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12,800 | Decision analysis Decision theory Derived noncommutative algebraic geometry Descriptive set theory a part of mathematical logic, more specifically a part of set theory dedicated to the study of Polish spaces. Differential algebraic geometry the adaption of methods and concepts from algebraic geometry to systems of alge... | Glossary of areas of mathematics | 0.816687 |
12,801 | Contact geometry a branch of differential geometry and topology, closely related to and considered the odd-dimensional counterpart of symplectic geometry. It is the study of a geometric structure called a contact structure on a differentiable manifold. Convex analysis the study of properties of convex functions and con... | Glossary of areas of mathematics | 0.816687 |
12,802 | Constructive quantum field theory a branch of mathematical physics that is devoted to showing that quantum theory is mathematically compatible with special relativity. Constructive set theory an approach to mathematical constructivism following the program of axiomatic set theory, using the usual first-order language o... | Glossary of areas of mathematics | 0.816687 |
12,803 | Computational geometry a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Computational group theory the study of groups by means of computers. Computational mathematics the mathematical research in areas of science where computing plays an essential role. | Glossary of areas of mathematics | 0.816687 |
12,804 | Computability theory a branch of mathematical logic originating in the 1930s with the study of computable functions and Turing degrees, but now includes the study of generalized computability and definability. It overlaps with proof theory and effective descriptive set theory. Computational algebraic geometry Computati... | Glossary of areas of mathematics | 0.816687 |
12,805 | Complex geometry the study of complex manifolds and functions of complex variables. It includes complex algebraic geometry and complex analytic geometry. Complexity theory the study of complex systems with the inclusion of the theory of complex systems. | Glossary of areas of mathematics | 0.816687 |
12,806 | Complex analytic geometry the application of complex numbers to plane geometry. Complex differential geometry a branch of differential geometry that studies complex manifolds. Complex dynamics the study of dynamical systems defined by iterated functions on complex number spaces. | Glossary of areas of mathematics | 0.816687 |
12,807 | Complex algebraic geometry the mainstream of algebraic geometry devoted to the study of the complex points of algebraic varieties. Complex analysis a part of analysis that deals with functions of a complex variable. Complex analytic dynamics a subdivision of complex dynamics being the study of the dynamic systems defin... | Glossary of areas of mathematics | 0.816687 |
12,808 | Combinatorics a branch of discrete mathematics concerned with countable structures. Branches of it include enumerative combinatorics, combinatorial design theory, matroid theory, extremal combinatorics and algebraic combinatorics, as well as many more. Commutative algebra a branch of abstract algebra studying commutati... | Glossary of areas of mathematics | 0.816687 |
12,809 | Combinatorial mathematics an area primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Combinatorial number theory Combinatorial optimization Combinatorial set theory also known as Infinitary combinatorics. see infinitary combinatorics Combinat... | Glossary of areas of mathematics | 0.816687 |
12,810 | Combinatorial design theory a part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have certain properties. Combinatorial game theory Combinatorial geometry see discrete geometry Combinatorial group theory the theory of free groups and the presen... | Glossary of areas of mathematics | 0.816687 |
12,811 | It frequently employs methods from one to address problems arising in the other. Polyhedral geometry also plays a significant role. | Glossary of areas of mathematics | 0.816687 |
12,812 | see Euclidean differential geometry. Classical algebraic topology see algebraic topology Classical analysis usually refers to the more traditional topics of analysis such as real analysis and complex analysis. It includes any work that does not use techniques from functional analysis and is sometimes called hard analys... | Glossary of areas of mathematics | 0.816687 |
12,813 | Character theory a branch of group theory that studies the characters of group representations or modular representations. Class field theory a branch of algebraic number theory that studies abelian extensions of number fields. Classical differential geometry also known as Euclidean differential geometry. | Glossary of areas of mathematics | 0.816687 |
12,814 | Catastrophe theory a branch of bifurcation theory from dynamical systems theory, and also a special case of the more general singularity theory from geometry. It analyses the germs of the catastrophe geometries. Categorical logic a branch of category theory adjacent to the mathematical logic. | Glossary of areas of mathematics | 0.816687 |
12,815 | Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. | Glossary of areas of mathematics | 0.816687 |
12,816 | C*-algebra theory a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties-(i) A is a topologically closed set in the norm topology of operators. (ii)A is closed under the operation of taking adjoints of operators. Cartesian geometry see analytic geometry Calculus An ... | Glossary of areas of mathematics | 0.816687 |
12,817 | Analogue to differential geometry, where differentiable functions are replaced with analytic functions. It is a subarea of both complex analysis and algebraic geometry. Analytic number theory An area of number theory that applies methods from mathematical analysis to solve problems about integers. | Glossary of areas of mathematics | 0.816687 |
12,818 | Analytic geometry 1. Also known as Cartesian geometry, the study of Euclidean geometry using Cartesian coordinates. 2. | Glossary of areas of mathematics | 0.816687 |
12,819 | Algebraic topology a branch that uses tools from abstract algebra for topology to study topological spaces. Algorithmic number theory also known as computational number theory, it is the study of algorithms for performing number theoretic computations. Anabelian geometry an area of study based on the theory proposed by... | Glossary of areas of mathematics | 0.816687 |
12,820 | Algebraic K-theory an important part of homological algebra concerned with defining and applying a certain sequence of functors from rings to abelian groups. Algebraic number theory The part of number theory devoted to the use of algebraic methods, mainly those of commutative algebra, for the study of number fields and... | Glossary of areas of mathematics | 0.816687 |
12,821 | Fundamentally, it studies algebraic varieties. Algebraic graph theory a branch of graph theory in which methods are taken from algebra and employed to problems about graphs. The methods are commonly taken from group theory and linear algebra. | Glossary of areas of mathematics | 0.816687 |
12,822 | It also refers to the application of methods from combinatorics to problems in abstract algebra. Algebraic computation An older name of computer algebra. Algebraic geometry a branch that combines techniques from abstract algebra with the language and problems of geometry. | Glossary of areas of mathematics | 0.816687 |
12,823 | Algebraic analysis motivated by systems of linear partial differential equations, it is a branch of algebraic geometry and algebraic topology that uses methods from sheaf theory and complex analysis, to study the properties and generalizations of functions. It was started by Mikio Sato. Algebraic combinatorics an area ... | Glossary of areas of mathematics | 0.816687 |
12,824 | It was invented by Lars Ahlfors. Algebra One of the major areas of mathematics. Roughly speaking, it is the art of manipulating and computing with operations acting on symbols called variables that represent indeterminate numbers or other mathematical objects, such as vectors, matrices, or elements of algebraic structu... | Glossary of areas of mathematics | 0.816687 |
12,825 | Affine geometry of curves The study of curve properties that are invariant under affine transformations. Affine differential geometry A type of differential geometry dedicated to differential invariants under volume-preserving affine transformations. Ahlfors theory A part of complex analysis being the geometric counter... | Glossary of areas of mathematics | 0.816687 |
12,826 | Additive combinatorics The part of arithmetic combinatorics devoted to the operations of addition and subtraction. Additive number theory A part of number theory that studies subsets of integers and their behaviour under addition. Affine geometry A branch of geometry that deals with properties that are independent from... | Glossary of areas of mathematics | 0.816687 |
12,827 | Abstract homotopy theory A part of topology that deals with homotopic functions, i.e. functions from one topological space to another which are homotopic (the functions can be deformed into one another). Actuarial science The discipline that applies mathematical and statistical methods to assess risk in insurance, fina... | Glossary of areas of mathematics | 0.816687 |
12,828 | Abstract differential geometry A form of differential geometry without the notion of smoothness from calculus. Instead it is built using sheaf theory and sheaf cohomology. Abstract harmonic analysis A modern branch of harmonic analysis that extends upon the generalized Fourier transforms that can be defined on locally ... | Glossary of areas of mathematics | 0.816687 |
12,829 | Absolute differential calculus An older name of Ricci calculus Absolute geometry Also called neutral geometry, a synthetic geometry similar to Euclidean geometry but without the parallel postulate. Abstract algebra The part of algebra devoted to the study of algebraic structures in themselves. Occasionally named modern... | Glossary of areas of mathematics | 0.816687 |
12,830 | Transformation geometry Trigonometry the study of triangles and the relationships between the length of their sides, and the angles between them. It is essential to many parts of applied mathematics. Tropical analysis see idempotent analysis Tropical geometry Twisted K-theory a variation on K-theory, spanning abstract ... | Glossary of areas of mathematics | 0.816687 |
12,831 | Theoretical physics a branch primarily of the science physics that uses mathematical models and abstraction of physics to rationalize and predict phenomena. Theory of computation Time-scale calculus Topology Topological combinatorics the application of methods from algebraic topology to solve problems in combinatorics.... | Glossary of areas of mathematics | 0.816687 |
12,832 | Tensor algebra, Tensor analysis, Tensor calculus, Tensor theory the study and use of tensors, which are generalizations of vectors. A tensor algebra is also an algebraic structure that is used in the formal definition of tensors. Tessellation when periodic tiling has a repeating pattern. | Glossary of areas of mathematics | 0.816687 |
12,833 | Symplectic topology Synthetic differential geometry a reformulation of differential geometry in the language of topos theory and in the context of an intuitionistic logic. Synthetic geometry also known as axiomatic geometry, it is a branch of geometry that uses axioms and logical arguments to draw conclusions as oppose... | Glossary of areas of mathematics | 0.816687 |
12,834 | Survey sampling Survey methodology Symbolic computation also known as algebraic computation and computer algebra. It refers to the techniques used to manipulate mathematical expressions and equations in symbolic form as opposed to manipulating them by the numerical quantities represented by them. Symbolic dynamics Symp... | Glossary of areas of mathematics | 0.816687 |
12,835 | Statistical mechanics Statistical modelling Statistical theory Statistics although the term may refer to the more general study of statistics, the term is used in mathematics to refer to the mathematical study of statistics and related fields. This includes probability theory. Steganography Stochastic calculus Stochast... | Glossary of areas of mathematics | 0.816687 |
12,836 | Spherical geometry a branch of non-Euclidean geometry, studying the 2-dimensional surface of a sphere. Spherical trigonometry a branch of spherical geometry that studies polygons on the surface of a sphere. Usually the polygons are triangles. | Glossary of areas of mathematics | 0.816687 |
12,837 | Spectral theory part of operator theory extending the concepts of eigenvalues and eigenvectors from linear algebra and matrix theory. Spectral theory of ordinary differential equations part of spectral theory concerned with the spectrum and eigenfunction expansion associated with linear ordinary differential equations.... | Glossary of areas of mathematics | 0.816687 |
12,838 | As a theory, it is a subset of synthetic differential geometry. Solid geometry Spatial geometry Spectral geometry a field that concerns the relationships between geometric structures of manifolds and spectra of canonically defined differential operators. Spectral graph theory the study of properties of a graph using me... | Glossary of areas of mathematics | 0.816687 |
12,839 | Sheaf cohomology Sieve theory Single operator theory deals with the properties and classifications of single operators. Singularity theory a branch, notably of geometry; that studies the failure of manifold structure. Smooth infinitesimal analysis a rigorous reformation of infinitesimal calculus employing methods of ca... | Glossary of areas of mathematics | 0.816687 |
12,840 | Real analysis a branch of mathematical analysis; in particular hard analysis, that is the study of real numbers and functions of Real values. It provides a rigorous formulation of the calculus of real numbers in terms of continuity and smoothness, whilst the theory is extended to the complex numbers in complex analysis... | Glossary of areas of mathematics | 0.816687 |
12,841 | Ramsey theory the study of the conditions in which order must appear. It is named after Frank P. Ramsey. Rational geometry Real algebra the study of the part of algebra relevant to real algebraic geometry. Real algebraic geometry the part of algebraic geometry that studies real points of the algebraic varieties. | Glossary of areas of mathematics | 0.816687 |
12,842 | Ordered geometry a form of geometry omitting the notion of measurement but featuring the concept of intermediacy. It is a fundamental geometry forming a common framework for affine geometry, Euclidean geometry, absolute geometry and hyperbolic geometry. Oscillation theory | Glossary of areas of mathematics | 0.816687 |
12,843 | Operad theory a type of abstract algebra concerned with prototypical algebras. Operation research Operator K-theory Operator theory part of functional analysis studying operators. Optimal control theory a generalization of the calculus of variations. Optimal maintenance Orbifold theory Order theory a branch that invest... | Glossary of areas of mathematics | 0.816687 |
12,844 | Noncommutative geometry Noncommutative harmonic analysis see representation theory Noncommutative topology Nonlinear analysis Nonlinear functional analysis Number theory a branch of pure mathematics primarily devoted to the study of the integers. Originally it was known as arithmetic or higher arithmetic. Numerical ana... | Glossary of areas of mathematics | 0.816687 |
12,845 | Neutral geometry See absolute geometry. Nevanlinna theory part of complex analysis studying the value distribution of meromorphic functions. It is named after Rolf Nevanlinna Nielsen theory an area of mathematical research with its origins in fixed point topology, developed by Jakob Nielsen Non-abelian class field theo... | Glossary of areas of mathematics | 0.816687 |
12,846 | Motivic cohomology Multilinear algebra an extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic number theory that deals with prime numbers, factorization and divisors. Multivariable calculus the extension of calculus... | Glossary of areas of mathematics | 0.816687 |
12,847 | Mathematical finance a field of applied mathematics, concerned with mathematical modeling of financial markets. Mathematical logic a subfield of mathematics exploring the applications of formal logic to mathematics. Mathematical optimization Mathematical physics The development of mathematical methods suitable for appl... | Glossary of areas of mathematics | 0.816687 |
12,848 | Malliavin calculus a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. Mathematical biology the mathematical modeling of biological phenomena. Mathematical chemistry the mathematical modeling of chemical phenomena.... | Glossary of areas of mathematics | 0.816687 |
12,849 | Local algebra a term sometimes applied to the theory of local rings. Local class field theory the study of abelian extensions of local fields. Low-dimensional topology the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. | Glossary of areas of mathematics | 0.816687 |
12,850 | Extensions of the methods used belong to multilinear algebra. Linear functional analysis Linear programming a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. List of graphical methods Included are diagram tech... | Glossary of areas of mathematics | 0.816687 |
12,851 | It has applications in fields such as abstract algebra and functional analysis; it can be represented in analytic geometry and it is generalized in operator theory and in module theory. Sometimes matrix theory is considered a branch, although linear algebra is restricted to only finite dimensions. | Glossary of areas of mathematics | 0.816687 |
12,852 | L-theory the K-theory of quadratic forms. Large deviations theory part of probability theory studying events of small probability (tail events). Large sample theory also known as asymptotic theory Lattice theory the study of lattices, being important in order theory and universal algebra Lie algebra theory Lie group th... | Glossary of areas of mathematics | 0.816687 |
12,853 | It is the study of Kähler manifolds. (named after Erich Kähler) KK-theory a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. Klein geometry More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which acts a... | Glossary of areas of mathematics | 0.816687 |
12,854 | (In particular twisted K-theory.) K-homology a homology theory on the category of locally compact Hausdorff spaces. Kähler geometry a branch of differential geometry, more specifically a union of Riemannian geometry, complex differential geometry and symplectic geometry. | Glossary of areas of mathematics | 0.816687 |
12,855 | K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry it is referred to as algebraic K-theory. In physics, K-theory has appeared in type II... | Glossary of areas of mathematics | 0.816687 |
12,856 | Partition theory Perturbation theory Picard–Vessiot theory Plane geometry Point-set topology see general topology Pointless topology Poisson geometry Polyhedral combinatorics a branch within combinatorics and discrete geometry that studies the problems of describing convex polytopes. Possibility theory Potential theory... | Glossary of areas of mathematics | 0.816687 |
12,857 | Umbral calculus the study of Sheffer sequences Uncertainty theory a new branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Universal algebra a field studying the formalization of algebraic structures itself. Universal hyperbolic trigonometry an app... | Glossary of areas of mathematics | 0.816687 |
12,858 | Infinitary combinatorics an expansion of ideas in combinatorics to account for infinite sets. Infinitesimal analysis once a synonym for infinitesimal calculus Infinitesimal calculus See calculus of infinitesimals Information geometry an interdisciplinary field that applies the techniques of differential geometry to stu... | Glossary of areas of mathematics | 0.816687 |
12,859 | hyperbolic trigonometry the study of hyperbolic triangles in hyperbolic geometry, or hyperbolic functions in Euclidean geometry. Other forms include gyrotrigonometry and universal hyperbolic trigonometry. Hypercomplex analysis the extension of real analysis and complex analysis to the study of functions where the argum... | Glossary of areas of mathematics | 0.816687 |
12,860 | Homological algebra the study of homology in general algebraic settings. Homology theory Homotopy theory Hyperbolic geometry also known as Lobachevskian geometry or Bolyai-Lobachevskian geometry. It is a non-Euclidean geometry looking at hyperbolic space. | Glossary of areas of mathematics | 0.816687 |
12,861 | Hodge theory a method for studying the cohomology groups of a smooth manifold M using partial differential equations. Hodge-Arakelov theory Holomorphic functional calculus a branch of functional calculus starting with holomorphic functions. | Glossary of areas of mathematics | 0.816687 |
12,862 | Hard analysis see classical analysis Harmonic analysis part of analysis concerned with the representations of functions in terms of waves. It generalizes the notions of Fourier series and Fourier transforms from the Fourier analysis. Higher arithmetic Higher category theory the part of category theory at a higher order... | Glossary of areas of mathematics | 0.816687 |
12,863 | Gauge theory General topology also known as point-set topology, it is a branch of topology studying the properties of topological spaces and structures defined on them. It differs from other branches of topology as the topological spaces do not have to be similar to manifolds. Generalized trigonometry developments of t... | Glossary of areas of mathematics | 0.816687 |
12,864 | Fractal geometry Fractional calculus a branch of analysis that studies the possibility of taking real or complex powers of the differentiation operator. Fractional dynamics investigates the behaviour of objects and systems that are described by differentiation and integration of fractional orders using methods of fract... | Glossary of areas of mathematics | 0.816687 |
12,865 | Field theory The branch of algebra dedicated to fields, a type of algebraic structure. Finite geometry Finite model theory a restriction of model theory to interpretations on finite structures, which have a finite universe. Finsler geometry a branch of differential geometry whose main object of study is Finsler manifol... | Glossary of areas of mathematics | 0.816687 |
12,866 | It is closely related to differential topology. Differential geometry of curves the study of smooth curves in Euclidean space by using techniques from differential geometry Differential geometry of surfaces the study of smooth surfaces with various additional structures using the techniques of differential geometry. Di... | Glossary of areas of mathematics | 0.816687 |
12,867 | Convex geometry part of geometry devoted to the study of convex sets. Coordinate geometry see analytic geometry CR geometry a branch of differential geometry, being the study of CR manifolds. Cryptography | Glossary of areas of mathematics | 0.816687 |
12,868 | Computational number theory also known as algorithmic number theory, it is the study of algorithms for performing number theoretic computations. Computational statistics Computational synthetic geometry Computational topology Computer algebra see symbolic computation Conformal geometry the study of conformal transforma... | Glossary of areas of mathematics | 0.816687 |
12,869 | Cobordism theory Coding theory the study of the properties of codes and their respective fitness for specific applications. Cohomology theory Combinatorial analysis Combinatorial commutative algebra a discipline viewed as the intersection between commutative algebra and combinatorics. | Glossary of areas of mathematics | 0.816687 |
12,870 | Classical mathematics the standard approach to mathematics based on classical logic and ZFC set theory. Classical projective geometry Classical tensor calculus Clifford algebra Clifford analysis the study of Dirac operators and Dirac type operators from geometry and analysis using clifford algebras. Clifford theory is ... | Glossary of areas of mathematics | 0.816687 |
12,871 | However it may also refer to mathematical analysis done according to the principles of classical mathematics. Classical analytic number theory Classical differential calculus Classical Diophantine geometry Classical Euclidean geometry see Euclidean geometry Classical geometry may refer to solid geometry or classical Eu... | Glossary of areas of mathematics | 0.816687 |
12,872 | Bifurcation theory the study of changes in the qualitative or topological structure of a given family. It is a part of dynamical systems theory Biostatistics the development and application of statistical methods to a wide range of topics in biology. Birational geometry a part of algebraic geometry that deals with the ... | Glossary of areas of mathematics | 0.816687 |
12,873 | A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures. Arithmetic geometry The use of algebraic geometry and more specially scheme theory for solving problems of number theory. Arithmetic topology a combination of algebraic number theory and topology studying analogies betw... | Glossary of areas of mathematics | 0.816687 |
12,874 | Arithmetic algebraic geometry See arithmetic geometry. Arithmetic combinatorics the study of the estimates from combinatorics that are associated with arithmetic operations such as addition, subtraction, multiplication and division. Arithmetic dynamics Arithmetic dynamics is the study of the number-theoretic properties... | Glossary of areas of mathematics | 0.816687 |
12,875 | Also known as elementary arithmetic, the methods and rules for computing with addition, subtraction, multiplication and division of numbers. 2. Also known as higher arithmetic, another name for number theory. | Glossary of areas of mathematics | 0.816687 |
12,876 | Analytic theory of L-functions Applied mathematics a combination of various parts of mathematics that concern a variety of mathematical methods that can be applied to practical and theoretical problems. Typically the methods used are for science, engineering, finance, economics and logistics. Approximation theory part ... | Glossary of areas of mathematics | 0.816687 |
12,877 | Sampling theory Scheme theory the study of schemes introduced by Alexander Grothendieck. It allows the use of sheaf theory to study algebraic varieties and is considered the central part of modern algebraic geometry. Secondary calculus Semialgebraic geometry a part of algebraic geometry; more specifically a branch of r... | Glossary of areas of mathematics | 0.816687 |
12,878 | Ricci calculus Also called absolute differential calculus. A foundation of tensor calculus, developed by Gregorio Ricci-Curbastro in 1887–1896, and later developed for its applications to general relativity and differential geometry. Ring theory Riemannian geometry a branch of differential geometry that is more specifi... | Glossary of areas of mathematics | 0.816687 |
12,879 | Recursion theory see computability theory Representation theory a subfield of abstract algebra; it studies algebraic structures by representing their elements as linear transformations of vector spaces. It also studies modules over these algebraic structures, providing a way of reducing problems in abstract algebra to ... | Glossary of areas of mathematics | 0.816687 |
12,880 | Quantum calculus a form of calculus without the notion of limits. Quantum geometry the generalization of concepts of geometry used to describe the physical phenomena of quantum physics Quaternionic analysis | Glossary of areas of mathematics | 0.816687 |
12,881 | Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers. This glossary is alphabetica... | Glossary of areas of mathematics | 0.816687 |
12,882 | Modern invariant theory the form of invariant theory that analyses the decomposition of representations into irreducibles. Modular representation theory a part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. Module th... | Glossary of areas of mathematics | 0.816687 |
12,883 | Modern algebra Occasionally used for abstract algebra. The term was coined by van der Waerden as the title of his book Moderne Algebra, which was renamed Algebra in the latest editions. Modern algebraic geometry the form of algebraic geometry given by Alexander Grothendieck and Jean-Pierre Serre drawing on sheaf theory... | Glossary of areas of mathematics | 0.816687 |
12,884 | Mathematical sociology the area of sociology that uses mathematics to construct social theories. Mathematical statistics the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Mathematical system theory Matrix algebra Matrix calculus Matr... | Glossary of areas of mathematics | 0.816687 |
12,885 | Mathematical psychology an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. Mathematical sciences refers to academic di... | Glossary of areas of mathematics | 0.816687 |
12,886 | As a major activity, AIAA currently publishes several technical journals. The AIAA Journal is published on a monthly basis and serves as the flagship journal of the society. In January 2015 the Journal of Guidance, Control, and Dynamics became the second AIAA journal published on a monthly basis. The other journals are... | American Institute of Aeronautics and Astronautics | 0.816683 |
12,887 | The American Institute of Aeronautics and Astronautics (AIAA) is a professional society for the field of aerospace engineering. The AIAA is the U.S. representative on the International Astronautical Federation and the International Council of the Aeronautical Sciences. In 2015, it had more than 30,000 members among aer... | American Institute of Aeronautics and Astronautics | 0.816683 |
12,888 | Advances in quantum computational chemistry methods have allowed for faster theoretical examination of dispersion effects in molecular chemistry. Standard density functional theory (DFT) does not account well for dispersion effects, but corrections like the popular -D3 correction can be used with DFT to provide efficie... | Dispersion stabilized molecules | 0.816683 |
12,889 | Dispersion stabilized molecules are molecules where the London dispersion force (LDF), a non-covalent attractive force between atoms and molecules, plays a significant role in promoting the molecule's stability. Distinct from steric hindrance, dispersion stabilization has only recently been considered in depth by organ... | Dispersion stabilized molecules | 0.816682 |
12,890 | Adding "steric hindrance" to a molecule's reactive site through bulky groups is a common strategy in molecular chemistry to stabilize reactive moieties within a molecule. In this case bulky ligands like terphenyls, bulky alkoxides, aryl-substituted NHCs, etc. serve as a protective wrapper on the molecule. Under the ste... | Dispersion stabilized molecules | 0.816682 |
12,891 | Dispersion forces in molecular chemistry are most apparent in molecules with large, bulky functional groups. Dispersion stabilization is often signified by atomic contacts below their van der Waals radii in a molecule's crystal structure. Especially for H•••H contacts between bulky, rigid, polarizable groups, short con... | Dispersion stabilized molecules | 0.816682 |
12,892 | Dispersion interactions are a stabilizing force arising from quantum mechanical electron correlation. Although quantum mechanical in nature, the energy of dispersion interactions can be approximated classically, showing a R−6 dependence on the distance between two atoms. This distance dependence helps make dispersion i... | Dispersion stabilized molecules | 0.816682 |
12,893 | The additional stability has been attributed to dispersion interactions between the adjacent, bulky tBu groups. Through computational analysis, the authors identified 9 H-H interactions that each provide -0.7 kcal/mol of energy, overcoming the steric penalty of bringing the tBu groups together. Geometry optimizations w... | Dispersion stabilized molecules | 0.816682 |
12,894 | Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem. The most... | Computability | 0.816671 |
12,895 | The language consisting of all Turing machine descriptions paired with all possible input streams on which those Turing machines will eventually halt, is not recursive. The halting problem is therefore called non-computable or undecidable. An extension of the halting problem is called Rice's theorem, which states that ... | Computability | 0.816671 |
12,896 | The halting problem is one of the most famous problems in computer science, because it has profound implications on the theory of computability and on how we use computers in everyday practice. The problem can be phrased: Given a description of a Turing machine and its initial input, determine whether the program, when... | Computability | 0.816671 |
12,897 | The Turing machine is capable of performing complex calculations which can have arbitrary duration. This model is perhaps the most important model of computation in computer science, as it simulates computation in the absence of predefined resource limits. Multitape Turing machine Here, there may be more than one tape;... | Computability | 0.816671 |
12,898 | A model of computation is a formal description of a particular type of computational process. The description often takes the form of an abstract machine that is meant to perform the task at hand. General models of computation equivalent to a Turing machine (see Church–Turing thesis) include: Lambda calculus A computat... | Computability | 0.816671 |
12,899 | A central idea in computability is that of a (computational) problem, which is a task whose computability can be explored. There are two key types of problems: A decision problem fixes a set S, which may be a set of strings, natural numbers, or other objects taken from some larger set U. A particular instance of the pr... | Computability | 0.816671 |
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