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

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imported>Aleksander Stos
(geometry)
imported>Aleksander Stos
(lie groups added)
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==[[Calculus]] topics==
==[[Calculus]] topics==
''Note:''' the ordering of topics in sections is a suggestion to students.


===Before calculus ([[precalculus]])===
===Before calculus ([[precalculus]])===
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**[[Wallpaper group]]
**[[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 functions]]===
*[[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]]

Revision as of 14:10, 15 March 2007

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 functions

Automorphic forms

People

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