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The Unified Modeling Language (UML) is a general-purpose visual modeling language that is intended to provide a standard way to visualize the design of a system.
UML provides a standard notation for many types of diagrams which can be roughly divided into three main groups: behavior diagrams, interaction diagrams, and ... | Wikipedia/Unified_Modeling_Language |
In systems engineering, information systems and software engineering, the systems development life cycle (SDLC), also referred to as the application development life cycle, is a process for planning, creating, testing, and deploying an information system. The SDLC concept applies to a range of hardware and software con... | Wikipedia/Systems_development_life_cycle |
In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite data type, i.e., a data type formed by combining other types.
Two common classes of algebraic types are product types (i.e., tuples, and records) and sum types (i.e., tagged or disjoint unions... | Wikipedia/Algebraic_data_types |
In computer science, computational learning theory (or just learning theory) is a subfield of artificial intelligence devoted to studying the design and analysis of machine learning algorithms.
== Overview ==
Theoretical results in machine learning mainly deal with a type of inductive learning called supervised learn... | Wikipedia/Computational_learning_theory |
In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts, data, or entities that pertain to one, many, or all domains of discourse. More simply, an ontology is a way of showing the properties of a subject area and ... | Wikipedia/Ontology_(information_science) |
In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness, which refers to the input–output behavior of the algorithm: for each input it produces an output satisfying the specification.
Within the latter notion, partial c... | Wikipedia/Correctness_(computer_science) |
The waterfall model is a breakdown of developmental activities into linear sequential phases, meaning that each phase is passed down onto each other, where each phase depends on the deliverables of the previous one and corresponds to a specialization of tasks.
This approach is typical for certain areas of engineering d... | Wikipedia/Waterfall_model |
Rapid application development (RAD), also called rapid application building (RAB), is both a general term for adaptive software development approaches, and the name for James Martin's method of rapid development. In general, RAD approaches to software development put less emphasis on planning and more emphasis on an ad... | Wikipedia/Rapid_application_development |
Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processing, scientific visualization, algorithms and systems to extract or extrapolate knowledge from potentially noisy, structured, or unstructured data.
Data science also integrates domain knowledge fr... | Wikipedia/Data_science |
Digital physics is a speculative idea suggesting that the universe can be conceived of as a vast, digital computation device, or as the output of a deterministic or probabilistic computer program. The hypothesis that the universe is a digital computer was proposed by Konrad Zuse in his 1969 book Rechnender Raum (Calcul... | Wikipedia/Digital_physics |
Electroencephalography (EEG)
is a method to record an electrogram of the spontaneous electrical activity of the brain. The bio signals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex and allocortex. It is typically non-invasive, with the EEG electrodes plac... | Wikipedia/Electroencephalography |
Diploma in Computer Science, originally known as the Diploma in Numerical Analysis and Automatic Computing, was a conversion course in computer science offered by the University of Cambridge. It is equivalent to a master's degree in present-day nomenclature but the title diploma was retained for historic reasons, "dipl... | Wikipedia/Cambridge_Diploma_in_Computer_Science |
A functional specification (also, functional spec, specs, functional specifications document (FSD), functional requirements specification) in systems engineering and software development is a document that specifies the functions that a system or component must perform (often part of a requirements specification) (ISO/... | Wikipedia/Functional_specification |
An entity–relationship model (or ER model) describes interrelated things of interest in a specific domain of knowledge. A basic ER model is composed of entity types (which classify the things of interest) and specifies relationships that can exist between entities (instances of those entity types).
In software engineer... | Wikipedia/Entity–relationship_model |
Systems modeling or system modeling is the interdisciplinary study of the use of models to conceptualize and construct systems in business and IT development.
A common type of systems modeling is function modeling, with specific techniques such as the Functional Flow Block Diagram and IDEF0. These models can be extende... | Wikipedia/Systems_modeling |
Universal Systems Language (USL) is a systems modeling language and formal method for the specification and design of software and other complex systems. It was designed by Margaret Hamilton based on her experiences writing flight software for the Apollo program. The language is implemented through the 001 Tool Suite s... | Wikipedia/Universal_Systems_Language |
Capability Maturity Model Integration (CMMI) is a process level improvement training and appraisal program. Administered by the CMMI Institute, a subsidiary of ISACA, it was developed at Carnegie Mellon University (CMU). It is required by many U.S. Government contracts, especially in software development. CMU claims CM... | Wikipedia/Capability_Maturity_Model_Integration |
2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. It may refer to the branch of computer science that comprises such techniques or to the models themselves.
2D computer g... | Wikipedia/2D_computer_graphics |
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by ... | Wikipedia/Randomized_algorithms |
A metamodel is a model of a model, and metamodeling is the process of generating such metamodels. Thus metamodeling or meta-modeling is the analysis, construction, and development of the frames, rules, constraints, models, and theories applicable and useful for modeling a predefined class of problems. As its name impli... | Wikipedia/Metamodeling |
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the ... | Wikipedia/Signal_detection_theory |
A data model is an abstract model that organizes elements of data and standardizes how they relate to one another and to the properties of real-world entities. For instance, a data model may specify that the data element representing a car be composed of a number of other elements which, in turn, represent the color an... | Wikipedia/Data_model |
In mathematics, operator K-theory is a noncommutative analogue of topological K-theory for Banach algebras with most applications used for C*-algebras.
== Overview ==
Operator K-theory resembles topological K-theory more than algebraic K-theory. In particular, a Bott periodicity theorem holds. So there are only two K... | Wikipedia/Operator_K-theory |
In mathematics, algebraic L-theory is the K-theory of quadratic forms; the term was coined by C. T. C. Wall,
with L being used as the letter after K. Algebraic L-theory, also known as "Hermitian K-theory",
is important in surgery theory.
== Definition ==
One can define L-groups for any ring with involution R: the qu... | Wikipedia/L-theory |
In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician Gennadi Kasparov in 1980.
It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem... | Wikipedia/KK-theory |
Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the study of combinations of protons and neutrons is called nuclear physics.
The funda... | Wikipedia/High_energy_physics |
In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves on ... | Wikipedia/Derived_noncommutative_algebraic_geometry |
In mathematics, a linear algebraic group is a subgroup of the group of invertible
n
×
n
{\displaystyle n\times n}
matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation
... | Wikipedia/Linear_algebraic_group_action |
In mathematics, KR-theory is a variant of topological K-theory defined for spaces with an involution. It was introduced by Atiyah (1966), motivated by applications to the Atiyah–Singer index theorem for real elliptic operators.
== Definition ==
A real space is a defined to be a topological space with an involution. ... | Wikipedia/KR-theory |
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have
N
... | Wikipedia/Type_II_string_theory |
In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirze... | Wikipedia/Topological_K-theory |
In string theory, K-theory classification refers to a conjectured application of K-theory (in abstract algebra and algebraic topology) to superstrings, to classify the allowed Ramond–Ramond field strengths as well as the charges of stable D-branes.
In condensed matter physics K-theory has also found important applicati... | Wikipedia/K-theory_(physics) |
In mathematics, twisted K-theory (also called K-theory with local coefficients) is a variation on K-theory, a mathematical theory from the 1950s that spans algebraic topology, abstract algebra and operator theory.
More specifically, twisted K-theory with twist H is a particular variant of K-theory, in which the twist i... | Wikipedia/Twisted_K-theory |
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information.
Cohere... | Wikipedia/Algebraic_vector_bundle |
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homo... | Wikipedia/Extraordinary_cohomology_theory |
K Theory is an electronic hip-hop act by Dylan Lewman, which formerly included Dustin Musser and Malcolm Anthony. The group was founded by Dylan Lewman and Dustin Musser in 2011. They have created remixes for Flo Rida's "GDFR", Rich Homie Quan's "Flex" and Fetty Wap's "Trap Queen".
== Career ==
On January 10, 2017, f... | Wikipedia/K_Theory |
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geome... | Wikipedia/Vertex_operator_algebra |
In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation.
Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is additionally compatible with all the operations of the algebra, in... | Wikipedia/Quotient_(universal_algebra) |
In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space
H
{\displaystyle H}
, such that the functional sending an operator
T
{\displaystyle T}
... | Wikipedia/Weak_operator_topology |
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/An_algebra |
In algebra, a septic equation is an equation of the form
a
x
7
+
b
x
6
+
c
x
5
... | Wikipedia/Septic_function |
Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the development of mathematics. It involves determining either a numerical approximation or a closed-form expression of the roots of a univariate polynomial, i.e., determinin... | Wikipedia/Polynomial_root-finding_algorithms |
In mathematics, a generalized hypergeometric series is a power 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 analytic continuation... | Wikipedia/Generalized_hypergeometric_function |
In mathematics, Felix Klein's j-invariant or j function is a modular function of weight zero for the special linear group
SL
(
2
,
Z
)
{\displaystyle \operatorname {SL} (2,\mathbb {Z} )}
defined on the uppe... | Wikipedia/Elliptic_modular_function |
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fra... | Wikipedia/Rate_(mathematics) |
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.
More formally, let
U
{\displaystyle U}
and
V
{\displaystyle V}
be open subsets of
... | Wikipedia/Conformal_transformation |
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position... | Wikipedia/Coordinate_transformation |
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geom... | Wikipedia/Transformation_geometry |
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative to a fixed frame of reference or coordinate system (alibi meaning "being somewhere else at the same time"); and passive or alias transformations which leave point... | Wikipedia/Active_and_passive_transformation |
In mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.
Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and ... | Wikipedia/Transformation_(mathematics) |
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations a... | Wikipedia/Lorentz_transformations |
Computer-aided design (CAD) is the use of computers (or workstations) to aid in the creation, modification, analysis, or optimization of a design.: 3 This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database... | Wikipedia/Computer-aided_design |
In algebra, a quartic function is a function of the formα
f
(
x
)
=
a
x
4
+
b
x
3
+
c
... | Wikipedia/Biquadratic_function |
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of... | Wikipedia/Biquadratic_rational_function |
In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the complex numbers (or more generally over an algebraically closed field) as the product of two linear... | Wikipedia/Degenerate_conic |
In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra "2" has some following in the literatur... | Wikipedia/Two-element_Boolean_algebra |
In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete.
The countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators. Up to isomorphis... | Wikipedia/Cantor_algebra |
A mixed-signal integrated circuit is any integrated circuit that has both analog circuits and digital circuits on a single semiconductor die. Their usage has grown dramatically with the increased use of cell phones, telecommunications, portable electronics, and automobiles with electronics and digital sensors.
== Ove... | Wikipedia/Mixed-signal_integrated_circuit |
Tensor Processing Unit (TPU) is an AI accelerator application-specific integrated circuit (ASIC) developed by Google for neural network machine learning, using Google's own TensorFlow software. Google began using TPUs internally in 2015, and in 2018 made them available for third-party use, both as part of its cloud inf... | Wikipedia/Tensor_Processing_Unit |
Gottfried Wilhelm Leibniz (or Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithme... | Wikipedia/Algebra_of_concepts |
In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for... | Wikipedia/Algebra_of_sets |
Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions.
Boolean differential calculus concepts are analogous to those of classical differential calculus, notably studying the changes in functio... | Wikipedia/Boolean_differential_calculus |
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design.
Generally, the circuit is constrained to a minimum chip area meeting a... | Wikipedia/Circuit_minimization_for_Boolean_functions |
In electronic design, wire routing, commonly called simply routing, is a step in the design of printed circuit boards (PCBs) and integrated circuits (ICs). It builds on a preceding step, called placement, which determines the location of each active element of an IC or component on a PCB. After placement, the routing ... | Wikipedia/Routing_(electronic_design_automation) |
Placement is an essential step in electronic design automation — the portion of the physical design
flow that assigns exact locations for various circuit components within the chip's core area. An inferior placement assignment will not only affect the chip's performance but might also make it non-manufacturable by prod... | Wikipedia/Placement_(electronic_design_automation) |
In computer graphics and digital photography, a raster graphic, raster image, or simply raster is a two-dimensional image or picture represented as a rectangular matrix or grid of pixels, viewable via a computer display, paper, or other display medium. A raster image is technically characterized by the width and height... | Wikipedia/Raster_graphics |
An application-specific integrated circuit (ASIC ) is an integrated circuit (IC) chip customized for a particular use, rather than intended for general-purpose use, such as a chip designed to run in a digital voice recorder or a high-efficiency video codec. Application-specific standard product chips are intermediate b... | Wikipedia/Application-specific_integrated_circuit |
Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing electronic systems such as integrated circuits and printed circuit boards. The tools work together in a design flow that chip designers use to design and analyze entire semicond... | Wikipedia/Electronics_design |
Transaction-level modeling (TLM) is an approach to modelling complex digital systems by using electronic design automation software.: 1955 TLM language (TLML) is a hardware description language, usually, written in C++ and based on SystemC library. TLMLs are used for modelling where details of communication among modu... | Wikipedia/Transaction-level_modeling |
In computer engineering, logic synthesis is a process by which an abstract specification of desired circuit behavior, typically at register transfer level (RTL), is turned into a design implementation in terms of logic gates, typically by a computer program called a synthesis tool. Common examples of this process inclu... | Wikipedia/Logic_design |
The Philosophical Magazine is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798; in 1822 Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since.
== Early history ==
The name of the journal dates from a period w... | Wikipedia/The_London,_Edinburgh,_and_Dublin_Philosophical_Magazine_and_Journal_of_Science |
A three-dimensional integrated circuit (3D IC) is a MOS (metal-oxide semiconductor) integrated circuit (IC) manufactured by stacking as many as 16 or more ICs and interconnecting them vertically using, for instance, through-silicon vias (TSVs) or Cu-Cu connections, so that they behave as a single device to achieve perf... | Wikipedia/Three-dimensional_integrated_circuit |
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used f... | Wikipedia/Model_(logic) |
Computer-aided design (CAD) is the use of computers (or workstations) to aid in the creation, modification, analysis, or optimization of a design.: 3 This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database... | Wikipedia/Computer_aided_design |
A hybrid integrated circuit (HIC), hybrid microcircuit, hybrid circuit or simply hybrid is a miniaturized electronic circuit constructed of individual devices, such as semiconductor devices (e.g. transistors, diodes or monolithic ICs) and passive components (e.g. resistors, inductors, transformers, and capacitors), bon... | Wikipedia/Hybrid_integrated_circuit |
Switching circuit theory is the mathematical study of the properties of networks of idealized switches. Such networks may be strictly combinational logic, in which their output state is only a function of the present state of their inputs; or may also contain sequential elements, where the present state depends on the ... | Wikipedia/Switching_circuit_theory |
In set theory, inner model theory is the study of certain models of ZFC or some fragment or strengthening thereof. Ordinarily these models are transitive subsets or subclasses of the von Neumann universe V, or sometimes of a generic extension of V. Inner model theory studies the relationships of these models to determi... | Wikipedia/Inner_model_theory |
In mathematics, fuzzy sets (also known as uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set.
At the same time, Salii (1965) defined a more general kind of structure called an "L-relation",... | Wikipedia/Fuzzy_set_theory |
Evolutionary dynamics is the study of the mathematical principles according to which biological organisms as well as cultural ideas evolve and evolved. This is mostly achieved through the mathematical discipline of population genetics, along with evolutionary game theory. Most population genetics considers changes in t... | Wikipedia/Evolutionary_dynamics |
Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen. It starts from basic notions, including the ZFC axioms, and quickly develops combinatorial notions such as trees, Suslin's problem, the diamond principle, and Martin's axiom. It develops some basic model... | Wikipedia/Set_Theory:_An_Introduction_to_Independence_Proofs |
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/Mathematical_function |
In mathematics, a structural set theory is an approach to set theory that emphasizes the aspect of sets as abstract structures. It is in contrast to a more traditional ZFC set-theory, which emphasizes membership. A prime example is Lawvere's Elementary Theory of the Category of Sets, which identifies sets in terms of r... | Wikipedia/Structural_set_theory |
In mathematics, a topos (US: , UK: ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion of localization. The Grothendieck topoi find applications in algebr... | Wikipedia/Topos_theory |
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be a... | Wikipedia/Discontinuous_function |
Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980). Thus effective descriptive set theory combines descriptive set theory with recursion theory.
== Con... | Wikipedia/Effective_descriptive_set_theory |
In mathematics, a filter on a set
X
{\displaystyle X}
is a family
B
{\displaystyle {\mathcal {B}}}
of subsets such that:
X
∈
... | Wikipedia/Filter_(set_theory) |
In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in several areas by mathematicians and philosophers.
Cantor's theorem implies that there are sets having cardinality greater... | Wikipedia/Philosophical_objections_to_Cantor's_theory |
Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his "revolutionary discovery" that the set of all real numbers is uncountably, rather than countably, infinite. This theorem is proved using Cant... | Wikipedia/Cantor's_first_set_theory_article |
In computability theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory.
The central focus of hyp... | Wikipedia/Hyperarithmetical_theory |
In mathematical logic, an alternative set theory is any of the alternative mathematical approaches to the concept of set and any alternative to the de facto standard set theory described in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory.
== Alternative set theories ==
Alternative set theories inclu... | Wikipedia/Alternative_set_theory |
Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is his "revolutionary discovery" that the set of all real numbers is uncountably, rather than countably, infinite. This theorem is proved using Cant... | Wikipedia/On_a_Property_of_the_Collection_of_All_Real_Algebraic_Numbers |
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, where all data are represented in terms of tuples, grouped into relations. A database organized in terms of the relat... | Wikipedia/Relational_model |
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/calculus |
In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative... | Wikipedia/Moment-generating_function |
In probability and statistics, the quantile function is a function
Q
:
[
0
,
1
]
↦
R
{\displaystyle Q:[0,1]\mapsto \mathbb {R} }
which maps some probability
x
∈... | Wikipedia/Quantile_function |
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are often employed for their succinct description of the sequence of probabilitie... | Wikipedia/Probability-generating_function |
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes ... | Wikipedia/Conversion_of_units |
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemann... | Wikipedia/Gauss-Codazzi_equations |
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemann... | Wikipedia/Gauss–Codazzi_equations |
For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian).
For Liouville's equation in quantum mechanics, see Von Neumann equation.
For Liouville's equation in Euclidean space, see Liouville–Bratu–Gelfand equation.
In differential geometry, Liouville's equation, named after Joseph Liouville, ... | Wikipedia/Liouville's_equation |
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