CZ:Mathematics Workgroup/List of mathematical topics: Difference between revisions

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If you are looking for suggestions of articles to write, below you'll find some lists of mathematical topics from Wikipedia. This does ''not'' imply any particular priority. However, it is possible that some readers may find useful what is listed below.
If you are looking for suggestions of articles to write, below you'll find some lists of mathematical topics from Wikipedia. This does ''not'' imply any particular priority. These lists are meant to be neither very systematic nor exhaustive. It is possible, however, that the articles listed below would be of some interest for potential readers.


==[[Calculus]] topics==
==[[Calculus]] topics==
''Note:''' the ordering of topics in sections is a suggestion to students.


===Before calculus ([[precalculus]])===
===Before calculus ([[precalculus]])===
*[[Graph of a function]]
*[[Graph of a function]]
*[[Linear function]]
*[[Linear function]]
*[[Secant]]
**[[Slope]]
*[[Slope]]
*[[Quadratic function]]
*[[Tangent]]
*[[Rational function]]
*[[Exponential function]]
*[[Trigonometric function|Trigonometry]]
**[[Radian]]
**[[Tangent]]
**[[Secant]]
*[[Concavity]]
*[[Concavity]]
*[[Finite difference]]
*[[Finite difference]]
*[[Radian]]
*[[Factorial]]
*[[Factorial]]
*[[Binomial theorem]]
*[[Binomial theorem]]
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**[[Linearity of integration]]
**[[Linearity of integration]]
*[[Arbitrary constant of integration]]
*[[Arbitrary constant of integration]]
*[[Fundamental theorem of calculus]]
*[[Fundamental Theorem of Calculus]]
*[[Integration by parts]]
*[[Integration by parts]]
*[[Inverse chain rule method]]
*[[Inverse chain rule method]]
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==[[Geometry]] topics==
*[[Geometric shape]] covers standard terms for plane shapes
*[[List of mathematical shapes]] covers all dimensions
*[[List of differential geometry topics]]
*[[List of geometers]]
*See also [[list of curves]], [[list of curve topics]].
*[[Synthetic geometry]]
*[[Transformation geometry]]
=== [[Euclidean geometry]], foundations===
*[[Hilbert's axioms]]
*[[Point (geometry)]]
*[[Locus (mathematics)]]
*[[Line (mathematics)|Line]]
*[[Parallel (geometry)]]
*[[Angle]]
**[[Concurrent lines]]
**[[Adjacent angles]]
**[[Central angle]]
**[[Complementary angles]]
**[[Inscribed angle]]
**[[Internal angle]]
**[[Supplementary angles]]
**[[compass and straightedge#Angle trisection|Trisecting the angle]]
*[[Congruence (geometry)|Congruence]]
**[[Reflection (mathematics)|Reflection]]
**[[Rotation]]
**[[Coordinate rotations and reflections]]
**[[Translation (geometry)|Translation]]
**[[Glide reflection]]
*[[Similarity (mathematics)]]
**[[Similarity transformation]]
**[[Homothety]]
*[[Shear]]
==== Euclidean [[plane geometry]] ====
*[[2D computer graphics]]
*[[2D geometric model]]
*[[Altitude (triangle)]]
*[[Brahmagupta's formula]]
*[[Compass and straightedge constructions]]
**[[Squaring the circle]]
*[[Complex geometry]]
*[[Conic section]]
**[[Focus (geometry)]]
**[[Circle]]
***[[List of circle topics]]
***[[Thales' theorem]]
***[[Circumcircle]]
***[[Concyclic]]
***[[Incircle and excircles of a triangle]]
***[[Orthocentric system]]
***[[Power center]]
***[[Nine-point circle]]
***[[Circle points segments proof]]
***[[Mrs. Miniver's problem]]
***[[Isoperimetric theorem]]
***[[Annulus]]
***[[Ptolemaios' theorem]]
**[[Eccentricity (mathematics)|Eccentricity]]
**[[Ellipse]]
***[[Semi-major axis]]
**[[Hyperbola]]
**[[Parabola]]
**[[Matrix representation of conic sections]]
**[[Dandelin spheres]]
*[[Coordinate notation]]
*[[Curve of constant width]]
*[[Cyclic quadrilateral]]
*[[Euler's line]]
*[[Equilateral triangle]]
*[[Frieze group]]
*[[Golden angle]]
*[[Heron's formula]]
**[[Heronian triangle]]
*[[Holditch's theorem]]
*[[Interactive geometry software]]
*[[Pappus's theorem]]
*[[Parallel postulate]]
*[[Pedal triangle]]
*[[Polygon]]
**[[Star polygon]]
**[[Pick's theorem]]
**[[Shape dissection]]
**[[Bolyai-Gerwien theorem]]
**[[Poncelet-Steiner theorem]]
**[[Polygon triangulation]]
*[[Pons asinorum]]
*[[Pythagorean triangle]]
*[[Sangaku]]
*[[Straightedge]]
*[[Symmedian]]
*[[Tiling]]
**[[Prototile]]
**[[Tessellation]]
**[[Aperiodic tiling]]
***[[Wang tile]]
***[[Penrose tiling]]
*[[Trapezoid]], [[trapezium]]
**[[Isosceles trapezoid]]
*[[Triangle (geometry)|Triangle]]
**[[Pythagorean theorem]]
**[[Triangle inequality]]
**[[Pedoe's inequality]]
*[[Trigonometric function|Trigonometry]]
**[[List of trigonometry topics]]
*[[Wallpaper group]]
==== 3-dimensional Euclidean geometry ([[solid geometry]])====
*[[3D projection]]
*[[3D computer graphics]]
**[[Binary space partitioning]]
**[[Ray tracing]]
**[[Graham scan]]
*[[Borromean rings]]
*[[Cross section (geometry)|Cross section]]
*[[Crystal]]
*[[Cuisenaire rods]]
*[[Desargues' theorem]]
*[[Right circular cone]]
*[[Hyperboloid]]
*[[Paraboloid]]
*[[Polyhedron]]
**[[Defect (geometry)]]
**[[Dihedral angle]]
**[[Prism (geometry)|Prism]]
**[[Prismatoid]]
**[[Honeycomb]]
**[[Pyramid (geometry)]]
**[[Parallelepiped]]
**[[Tetrahedron]]
***[[Heronian tetrahedron]]
**[[Platonic solid]]
**[[Archimedean solid]]
**[[Kepler-Poinsot polyhedra]]
**[[Johnson solid]]
**[[Uniform polyhedron]]
**[[Polyhedral compound]]
**[[Hilbert's third problem]]
**[[Deltahedron]]
**[[Surface normal]]
*[[3-sphere]], [[spheroid]], [[ellipsoid]]
**[[Parabolic microphone]]
**[[Parabolic reflector]]
*[[Soddy's hexlet]]
*[[Sphericon]]
*[[Stereographic projection]]
*[[Stereometry]]
==== ''n''-dimensional Euclidean geometry ====
*[[Ball (mathematics)#Geometry|Ball]]
*[[:Category:Convex geometry|Convex]]
**[[Convex hull]]
*[[Coxeter group]]
*[[Euclidean distance]]
*[[Hyperplane]]
*[[Lattice (group)|Lattice]]
**[[Ehrhart polynomial]]
**[[Leech lattice]]
**[[Minkowski's theorem]]
*[[Packing and covering]]
**[[Sphere packing]]
***[[Kepler conjecture]]
***[[Kissing number problem]]
**[[Tiling]]
***[[Andreini tessellation]]
***[[Uniform tessellation]]
***[[Voronoi tessellation]]
***[[Delaunay triangulation]]
***[[Quasicrystal]]
*[[Parallelogram law]]
*[[Polytope]]
**[[Schläfli symbol]]
**[[Regular polytope]]
**''[[Regular Polytopes (book)]]''
*[[Sphere]]
*[[Quadric]]
**[[Hypersphere]], [[sphere]]
**[[Spheroid]]
**[[Ellipsoid]]
**[[Hyperboloid]]
**[[Paraboloid]]
**[[Cone (geometry)]]
*[[Torus]]
*[[Root system]]
*[[Similarity (mathematics)]]
*[[Zonotope]]
=== Non-Euclidean geometry ===
*[[Projective geometry]]
**[[Desargues' theorem]]
**[[Girard Desargues]]
**[[Desarguesian plane]]
**[[Line at infinity]]
**[[Point at infinity]]
**[[Plane at infinity]]
**[[Hyperplane at infinity]]
**[[Projective line]]
**[[Projective plane]]
***[[Roman surface]]
**[[Projective space]]
**[[Complex projective line]]
**[[Complex projective plane]]
**[[Fundamental theorem of projective geometry]]
**[[Projective transformation]]
***[[Möbius transformation]]
**[[Cross-ratio]]
**[[Duality (projective geometry)]]
**[[Homogeneous coordinates]]
**[[Pappus's hexagon theorem]]
**[[Incidence (geometry)]]
**[[Pascal's theorem]]
*[[Affine geometry]]
**[[Affine space]]
**[[Affine transformation]]
*[[Finite geometry]]
*[[Differential geometry]]
**[[Contact geometry]]
**[[Riemannian geometry]]
**[[Symplectic geometry]]
*[[Non-Euclidean geometry|Non-Euclidean plane geometry]]
*[[Angle excess]]
*[[Hyperbolic geometry]]
**[[Pseudosphere]]
**[[Tractricoid]]
*[[Elliptic geometry]]
**[[Spherical geometry]]
*[[Minkowski space]]
*[[Thurston's conjecture]]
=== Numerical geometry ===
* [[Curve interpolation]]
* [[Parametric curve]]
** [[Bezier curve]]
** [[Spline (mathematics)|Spline]]
***[[Hermite spline]]
****[[Beta spline]]
*****[[B-spline]]
***[[Higher-order spline]]
***[[NURBS]]
* [[Parametric surface]]
** [[Parametric patch]]
===Geometric algorithms===
* [[Convex hull]] construction
* [[Point in polygon]]
* [[Point location]]
* [[Hidden line removal]]
===[[Mathematical morphology]]===
* [[Minkowski addition]]
===Generalizations===
*[[Noncommutative geometry]]
*[[Topology]]
=== Various ===
*[[Chirality (mathematics)|Chirality]]
**[[Handedness]]
**[[Left and right]]
**[[Mirror image]]
*[[Erlangen program]]
*[[Four dimensions]]
*[[Group action]], [[invariant]]
*[[Hadwiger's theorem]]
*[[Infinitesimal transformation]]
*[[List of terms based on the word cube]]
*[[Pi]]
*[[Symmetry]], [[shape]], [[pattern]]
**[[Crystal system]]
**[[Frieze group]]
**[[Isometry]]
**[[Lattice (group)]]
**[[Point group]]
**[[Point groups in two dimensions]]
**[[Point groups in three dimensions]]
**[[Space group]]
**[[Symmetry group]]
**[[Translational symmetry]]
**[[Wallpaper group]]
==[[Lie group]] topics==
===Examples===
''See [[Table of Lie groups]] for a list''
*[[General linear group]], [[special linear group]]
*[[Unitary group]], [[special unitary group]]
**[[SU(2)]]
**[[SU(3)]]
*[[Orthogonal group]], [[special orthogonal group]]
**[[Rotation group]] = [[SO(3)]]
**[[SO(8)]]
**[[Generalized orthogonal group]], [[generalized special orthogonal group]]
***The special unitary group SU(1,1) is the unit sphere in the ring of [[coquaternion]]s.It is the group of [[hyperbolic motion]]s of the Poincare disk model of the [[hyperbolic plane]].
***[[Lorentz group]]
**[[Spinor group]]
*[[Symplectic group]]
*Exceptional groups
**[[G2 (mathematics)|G<sub>2</sub>]]
**[[F4 (mathematics)|F<sub>4</sub>]]
**[[E6 (mathematics)|E<sub>6</sub>]]
**[[E7 (mathematics)|E<sub>7</sub>]]
**[[E8 (mathematics)|E<sub>8</sub>]]
*[[Affine group]]
*[[Euclidean group]]
*[[Poincaré group]]
*[[Heisenberg group]]
===[[Lie algebra]]s===
*[[Commutator]]
*[[Jacobi identity]]
*[[Universal enveloping algebra]]
*[[Campbell-Hausdorff formula]]
*[[Casimir invariant]]
*[[Kac-Moody algebra]]
*[[Affine Lie algebra]]
*[[Loop algebra]]
===Foundational results===
*[[One-parameter group]], [[One-parameter subgroup]]
*[[Matrix exponential]]
*[[Infinitesimal transformation]]
*[[Maurer-Cartan form]]
*[[Cartan's theorem]]
*[[Hausdorff paradox]]
*[[Local Lie group]]
*[[Formal group law]]
*[[Hilbert's fifth problem]]
*[[Hilbert-Smith conjecture]]
*[[Lie group decompositions]]
===Semisimple theory===
*[[Simple Lie group]], [[compact Lie group]]
*[[Root system]]
*[[Simply laced group]]
**[[ADE classification]]
*[[Maximal torus]]
*[[Weyl group]]
*[[Dynkin diagram]]
*[[Coxeter group]]
===Representation theory===
''See also'': [[List of harmonic analysis and representation theory topics]]
*[[Representation of a Lie group]]
*[[Representation of a Lie algebra]]
*[[Adjoint representation]]
*[[Adjoint representation of a Lie algebra]]
*[[Unitary representation]]
*[[Weight (representation theory)|Weight]]
*[[Peter-Weyl theorem]]
*[[Kirillov character formula]]
===Applications===
====Physical theories====
*[[Pauli matrices]]
*[[Gell-Mann matrices]]
*[[Poisson bracket]]
*[[Noether's theorem]]
*[[Wigner's classification]]
*[[Gauge theory]]
*[[Grand unification theory]]
*[[Supergroup (physics)|Supergroup]]
*[[Lie superalgebra]]
*[[Twistor]]
*[[Anyon]]
*[[Witt algebra]]
*[[Virasoro algebra]]
====Geometry====
*[[Erlangen programme]]
*[[Homogeneous space]]
**[[Principal homogeneous space]]
*[[Invariant theory]]
*[[Lie derivative]]
*[[Lie groupoid]]
*[[Lie algebroid]]
====[[Discrete group]]s====
*[[Lattice (group)]]
*[[Frieze group]]
*[[Wallpaper group]]
*[[Space group]]
*[[Crystallographic group]]
*[[Fuchsian group]]
*[[Modular group]]
*[[Congruence subgroup]]
*[[Kleinian group]]
*[[Discrete Heisenberg group]]
*[[Clifford-Klein form]]
====[[Algebraic group]]s====
*[[Borel subgroup]]
*[[Parabolic subgroup]]
*[[Arithmetic group]]
===[[Special function]]===
*[[Dunkl operator]]
====Automorphic forms====
*[[Modular form]]
*[[Langlands program]]
===People===
*[[Sophus Lie]] (1842 &ndash; 1899)
*[[Wilhelm Killing]] (1847 &ndash; 1923)
*[[Élie Cartan]] (1869 &ndash; 1951)
*[[Hermann Weyl]] (1885 &ndash; 1955)
*[[Izrael Gelfand]] (1913 &ndash; )
*[[Harish Chandra]]  (1923 &ndash;  1983)
*[[Armand Borel]]  (1923 &ndash; 2003)
*[[Robert Langlands]]  (1936 &ndash; )




[[Category:Mathematics Workgroup]]
[[Category:Mathematics Workgroup]]

Latest revision as of 09:05, 16 December 2024

If you are looking for suggestions of articles to write, below you'll find some lists of mathematical topics from Wikipedia. This does not imply any particular priority. These lists are meant to be neither very systematic nor exhaustive. It is possible, however, that the articles listed below would be of some interest for potential readers.

Calculus topics

Before calculus (precalculus)

Limits

Differential calculus

Integral calculus

Special functions and numbers

Numerical integration

See also list of numerical analysis topics

Lists and tables

Multivariable

Series

History

Nonstandard calculus

For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics.


Geometry topics

Euclidean geometry, foundations

Euclidean plane geometry

3-dimensional Euclidean geometry (solid geometry)

n-dimensional Euclidean geometry

Non-Euclidean geometry

Numerical geometry

Geometric algorithms

Mathematical morphology

Generalizations

Various

Lie group topics

Examples

See Table of Lie groups for a list

Lie algebras

Foundational results

Semisimple theory

Representation theory

See also: List of harmonic analysis and representation theory topics

Applications

Physical theories

Geometry

Discrete groups

Algebraic groups

Special function

Automorphic forms

People

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