Flashcards: Functions and mappings

In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.

In mathematics, the Dirac delta function, or δ function, is a generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).

In mathematics, physics, and engineering, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).

In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

Exponential growth is a phenomenon that occurs when the growth rate of the value of a mathematical function is proportional to the function's current value, resulting in its growth with time being an exponential function.

Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration).

In geometry, curve sketching (or curve tracing) includes techniques that can be used to produce a rough idea of overall shape of a plane curve given its equation without computing the large numbers of points required for a detailed plot.

In mathematics, an empty function is a function whose domain is the empty set ∅.

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (, pages 171–172).

In mathematics, especially in singularity theory the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point.

3D projection is any method of mapping three-dimensional points to a two-dimensional plane.

In mathematics, Pfaffian functions are a certain class of functions introduced by Askold Georgevich Khovanskiǐ in the 1970s.

In mathematics, a constant function is a function whose (output) value is the same for every input value.

In mathematics, a partial function from X to Y (written as f: X ↛ Y) is a function f: X ′ → Y, for some subset X ′ of X.

A two-dimensional graph is a set of points in two-dimensional space.

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.

In mathematics, unimodality means possessing a unique mode.