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Mathematical Model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract And Concrete
In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, human beings and planets while things like numbers, sets and propositions are abstract objects. There is no general consensus as to what the characteristic marks of concreteness and abstractness are. Popular suggestions include defining the distinction in terms of the difference between (1) existence inside or outside space-time, (2) having causes and effects or not, (3) having contingent or necessary existence, (4) being particular or universal and (5) belonging to either the physical or the mental realm or to neither. Despite this diversity of views, there is broad agreement concerning most objects as to whether they are abstract or concrete. So under most interpretations, all these views would agree that, for example, plants are concrete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Science
Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and laws. Modern political science can generally be divided into the three subdisciplines of comparative politics, international relations, and political theory. Other notable subdisciplines are public policy and administration, domestic politics and government, political economy, and political methodology. Furthermore, political science is related to, and draws upon, the fields of economics, law, sociology, history, philosophy, human geography, political anthropology, and psychology. Political science is methodologically diverse and appropriates many methods originating in psychology, social research, and political philosophy. Approaches include positivism, interpretivism, rational choice theory, behaviouralism, structuralism, post-struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Defining Equation (physics)
In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units. Description of units and physical quantities Physical quantities and units follow the same hierarchy; ''chosen base quantities'' have ''defined base units'', from these any other ''quantities may be derived'' and have corresponding ''derived units''. Colour mixing analogy Defining quantities is analogous to mixing colours, and could be classified a similar way, although this is not standard. Primary colours are to base quantities; as secondary (or tertiary etc.) colours are to derived quantities. Mixing colours is analogous to combining quantities using mathematical operations. But colours could be for light or paint, and analogously the system of units could be one of many forms: such as SI (now most common), CGS, Gaussian, old imperial units, a specific form of natural units or even arbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Governing Equation
The governing equations of a mathematical model describe how the values of the unknown variables (i.e. the dependent variables) change when one or more of the known (i.e. independent) variables change. Mass balance A mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. It is the simplest governing equation, and it is simply a budget (balance calculation) over the quantity in question: \text + \text = \text + \text \ + \text Differential equation Physics The governing equations in classical physics that are lectured at universities are listed below. * balance of mass * balance of (linear) momentum * balance of angular momentum * balance of energy * balance of entropy * Maxwell-Faraday equation for induced electric field * Ampére-Maxwell equation for induced magnetic field * Gauss equation for electric flux * Gauss equation for magnetic flux Classical continuum mechanics The basic equations in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Sciences
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". Definition Physical science can be described as all of the following: * A branch of science (a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe)."... modern science is a discovery as well as an invention. It was a discovery that nature generally acts regularly enough to be described by laws and even by mathematics; and required invention to devise the techniques, abstractions, apparatus, and organization for exhibiting the regularities and securing their law-like descriptions." —p.vii, J. L. Heilbron, (2003, editor-in-chief). ''The Oxford Companion to the History of Modern Science''. New York: Oxford University Press. . ** A branch of natural science – natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself. In particular, model theorists also investigate the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes back to Alfred Tarski, who first used the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equations
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the data-generating process. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. Introduction Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Philosophy
Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, United States, Canada, Australia, New Zealand, and Scandinavia, and continues today. Analytic philosophy is often contrasted with continental philosophy, coined as a catch-all term for other methods prominent in Europe. Central figures in this historical development of analytic philosophy are Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures in its history include the logical positivists (particularly Rudolf Carnap), W. V. O. Quine, and Karl Popper. After the decline of logical positivism, Saul Kripke, David Lewis, and others led a revival in metaphysics. Elizabeth Anscombe, Peter Geach, Anthony Kenny and others brought analytic approach to Thomism. Analytic philosophy is characterized by an empha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
