Generally speaking, analytic (from Greek Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical ancient Greek literature and the New Testament of ἀναλυτικός - analytikos) refers to the "having the ability to analyze" or "division into elements or principles."

It can also have the following meanings:

Natural Sciences

• In chemistry:
  • Analytical chemistry Analytical chemistry is the study of the chemical composition of natural and artificial materials. Properties studied in analytical chemistry include geometric features such as molecular morphologies and distributions of species, as well as features such as composition and species identity. Unlike the sub disciplines inorganic chemistry and, the analysis of material samples to learn their chemical composition and structure
  • Analytical technique An analytical technique is a method that is used to determine the concentration of a chemical compound or chemical element. There are a wide variety of techniques used for analysis, from simple weighing to titrations (titrimetric)to very advanced techniques using highly specialized instrumentation. The most common techniques used in analytical
  • Analytical concentration In chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in the solvent
• In mathematics:
  • Analytic geometry Analytic geometry, also known as coordinate geometry, analytical geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on, the study of geometry using the principles of algebra
  • Analytic combinatorics Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, which are often analytic functions, but sometimes formal power series
  • Analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve number-theoretical problems. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. Another major milestone in the, a branch of number theory that uses methods from mathematical analysis
  • Abstract analytic number theory Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to a variety of different mathematical fields. The classical prime number theorem serves as a prototypical example, and the emphasis is on abstract asymptotic distribution results. The theory was, the application of ideas and techniques from analytic number theory to other mathematical fields
  • Analytic function In mathematics, an analytic function is a function that is locally given by a convergent power series. Analytic functions can be thought of as a bridge between polynomials and general functions. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Functions of
  • Analytic continuation In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes, a technique to extend the domain of definition of a given analytic function
  • Analytic variety In mathematics, specifically geometry, an analytic variety is defined locally as the set of common solutions of several equations involving analytic functions. It is analogous to the included concept of complex algebraic variety, and any complex manifold is an analytic variety. Since algebraic varieties may have singular points, not all analytic, the set of common solutions of several equations involving analytic functions
  • Analytic capacity In complex analysis, the analytic capacity of a compact subset K of the complex plane is a number that denotes "how big" a bounded analytic function from can become. Roughly speaking, γ measures the size of the unit ball of the space of bounded analytic functions outside K
  • Analytic solution: a solution to a problem that can be written in "closed form" in terms of known functions, constants, etc. ^[1]
  • In set theory:
    • Analytic set In descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space. These sets were first defined by Luzin and his student Souslin (1917)
    • Analytical hierarchy In mathematical logic and descriptive set theory, the analytical hierarchy is a higher type analogue of the arithmetical hierarchy. It thus continues the classification of sets by the formulas that define them
    • Lightface analytic game In descriptive set theory, a lightface analytic game is a game whose payoff set A is a subset of Baire space; that is, there is a tree T on which is a computable subset of , such that A is the projection of the set of all branches of T
  • In proof theory:
    • Analytic proof In mathematical analysis, an analytical proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not make use of results from geometry. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided proof of, in structural proof theory, a proof whose structure is simple in a special way
    • Method of analytic tableaux In proof theory, the semantic tableau is a decision procedure for sentential and related logics, and a proof procedure for formulas of first-order logic. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics, a fundamental concept in automated theorem proving
  • Other mathematical areas:
    • Analytic element method The analytic element method is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota. It is similar in nature to the boundary element method (BEM), as it does not rely upon discretization of volumes or areas in the modeled system; only internal and, a numerical method used to solve partial differential equations
    • Analytic manifold In mathematics, an analytic manifold is a topological manifold with analytic transition maps. Every complex manifold is an analytic manifold, a topological manifold with analytic transition maps
• In Computer Science:
  • Analytic grammar, a kind of formal grammar A formal grammar is a set of rules of a specific kind, for forming strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context —only their form that works by successively reducing input strings to simpler forms
  • Analytical IT
  • Analytical software Analytical software is software that is designed specifically for analysis and development of a particular environment or object
• Other scientific areas:
  • Analytic signal In mathematics and signal processing, the analytic representation of a real-valued function or signal facilitates many mathematical manipulations of the signal. The basic idea is that the negative frequency components of the Fourier transform of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. They can be, a particular representation of a signal
  • Analytical mechanics Analytical mechanics is a term used for a refined, highly mathematical form of classical mechanics, constructed from the eighteenth century onwards as a formulation of the subject as founded by Isaac Newton. Often the term vectorial mechanics is applied to the form based on Newton's work, to contrast it with analytical mechanics. This distinction, a refined, highly mathematical form of classical mechanics
  • Analytical balance, a very high precision (0.1 mg or better) weighing scale A weighing scale is a measuring instrument for determining the weight or mass of an object. A spring scale measures weight by the distance a spring deflects under its load. A balance compares the unknown weight to a standard weight using a horizontal lever. Weighing scales are used in many industrial and commercial applications, and products from
  • Analytical ultracentrifuge, an ultracentrifuge The ultracentrifuge is a centrifuge optimized for spinning a rotor at very high speeds, capable of generating acceleration as high as 1,000,000 g . There are two kinds of ultracentrifuges, the preparative and the analytical ultracentrifuge. Both classes of instruments find important uses in molecular biology, biochemistry and polymer science that can monitor samples while they're being spun

Philosophy

• Analytic philosophy Analytic philosophy is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. In the United States, United Kingdom, Canada, Scandinavia, Australia, and New Zealand, the overwhelming majority of university philosophy departments identify themselves as "analytic" departments. Analytic
• Analytic proposition The analytic-synthetic distinction, , is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are those which are true simply by virtue of their meaning while synthetic propositions are not; however, philosophers have used the, a statement whose truth can be determined solely through analysis of its meaning
• Analytical Thomism Analytical Thomism is a philosophical movement which promotes the interchange of ideas between the thought of Saint Thomas Aquinas , and modern analytic philosophy, the movement to present the thought of Thomas Aquinas in the style of modern analytic philosophy
• Postanalytic philosophy Postanalytic philosophy describes a detachment from the mainstream philosophical movement of analytic philosophy, which is the predominant school of thought in English-speaking countries. Postanalytic philosophy derives mainly from contemporary American thought, especially from the works of philosophers Richard Rorty, Donald Davidson, Hilary

Social Sciences

• In psychology:
  • Analytical psychology Analytical psychology is the school of psychology originating from the ideas of Swiss psychiatrist Carl Jung, and then advanced by his students and other thinkers who followed in his tradition. It is distinct from Freudian psychoanalysis but also has a number of similarities. Its aim is the apprehension and integration of the deep forces and, part of the Jungian psychology movement
  • Analytical psychodrama
  • Individual analytical psychodrama Individual analytical psychodrama is a therapy based on role-playing and the observation of the unconscious mind.See book 2001. : `Good Practice in Psychodrama. An Analytic Perspective.` by Don Feasey. Publisher Wiley UK. Still in print
  • Cognitive analytic therapy Cognitive analytic therapy was developed by Anthony Ryle. This brief therapy was developed in the context of the National Health Service in the United Kingdom with the aim of providing effective and affordable psychological treatment which could be realistically provided in a resource constrained National Health Service
  • Psychoanalysis Psychoanalysis is a body of ideas developed by Austrian physician Sigmund Freud and continued by others. It is primarily devoted to the study of human psychological functioning and behavior, although it also can be applied to societies
• In sociology:
  • Analytic induction Analytic induction refers to a systematic examination of similarities between various social phenomena in order to develop concepts or ideas. Social scientists doing social research use analytic induction to search for those similarities in broad categories and then develop subcategories. For example, social scientist may examine the category of ', the systematic examination of similarities between various social phenomena to develop concepts or ideas
  • Analytic frame Analytic frame is a detailed sketch or outline of some social phenomenon, representing initial idea of a scientist analyzing this phenomenon. Charles C. Ragin defines it as one of the four building blocks of social research (the other three being ideas , evidence (data) and images (new ideas synthetised from existing data). Thus analytic frames, a detailed sketch or outline of some social phenomenon, representing initial idea of a scientist analyzing this phenomenon
• In politics:
  • Analytical Marxism Analytical Marxism refers to a style of thinking about Marxism that was prominent amongst English-speaking philosophers and social scientists during the 1980s. It was mainly associated with the September Group of academics, so called because of their biennial September meetings to discuss common interests. The group also dubbed itself "Non-, an interpretation of Marxism

Other areas

• Analytical jurisprudence Analytical jurisprudence is a legal theory that draws on the resources of modern analytical philosophy to try to understand the nature of law. Since the boundaries of analytical philosophy are somewhat vague, it is difficult to say how far it extends. H. L. A. Hart was probably the most influential writer in the modern school of analytical, the use of analytical reasoning to study legal theory
• Analytic cubism Cubism was a 20th century avant-garde art movement, pioneered by Pablo Picasso and Georges Braque, that revolutionized European painting and sculpture, and inspired related movements in music and literature. The first branch of cubism, known as "Analytic Cubism", was both radical and influential as a short but highly significant art, one of two major branches of the cubism artistic movement
• Analytical skills Analytical skill is the ability to visualize, articulate, and solve complex problems and concepts, and make decisions that make sense based on available information. Such skills include demonstration of the ability to apply logical thinking to gathering and analyzing information, designing and testing solutions to problems, and formulating plans

• In linguistics:
  • Analytic language In morphological typology , an isolating language (in fact the most extreme case of an analytic language) is any language in which words are composed of a single morpheme. This is in contrast to a synthetic language which can have words composed of multiple morphemes, a natural language in which most morphemes are free (separate), instead of fused together
• Analytical-Literal Translation, a very literal translation of the Bible

See also

• Synthesis (disambiguation) In general, the noun synthesis refers to the combining of two or more entities to form something new. The corresponding verb, to synthesise (or synthesize), means to make or form a synthesis
• Analytical engine The analytical engine, an important step in the history of computers, was the design of a mechanical general-purpose computer by the British mathematician Charles Babbage. It was first described in 1837, but Babbage continued to work on the design until his death in 1871. Because of financial, political, and legal issues, the engine was never, a 19th century mechanical general-purpose computer designed by Charles Babbage
• Analytical Society The Analytical Society was a group of individuals in early-19th century Britain whose aim was to promote the use of Leibnizian or analytical calculus as opposed to Newtonian calculus. The latter system came into being in the 18th century as an invention of Sir Isaac Newton, and was in use throughout Great Britain for political rather than, a 19th century British group who promoted the use of Leibnizian or analytical calculus, as opposed to Newtonian calculus

References

1. ^ Weisstein, Eric W. "Analytic." From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/Analytic.html

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