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In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting o... | Wikipedia/Quotient_associative_algebra |
In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism is a function that preserves the underlying algebraic structure in the domain to its image.
When the algebraic structures involved have an underlying group struc... | Wikipedia/Kernel_(ring_theory) |
In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained in some other set. One may also call this "inclusion of classes".
That is, given classes A and B, A is a subclass of B if and only if every member of A is also ... | Wikipedia/Subclass_(set_theory) |
In mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] (the univariate polynomial ring with coefficients in F) has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it.
Every field
K
{... | Wikipedia/Algebraically_closed_field |
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector... | Wikipedia/Module_(algebra) |
Distributions, also known as Schwartz distributions are a kind of generalized function in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative.
Distributions ... | Wikipedia/Theory_of_distributions |
In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that a = a2 = a3 = a4 = ... = an for any positive integer n. For example, an idempot... | Wikipedia/Idempotent_element_(ring_theory) |
In mathematical analysis, a bump function (also called a test function) is a function
f
:
R
n
→
R
{\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} }
... | Wikipedia/Test_function |
In mathematics, a group action of a group
G
{\displaystyle G}
on a set
S
{\displaystyle S}
is a group homomorphism from
G
{\displaystyle G}
to some group (under function composition) of fu... | Wikipedia/Stabilizer_(group_theory) |
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over
Q
{\displaystyle \mathbb {Q} }
), simplic... | Wikipedia/Derived_algebraic_geometry |
In mathematics, Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic p. Artin and Schreier (1927) introduced Artin–Schreier theory for extensions of prime degree p, and Witt (1936) generalized ... | Wikipedia/Artin–Schreier_theory |
In mathematics, a function of
n
{\displaystyle n}
variables is symmetric if its value is the same no matter the order of its arguments. For example, a function
f
(
x
... | Wikipedia/Symmetric_function |
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An... | Wikipedia/Lattice_(order_theory) |
In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It provides, in the classical setting of field theory, an alternative perspective to that... | Wikipedia/Grothendieck's_Galois_theory |
The French Academy of Sciences (French: Académie des sciences, [akademi de sjɑ̃s]) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of scientific developments in Europe in the 17th an... | Wikipedia/Paris_Academy_of_Sciences |
In mathematics, differential Galois theory is the field that studies extensions of differential fields.
Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. fields that are equipped with a derivation, D. Much of the theory of ... | Wikipedia/Differential_Galois_theory |
In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by Vladimir Arnold and concerns the applications of some topological concepts to some problems in the field of Galois theory. It connects many ideas from algebra to ideas in... | Wikipedia/Topological_Galois_theory |
In mathematics, a derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law:
D
(
a
b
)
... | Wikipedia/Derivation_(differential_algebra) |
In algebra, the cofree coalgebra of a vector space or module is a coalgebra analog of the free algebra of a vector space. The cofree coalgebra of any vector space over a field exists, though it is more complicated than one might expect by analogy with the free algebra.
== Definition ==
If V is a vector space over a f... | Wikipedia/Cofree_coalgebra |
In mathematics, a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfeld category of a Hopf algebra H, particularly the Nichols algebra of a braided vector space in that category.
The notion should not be confused with quasitriangula... | Wikipedia/Braided_Hopf_algebra |
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which ar... | Wikipedia/Tensor_order |
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms i... | Wikipedia/Unital_algebra |
In mathematics, any vector space
V
{\displaystyle V}
has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on
V
,
{\displaystyle V,}
together with the vector space structure of p... | Wikipedia/Duality_(linear_algebra) |
In mathematics, coalgebras or cogebras are structures that are dual (in the category-theoretic sense of reversing arrows) to unital associative algebras. The axioms of unital associative algebras can be formulated in terms of commutative diagrams. Turning all arrows around, one obtains the axioms of coalgebras.
Every c... | Wikipedia/Coalgebra |
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Informa... | Wikipedia/Natural_transformation |
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication,... | Wikipedia/Order_(group_theory) |
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra... | Wikipedia/Modern_algebra |
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve problems ... | Wikipedia/Integral_calculus |
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric fu... | Wikipedia/Entire_function |
In linear algebra, an eigenvector ( EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector
v
{\displaystyle \mathbf {v} }
of a linear transformation
... | Wikipedia/Eigenvalue |
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated points, which are poles of the function. The term comes from the Greek meros (μέρος), meaning "part".
Every meromorphic function on D... | Wikipedia/Meromorphic_function |
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real anal... | Wikipedia/Analytic_function |
In mathematics, an algebraic extension is a field extension L/K such that every element of the larger field L is algebraic over the smaller field K; that is, every element of L is a root of a non-zero polynomial with coefficients in K. A field extension that is not algebraic, is said to be transcendental, and must cont... | Wikipedia/Algebraic_extension |
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x1/n).
All element... | Wikipedia/Elementary_function_(differential_algebra) |
The rank–nullity theorem is a theorem in linear algebra, which asserts:
the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and
the dimension of the domain of a linear transformation f is the sum of the rank of f (the dimension of the image of f) and the nullity of f (the dimension of... | Wikipedia/Fundamental_theorem_of_linear_algebra |
In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers
R
{\displaystyle \mathbb {R} }
, or a subset of
... | Wikipedia/Real_function |
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces... | Wikipedia/Affine_transformation |
In mathematics, an even function is a real function such that
f
(
−
x
)
=
f
(
x
)
{\displaystyle f(-x)=f(x)}
for every
x
{\displaystyle x}
in its domain. Simil... | Wikipedia/Odd_function |
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well... | Wikipedia/Continuously_differentiable_function |
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is i... | Wikipedia/Concave_function |
Graphic design is a profession, academic discipline and applied art that involves creating visual communications intended to transmit specific messages to social groups, with specific objectives. Graphic design is an interdisciplinary branch of design and of the fine arts. Its practice involves creativity, innovation a... | Wikipedia/Graphic_design |
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.
Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsic... | Wikipedia/Differential_geometry_of_surfaces |
Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization.
== Overview ==
Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in ... | Wikipedia/Statistical_graphics |
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e... | Wikipedia/Boolean-valued_function |
In mathematics, the term linear function refers to two distinct but related notions:
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine fun... | Wikipedia/Linear_function |
In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in its range for at least one point in its domain. It is a set-valued function with additional properties depending on context; some authors do not distinguish between set-... | Wikipedia/Multivalued_function |
In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following:
takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure),
returns a function as its result.
All other functions are firs... | Wikipedia/Higher-order_function |
In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form:
f
(
x
1
,... | Wikipedia/Integral_equation |
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics... | Wikipedia/Trigonometric_function |
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between varia... | Wikipedia/Plot_(graphics) |
The Method of Mechanical Theorems (Greek: Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving works of the ancient Greek polymath Archimedes. The Method takes the form of a letter from Archimedes to Eratosthenes, the chief librarian at the Library of Alexandr... | Wikipedia/The_Method_of_Mechanical_Theorems |
In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when f is the identity function, the equality f(x) = x is true for all values of x to which f can be applied.
... | Wikipedia/Identity_function |
A photograph (also known as a photo, or more generically referred to as an image or picture) is an image created by light falling on a photosensitive surface, usually photographic film or an electronic image sensor. The process and practice of creating such images is called photography.
Most photographs are now created... | Wikipedia/Photograph |
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as w... | Wikipedia/Complex-valued_function |
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as w... | Wikipedia/Function_of_a_complex_variable |
Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image).
Imaging technology is the application of materials and methods to create, preserve, or duplicate images.
Imaging science is a multidisciplinary field concerned with the generation, c... | Wikipedia/Imaging_science |
Information science is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. Practitioners within and outside the field study the application and the usage of knowledge in organizations in addi... | Wikipedia/Information_science |
In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of
n
{\displaystyle n}
. It is named after James Stirling, though a related but less pr... | Wikipedia/Stirling's_approximation |
In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers
R
{\displaystyle \mathbb {R} }
, or a subset of
... | Wikipedia/Function_of_a_real_variable |
In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative, all of which can be shown to be equivalent via trigonometric identities,
∫
sec
θ
d
θ
... | Wikipedia/Integral_of_the_secant_function |
In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of r... | Wikipedia/Related_rates |
Method of Fluxions (Latin: De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736.
== Background ==
Fluxion is Newton's term for a derivative. He originally... | Wikipedia/Method_of_Fluxions |
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is.
== Usage in science and engineering ==
In formal expressions, the ordinal number used before the word order refers to the highest power in the series expan... | Wikipedia/Order_of_approximation |
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function.
== General first order linear equations ==
The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form
... | Wikipedia/Integro-differential_equation |
In mathematics, an implicit equation is a relation of the form
R
(
x
1
,
…
,
x
n
)
=
0
,
{\d... | Wikipedia/Implicit_function |
In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange, particularly in manipulating infinite series. According to Koetsier, the generality o... | Wikipedia/Generality_of_algebra |
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into two or three major branches: the natural sciences (e.g., physics, chemistry, and biology), which study the physical world; and the social... | Wikipedia/Science |
Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real ... | Wikipedia/Scientific_modelling |
Infographics (a clipped compound of "information" and "graphics") are graphic visual representations of information, data, or knowledge intended to present information quickly and clearly. They can improve cognition by using graphics to enhance the human visual system's ability to see patterns and trends. Similar pur... | Wikipedia/Infographic |
User interface (UI) design or user interface engineering is the design of user interfaces for machines and software, such as computers, home appliances, mobile devices, and other electronic devices, with the focus on maximizing usability and the user experience. In computer or software design, user interface (UI) desig... | Wikipedia/User_interface_design |
In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real value... | Wikipedia/Function_of_several_real_variables |
In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain.
The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnecte... | Wikipedia/Integer-valued_function |
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral ... | Wikipedia/Infinitesimal_calculus |
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. Graphs are a visual representation of the relationship between varia... | Wikipedia/Surface_plot_(graphics) |
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function.
Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns... | Wikipedia/Limit_of_a_function |
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every point on its domain) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speak... | Wikipedia/Fundamental_theorem_of_calculus |
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the result that an incorrect conclusion may be derived from it.
Graphs may be misleading by being excessively complex or poorly constructed. Even when constructed to displ... | Wikipedia/Misleading_graph |
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory.
Set-v... | Wikipedia/Set-valued_function |
In mathematics, the epigraph or supergraph of a function
f
:
X
→
[
−
∞
,
∞
]
{\displaystyle f:X\to [-\infty ,\infty ]}
valued in the extended real numbers
[
−
∞
... | Wikipedia/Epigraph_(mathematics) |
Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus.
Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represe... | Wikipedia/Differential_geometry_of_curves |
In mathematics, the range of a function may refer to either the function's codomain or image. In some cases the codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function
f
:
X
→
Y
,... | Wikipedia/Range_of_a_function |
A graphic organizer, also known as a knowledge map, concept map, story map, cognitive organizer, advance organizer, or concept diagram, is a pedagogical tool that uses visual symbols to express knowledge and concepts through relationships between them.
The main purpose of a graphic organizer is to provide a visual aid ... | Wikipedia/Graphic_organizer |
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions.
The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algeb... | Wikipedia/Differential_(mathematics) |
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
In si... | Wikipedia/Convex_function |
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer scien... | Wikipedia/Differential_operator |
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
A drawing of a graph or network... | Wikipedia/Graph_drawing |
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition or natural domain of f. If S equals X, that is, if f is defined on every element in X, then ... | Wikipedia/Partial_function |
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Functions were originally the idealization of how a varying quantity depends on another quantity. For example, th... | Wikipedia/Bivariate_function |
In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in direct analogy to the definition that a continuous function between topologi... | Wikipedia/Measurable_function |
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices... | Wikipedia/Matrix_calculus |
Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules... | Wikipedia/Molecular_graphics |
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of
f
{\displaystyle f}
is denoted as
... | Wikipedia/Inverse_functions_and_differentiation |
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve.
The primary objects of study in differential calculus are the derivative of ... | Wikipedia/Differential_calculus |
In graph theory, a pseudoforest is an undirected graph in which every connected component has at most one cycle. That is, it is a system of vertices and edges connecting pairs of vertices, such that no two cycles of consecutive edges share any vertex with each other, nor can any two cycles be connected to each other b... | Wikipedia/Functional_graph |
Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
== Overview ==
Computer graphic... | Wikipedia/Computer_graphics_(computer_science) |
The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space
C
n
{\displaystyle \mathbb {C} ^{n}}
, that is, n-tupl... | Wikipedia/Function_of_several_complex_variables |
In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and B are any two pure elements of L and X and Y are any two pure elements of V, then
(
c
... | Wikipedia/Representation_of_a_Lie_superalgebra |
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.
== Definition ==
In formal terms, a directed graph is an ordered pair G = (V, A) where
V is a set whose elements are called vertices, no... | Wikipedia/Directed_graph |
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing the first four positive integers (
A
=
{
1
,
2
,
3
,
4
}
... | Wikipedia/Element_(set_theory) |
In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially ... | Wikipedia/Character_theory |
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