[Conic section]]s
** [[Circle|Circles]]
** [[Circle]]s
** [[Ellipse|Ellipses]]
** [[Ellipse]]s
** [[Parabola|Parabolas]]
** [[Parabola]]s
** [[Hyperbola|Hyperbolas]]
** [[Hyperbola]]s
* [[Sphere|Spheres]], [[Ellipsoid|Ellipsoids]], [[Paraboloid|Paraboloids]], [[Hyperboloid|Hyperboloids]],
* [[Sphere]]s, [[Ellipsoid]]s, [[Paraboloid]]s, [[Hyperboloid]]s,
* [[Cylinder|Cylinders]], [[Cone|Cones]]
* [[Cylinder]]s, [[Cone]]s


==== [[Fractal geometry]] ====
==== [[Fractal geometry]] ====


* [[Mandelbrot set]]
* [[Mandelbrot set]]
* [[Julia set|Julia sets]]
* [[Julia set]]s
* [[Sierpiński triangle]]
* [[Sierpiński triangle]]
* [[Sierpiński carpet]], [[Menger sponge]]
* [[Sierpiński carpet]], [[Menger sponge]]
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=== [[Mathematical logic]] ===
=== [[Mathematical logic]] ===


* [[Truth value|Truth values]]
* [[Truth value]]s
* [[Logical connective|Logical connectives]]
* [[Logical connective]]s
* [[Proposition|Propositions]] and [[Predicate (mathematical logic)|Predicates]]
* [[Proposition]]s and [[Predicate (mathematical logic)|Predicates]]
* [[Well-formed formula|Formulas]]
* [[Well-formed formula|Formulas]]
* [[Term (logic)|Terms]]
* [[Term (logic)|Terms]]
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=== [[Number theory]] ===
=== [[Number theory]] ===


* [[Number|Numbers]]
* [[Number]]s
** [[Natural numbers]]
** [[Natural numbers]]
** [[Integers]]
** [[Integers]]
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* [[Function (mathematics)|Functions]], and [[Relation (mathematics)|Relations]]
* [[Function (mathematics)|Functions]], and [[Relation (mathematics)|Relations]]
* [[Membership relation]]
* [[Membership relation]]
* [[Cardinal number|Cardinal numbers]]
* [[Cardinal number]]s
* [[Ordinal number|Ordinal numbers]]
* [[Ordinal number]]s


=== [[Topology]] ===
=== [[Topology]] ===


* [[Closed set|Closed sets]]
* [[Closed set]]s
* [[Filters in topology|Filters]]
* [[Filters in topology|Filters]]
* [[Neighbourhood (mathematics)|Neighborhoods]]
* [[Neighbourhood (mathematics)|Neighborhoods]]
* [[Net (mathematics)|Nets]]
* [[Net (mathematics)|Nets]]
* [[Open set|Open sets]]
* [[Open set]]s
* [[Topological space|Topological spaces]]
* [[Topological space]]s
* [[Uniform space|Uniformities]]
* [[Uniform space|Uniformities]]
* [[Manifold|Manifolds]]
* [[Manifold]]s
** [[Atlas (topology)#Formal definition of atlas|Atlases]]
** [[Atlas (topology)#Formal definition of atlas|Atlases]]
** [[Topological manifold#Coordinate charts|Charts]]
** [[Topological manifold#Coordinate charts|Charts]]
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==== [[Algebraic topology]] ====
==== [[Algebraic topology]] ====


* [[Cohomology group|Cohomology groups]]
* [[Cohomology group]]s
* [[Cohomotopy group|Cohomotopy groups]]<ref>{{cite book |last=Hu |first=Sze-Tsen |url=https://www.maths.ed.ac.uk/~v1ranick/papers/hu2.pdf |title=Homotopy theory |publisher=Academic Press |year=1971 |pages=205-228 |chapter=Chapter VII. Cohomotopy Groups |lccn=59-11526 |access-date=August 28, 2024 |orig-date=1959 |chapter-url=https://www.maths.ed.ac.uk/~v1ranick/papers/hu2.pdf#page=217 |authorlink=Sze-Tsen Hu}}</ref>
* [[Cohomotopy group]]s<ref>{{cite book |last=Hu |first=Sze-Tsen |url=https://www.maths.ed.ac.uk/~v1ranick/papers/hu2.pdf |title=Homotopy theory |publisher=Academic Press |year=1971 |pages=205–228 |chapter=Chapter VII. Cohomotopy Groups |lccn=59-11526 |access-date=August 28, 2024 |orig-date=1959 |chapter-url=https://www.maths.ed.ac.uk/~v1ranick/papers/hu2.pdf#page=217 |author-link=Sze-Tsen Hu}}</ref>
* [[Homology group|Homology groups]]
* [[Homology group]]s
* [[Homotopy group|Homotopy groups]]
* [[Homotopy group]]s

* [[Knot (mathematics)|Knots]]
* [[Knot (mathematics)|Knots]]
** [[Unknot]]
** [[Unknot]]
** [[Trefoil knot]]
** [[Trefoil knot]]

* [[Hole (topology)|Holes]]
* [[Hole (topology)|Holes]]
* [[Torus|Toruses]]
* [[Torus]]es
* [[Alexander horned sphere]]
* [[Alexander horned sphere]]


==== [[Differential topology]] ====
==== [[Differential topology]] ====


* [[Differentiable manifold|Differentiable manifolds]]
* [[Differentiable manifold]]s
* [[Hairy ball theorem|Hairy balls]]
* [[Hairy ball theorem|Hairy balls]]


Revision as of 01:48, 15 October 2024

This is a list of mathematical objects, organized by branch.

List of mathematical objects by branch

Algebra

Elementary algebra

Linear algebra

Abstract algebra

Calculus and Mathematical Analysis

Nonstandard analysis

Differential equations

Category theory

Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects

Combinatorics

Computer science and Theoretical computer science

Geometry

Euclidian geometry

Fractal geometry

Graph theory

Mathematical logic

Number theory

Set theory

Topology

Algebraic topology

Differential topology

References

  1. ^ Hu, Sze-Tsen (1971) [1959]. "Chapter VII. Cohomotopy Groups" (PDF). Homotopy theory (PDF). Academic Press. pp. 205–228. LCCN 59-11526. Retrieved August 28, 2024.
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