CZ:Mathematics Workgroup/List of mathematical topics: Difference between revisions
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imported>Greg Martin m (→Integral calculus: capitalized "Fundamental Theorem of Calculus") |
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Latest revision as of 09:51, 4 October 2013
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)
- Graph of a function
- Linear function
- Quadratic function
- Rational function
- Exponential function
- Trigonometry
- Concavity
- Finite difference
- Factorial
- Binomial theorem
- Free variables and bound variables
Limits
- Limit of a sequence
- Upper limit, Lower limit
- Limit of a function
- Indeterminate form
- Orders of approximation
- Trigonometric rational function
Differential calculus
- Derivative
- Notations
- Simplest rules
- Derivative (examples)
- Chain rule
- Product rule
- Quotient rule
- Inverse functions and differentiation
- Implicit differentiation
- Stationary point
- Differential equation
- Differential operator
- Newton's method
- Taylor's theorem
- L'Hopital's rule
- Leibniz's rule
- Mean value theorem
- Logarithmic derivative
- Differential (calculus)
- Related rates
Integral calculus
- Antiderivative, Indefinite integral
- Simplest rules
- Arbitrary constant of integration
- Fundamental Theorem of Calculus
- Integration by parts
- Inverse chain rule method
- Substitution rule
- Differentiation under the integral sign
- Trigonometric substitution
- Partial fractions in integration
- A simple proof that 22/7 exceeds pi|A simple proof that 22/7 exceeds π
- Trapezium rule
Special functions and numbers
- Natural logarithm
- E (mathematical constant)
- Exponential function
- Stirling's approximation
- Bernoulli numbers
Numerical integration
See also list of numerical analysis topics
Lists and tables
- Table of common limits
- Table of derivatives
- Table of integrals
- Table of mathematical symbols
- List of integrals
- List of integrals of rational functions
- List of integrals of irrational functions
- List of integrals of trigonometric functions
- List of integrals of hyperbolic functions
- List of integrals of exponential functions
- List of integrals of logarithmic functions
- List of integrals of arc functions
- List of integrals of area functions
Multivariable
- Partial derivative
- Disk integration
- Shell integration
- Gabriel's horn
- Jacobian matrix
- Hessian matrix
- Curvature
- Green's theorem
- Divergence theorem
- Stokes' theorem
Series
History
- Infinitesimal
- Gottfried Leibniz
- Isaac Newton
- Method of Fluxions
- Infinitesimal calculus
- Brook Taylor
- Colin Maclaurin
- Leonhard Euler
Nonstandard calculus
For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics.
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.
Euclidean geometry, foundations
- Hilbert's axioms
- Point (geometry)
- Locus (mathematics)
- Line
- Parallel (geometry)
- Angle
- Congruence
- Similarity (mathematics)
- Shear
Euclidean plane geometry
- 2D computer graphics
- 2D geometric model
- Altitude (triangle)
- Brahmagupta's formula
- Compass and straightedge constructions
- Complex geometry
- Conic section
- Coordinate notation
- Curve of constant width
- Cyclic quadrilateral
- Euler's line
- Equilateral triangle
- Frieze group
- Golden angle
- Heron's formula
- Holditch's theorem
- Interactive geometry software
- Pappus's theorem
- Parallel postulate
- Pedal triangle
- Polygon
- Pons asinorum
- Pythagorean triangle
- Sangaku
- Straightedge
- Symmedian
- Tiling
- Trapezoid, trapezium
- Triangle
- Trigonometry
- Wallpaper group
3-dimensional Euclidean geometry (solid geometry)
- 3D projection
- 3D computer graphics
- Borromean rings
- Cross section
- Crystal
- Cuisenaire rods
- Desargues' theorem
- Right circular cone
- Hyperboloid
- Paraboloid
- Polyhedron
- 3-sphere, spheroid, ellipsoid
- Soddy's hexlet
- Sphericon
- Stereographic projection
- Stereometry
n-dimensional Euclidean geometry
- Ball
- Convex
- Coxeter group
- Euclidean distance
- Hyperplane
- Lattice
- Packing and covering
- Parallelogram law
- Polytope
- Sphere
- Quadric
- 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
- Projective space
- Complex projective line
- Complex projective plane
- Fundamental theorem of projective geometry
- Projective transformation
- Cross-ratio
- Duality (projective geometry)
- Homogeneous coordinates
- Pappus's hexagon theorem
- Incidence (geometry)
- Pascal's theorem
- Affine geometry
- Finite geometry
- Differential geometry
- Non-Euclidean plane geometry
- Angle excess
- Hyperbolic geometry
- Elliptic geometry
- Minkowski space
- Thurston's conjecture
Numerical geometry
Geometric algorithms
- Convex hull construction
- Point in polygon
- Point location
- Hidden line removal
Mathematical morphology
Generalizations
Various
- Chirality
- Erlangen program
- Four dimensions
- Group action, invariant
- Hadwiger's theorem
- Infinitesimal transformation
- List of terms based on the word cube
- Pi
- Symmetry, shape, pattern
Lie group topics
Examples
See Table of Lie groups for a list
- General linear group, special linear group
- Unitary group, special unitary group
- 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 coquaternions.It is the group of hyperbolic motions of the Poincare disk model of the hyperbolic plane.
- Lorentz group
- Spinor group
- Symplectic group
- Exceptional groups
- Affine group
- Euclidean group
- Poincaré group
- Heisenberg group
Lie algebras
- 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
- 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
- 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
- Lie superalgebra
- Twistor
- Anyon
- Witt algebra
- Virasoro algebra
Geometry
Discrete groups
- 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 groups
Special function
Automorphic forms
People
- Sophus Lie (1842 – 1899)
- Wilhelm Killing (1847 – 1923)
- Élie Cartan (1869 – 1951)
- Hermann Weyl (1885 – 1955)
- Izrael Gelfand (1913 – )
- Harish Chandra (1923 – 1983)
- Armand Borel (1923 – 2003)
- Robert Langlands (1936 – )