Topics including "Gauss"

• Carl Friedrich Gauss Prize
  Carl Friedrich Gauss Prize
  The Carl Friedrich Gauss Prize for Applications of Mathematics is a mathematics award, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics". The award...
  
  , a mathematics award
• Degaussing
  Degaussing
  Degaussing is the process of decreasing or eliminating an unwanted magnetic field. It is named after Carl Friedrich Gauss, an early researcher in the field of magnetism...
  
  , to demagnetize an object
• Gauss (unit)
  Gauss (unit)
  The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B , named after the German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter; it equals 1 tesla...
  
  , a unit of magnetic field
  Magnetic field
  A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
  
   (B)
• Gauss–Bolyai–Lobachevsky space, a hyperbolic geometry
  Hyperbolic geometry
  In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
  
  
• Gauss–Bonnet theorem
  Gauss–Bonnet theorem
  The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry to their topology...
  
  , a theorem about curvature in differential geometry
• Gauss–Codazzi equations
  Gauss–Codazzi equations
  In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds...
  
  
• Gauss code
• Gauss–Hermite quadrature
• Gauss–Jacobi quadrature
• Gauss–Jordan elimination
  Gauss–Jordan elimination
  In linear algebra, Gauss–Jordan elimination is an algorithm for getting matrices in reduced row echelon form using elementary row operations. It is a variation of Gaussian elimination. Gaussian elimination places zeros below each pivot in the matrix, starting with the top row and working downwards....
  
  , a method in linear algebra
  Linear algebra
  Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
  
  
• Gauss–Kronrod quadrature formula
• Gauss–Kuzmin distribution, a discrete probability distribution
• Gauss–Kuzmin–Wirsing constant, a constant in number theory
  Number theory
  Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
  
  
• Gauss–Manin connection, a connection on a vector bundle over a family of algebraic varieties
• Gauss–Markov process
  Gauss–Markov process
  Gauss–Markov stochastic processes are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. The stationary Gauss–Markov process is a very special case because it is unique, except for some trivial exceptions...
  
  
• Gauss–Markov theorem
  Gauss–Markov theorem
  In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator of the coefficients is given by the...
  
  
• Gauss–Laplace pyramid, sometimes called the Burt–Adelson pyramid.
• Gauss' law for gravity
  Gauss' law for gravity
  In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics which is essentially equivalent to Newton's law of universal gravitation...
  
  
• Gauss linking integral (knot theory
  Knot theory
  In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
  
  )
• Gauss iterated map
  Gauss iterated map
  In mathematics, the Gauss map , is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:where α and β are real parameters....
  
   (dynamical systems)
• Gauss–Krüger coordinate system
• Gauss–Seidel method
• Gauss–Newton algorithm
• Gauss–Legendre algorithm
• Gauss–Lucas theorem
• Gauss' area formula
• Gauss' principle of least constraint
• Gauss's constant
  Gauss's constant
  In mathematics, Gauss's constant, denoted by G, is defined as the reciprocal of the arithmetic-geometric mean of 1 and the square root of 2:The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered thatso that...
  
  , the reciprocal
  Multiplicative inverse
  In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...
  
   of the AGM of 1 and , in number theory
  Number theory
  Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
  
  .
• Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions.
• Gauss's criterion
• Gauss's digamma theorem, a theorem about the digamma function.
• Gauss error function
  Error function
  In mathematics, the error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations...
  
  
• Gauss' generalization of Wilson's theorem.
• Gauss gun
• Gauss's hypergeometric theorem, an identity on hypergeometric series
  Hypergeometric series
  In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by...
  
  .
• Gauss's law
  Gauss's law
  In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:...
  
  , giving the relationship between flux
  Flux
  In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
  
   through a closed surface and the enclosed source.
• Gauss's law for magnetism
• Gauss's lemma
  Gauss's lemma (polynomial)
  In algebra, in the theory of polynomials , Gauss's lemma is either of two related statements about polynomials with integer coefficients:...
  
   in relation to polynomial
  Polynomial
  In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
  
  s
• Gauss's lemma
  Gauss's lemma (number theory)
  Gauss's lemma in number theory gives a condition for an integer to be a quadratic residue. Although it is not useful computationally, it has theoretical significance, being involved in some proofs of quadratic reciprocity....
  
   in number theory
  Number theory
  Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
  
  
• Gauss's lemma
  Gauss's lemma (Riemannian geometry)
  In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M...
  
   in Riemannian geometry
  Riemannian geometry
  Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...
  
  
• Gauss map
  Gauss map
  In differential geometry, the Gauss map maps a surface in Euclidean space R3 to the unit sphere S2. Namely, given a surface X lying in R3, the Gauss map is a continuous map N: X → S2 such that N is a unit vector orthogonal to X at p, namely the normal vector to X at p.The Gauss map can be defined...
  
  
• Gauss Peninsula
  Gauss Peninsula
  Gauss Peninsula is a peninsula in eastern Greenland. It is located on the coast of Greenland Sea in the Northeast Greenland National Park, between Muskusoksefjord and Kejser Franz Joseph Fjord.- History :...
  
  , East Greenland
• Gauss sum
  Gauss sum
  In mathematics, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typicallyG := G= \sum \chi\cdot \psi...
  
  , an exponential sum
  Exponential sum
  In mathematics, an exponential sum may be a finite Fourier series , or other finite sum formed using the exponential function, usually expressed by means of the functione = \exp.\,...
  
   over Dirichlet character
  Dirichlet character
  In number theory, Dirichlet characters are certain arithmetic functions which arise from completely multiplicative characters on the units of \mathbb Z / k \mathbb Z...
  
  s.
• Gauss' theorem may refer to the divergence theorem
  Divergence theorem
  In vector calculus, the divergence theorem, also known as Gauss' theorem , Ostrogradsky's theorem , or Gauss–Ostrogradsky theorem is a result that relates the flow of a vector field through a surface to the behavior of the vector field inside the surface.More precisely, the divergence theorem...
  
  , which is also known as the Ostrogradsky–Gauss theorem.
• Gauss composition
• Generalized Gauss–Bonnet theorem
• Gauss pseudospectral method
  Gauss pseudospectral method
  The Gauss pseudospectral method , one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program . The Gauss pseudospectral method differs from several other pseudospectral methods in that the...
  
  
• Gauss Tower
  Gauss Tower
  The Gauss Tower is a reinforced concrete observation tower on the summit of the High Hagens in Dransfeld, Germany. The tower can be reached directly by car...
  
  
• Gauss (ship)
  Gauss (ship)
  Gauss was a ship used for the Gauss expedition to Antarctica. led by Arctic veteran and geology professor Erich von Drygalski....
  
  
• Gaussberg
  Gaussberg
  Gaussberg is an extinct volcanic cone, 370 metres high , fronting on Davis Sea immediately west of the Posadowsky Glacier in Kaiser Wilhelm II Land in Antarctica....
  
  , or Mount Gauss, an extinct volcano in Antarctica
• The Gauss expedition, the first German expedition to Antarctica

Topics including "Gaussian"

• Additive white Gaussian noise
  Additive white Gaussian noise
  Additive white Gaussian noise is a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density and a Gaussian distribution of amplitude. The model does not account for fading, frequency selectivity, interference,...
  
  
• Gaussian beam
  Gaussian beam
  In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
  
  
• Gaussian binomial coefficient, also called Gaussian polynomial or Gaussian coefficient
• Gaussian blur
  Gaussian blur
  A Gaussian blur is the result of blurring an image by a Gaussian function. It is a widely used effect in graphics software, typically to reduce image noise and reduce detail...
  
  , a technique in image processing
  Image processing
  In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...
  
  .
• Gaussian bracket
• Gaussian copula
• Gaussian curvature
  Gaussian curvature
  In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way...
  
  
• Gaussian distribution, also named the Normal distribution, a type of probability distribution
  Probability distribution
  In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
  
  .
• Gaussian elimination
  Gaussian elimination
  In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix...
  
  
• Gaussian function related to the Gaussian distribution
• Gaussian filter
  Gaussian filter
  In electronics and signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters are designed to give no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian...
  
  
• Gaussian fixed point
  Gaussian fixed point
  A Gaussian fixed point is a fixed point of the renormalization group flow which is noninteracting in the sense that it is described by a free field theory. The word Gaussian comes from the fact that the probability distribution is Gaussian at the Gaussian fixed point. This means that Gaussian fixed...
  
  
• Gaussian free field
  Gaussian free field
  In probability theory and statistical mechanics, the Gaussian free field is a Gaussian random field, a central model of random surfaces . A nice survey is ....
  
  
• Gaussian graph
• Gaussian gravitational constant
  Gaussian gravitational constant
  The Gaussian gravitational constant is an astronomical constant first proposed by German polymath Carl Friedrich Gauss in his 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum , although he had already used the concept to great success in predicting the...
  
  
• Gaussian grid
  Gaussian grid
  A Gaussian grid is used in the earth sciences as a gridded horizontal coordinate system for scientific modeling on a sphere...
  
  
• Gaussian's modular arithmetic
  Modular arithmetic
  In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....
  
  
• Gaussian integer
  Gaussian integer
  In number theory, a Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. The Gaussian integers are a special case of the quadratic...
  
  
• Gaussian integral
  Gaussian integral
  The Gaussian integral, also known as the Euler-Poisson integral or Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.It is named after the German mathematician and...
  
  
• Gaussian isoperimetric inequality
• Gaussian measure
  Gaussian measure
  In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces...
  
  
• Gaussian model; see Variogram
  Variogram
  In spatial statistics the theoretical variogram 2\gamma is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z...
  
  
• Gaussian network model
  Gaussian network model
  The Gaussian network model is a representation of a biological macromolecule as an elastic mass-and-spring network to study, understand, and characterize mechanical aspects of its long-scale dynamics...
  
  
• Gaussian method
• Gaussian noise
  Gaussian noise
  Gaussian noise is statistical noise that has its probability density function equal to that of the normal distribution, which is also known as the Gaussian distribution. In other words, the values that the noise can take on are Gaussian-distributed. A special case is white Gaussian noise, in which...
  
  
• Gaussian optics
  Gaussian optics
  Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. In this approximation, trigonometric functions can...
  
  
• Gaussian orbital
  Gaussian orbital
  In computational chemistry and molecular physics, Gaussian orbitals are functions used as atomic orbitals in the LCAO method for the computation of electron orbitals in molecules and numerous properties that depend on these.- Rationale :The principal reason for the use of Gaussian basis functions...
  
  
• Gaussian period
  Gaussian period
  In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity. The periods permit explicit calculations in cyclotomic fields connected with Galois theory and with harmonic analysis . They are basic in the classical theory called cyclotomy...
  
  
• Gaussian polynomial; see Gaussian binomial coefficient
• Gaussian prime
• Gaussian process
  Gaussian process
  In probability theory and statistics, a Gaussian process is a stochastic process whose realisations consist of random values associated with every point in a range of times such that each such random variable has a normal distribution...
  
  
• Gaussian quadrature
  Gaussian quadrature
  In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration....
  
  
• Gaussian rational
  Gaussian rational
  In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers....
  
  
• Gaussian smoothing
• Gaussian surface
  Gaussian surface
  A Gaussian surface is a closed surface in three dimensional space through which the flux of an electromagnetic field is calculated. It is an arbitrary closed surface S=\partial V used in conjunction with Gauss's law in order to calculate the total enclosed electric charge by performing a surface...
  
  
• Gaussian year
  Gaussian year
  A Gaussian year is defined as 365.2568983 days. It was adopted by Carl Friedrich Gauss as the length of the sidereal year in his studies of the dynamics of the solar system.A slightly different value is now accepted as the length of the sidereal year,...
  
  
• Inverse Gaussian distribution
  Inverse Gaussian distribution
  | cdf = \Phi\left +\exp\left \Phi\left...
  
  , also known as the Wald distribution
• The GAUSSIAN software program
  GAUSSIAN
  Gaussian is a computational chemistry software program initially released in 1970 by John Pople and his research group at Carnegie-Mellon University as Gaussian 70. It has been continuously updated since then...
  
  

Gauss's proofs

• The quadratic reciprocity
  Quadratic reciprocity
  In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic which gives conditions for the solvability of quadratic equations modulo prime numbers...
  
   law
• The fundamental theorem of algebra
  Fundamental theorem of algebra
  The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root...
  
  
• Fermat polygonal number theorem
  Fermat polygonal number theorem
  In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers. That is, every positive number can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of...
  
   for n = 3

• Discovered and proved the theorema egregium
  Theorema Egregium
  Gauss's Theorema Egregium is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces...
  
  .

Gauss's identities

• Gauss multiplication formula may refer to the multiplication theorem
  Multiplication theorem
  In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a product of values; thus the name...
  
  .
• Gauss interpolation formula
• Gauss–Kummer series
• Gauss formula
• Gauss transformation
• Gauss's inequality
  Gauss's inequality
  In probability theory, Gauss's inequality gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode....
  
  
• Gauss theorems (two theorems) about the Euler function.
• Gauss test

Gauss conjectures

• The prime number theorem
  Prime number theorem
  In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
  
  
• Gauss–Kuzmin distribution, the distribution of integers in a continued fraction.
• Gauss circle problem
  Gauss circle problem
  In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centred at the origin and with radius r. The first progress on a solution was made by Carl Friedrich Gauss, hence its name....
  
  
• Gauss class number problem.
• Gauss made progress toward proving the Kepler conjecture
  Kepler conjecture
  The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...
  
  .