Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.
Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.
Logic is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, thus, hence, ergo, and so on.
The word comes from the Ancient Greek ἀνάλυσις (análusis, "a breaking up", from ana- "up, throughout" and lusis "a loosening").
The Ancient Greek language includes the forms of Greek used in Ancient Greece and the ancient world from around the 9th century BCE to the 6th century CE. It is often roughly divided into the Archaic period, Classical period, and Hellenistic period. It is antedated in the second millennium BCE by Mycenaean Greek and succeeded by Medieval Greek.
As a formal concept, the method has variously been ascribed to Alhazen,René Descartes ( Discourse on the Method ), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
René Descartes was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–1649) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. One of the most notable intellectual figures of the Dutch Golden Age, Descartes is also widely regarded as one of the founders of modern philosophy.
Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences is a philosophical and autobiographical treatise published by René Descartes in 1637. It is best known as the source of the famous quotation "Je pense, donc je suis", which occurs in Part IV of the work. A similar argument, without this precise wording, is found in Meditations on First Philosophy (1641), and a Latin version of the same statement Cogito, ergo sum is found in Principles of Philosophy (1644).
Galileo Galilei was an astronomer, physicist and engineer, sometimes described as a polymath from Pisa. Galileo has been called the "father of observational astronomy", the "father of modern physics", the "father of the scientific method", and the "father of modern science".
The field of chemistry uses analysis in at least three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyse neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a device. Chemical analysis is an important element of national security among the major world powers with materials
Chemistry is the scientific discipline involved with elements and compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a reaction with other substances.
A chemical compound is a chemical substance composed of many identical molecules composed of atoms from more than one element held together by chemical bonds. Two atoms of the same element bonded in a molecule do not form a chemical compound, since this would require two different elements.
In chemistry, a mixture is a material made up of two or more different substances which are physically combined.A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspension and colloids.
Chemists can use isotope analysis to assist analysts with issues in anthropology, archeology, food chemistry, forensics, geology, and a host of other questions of physical science. Analysts can discern the origins of natural and man-made isotopes in the study of environmental radioactivity.
Isotope analysis is the identification of isotopic signature, the abundance of certain stable isotopes and chemical elements within organic and inorganic compounds. Isotopic analysis can be used to understand the flow of energy through a food web, to reconstruct past environmental and climatic conditions, to investigate human and animal diets in the past, for food authentification, and a variety of other physical, geological, palaeontological and chemical processes. Stable isotope ratios are measured using mass spectrometry, which separates the different isotopes of an element on the basis of their mass-to-charge ratio.
Anthropology is the scientific study of humans and human behavior and societies in the past and present. Social anthropology studies patterns of behaviour and cultural anthropology studies cultural meaning, including norms and values. Linguistic anthropology studies how language influences social life. Biological or physical anthropology studies the biological development of humans.
Food chemistry is the study of chemical processes and interactions of all biological and non-biological components of foods. The biological substances include such items as meat, poultry, lettuce, beer, and milk as examples. It is similar to biochemistry in its main components such as carbohydrates, lipids, and protein, but it also includes areas such as water, vitamins, minerals, enzymes, food additives, flavors, and colors. This discipline also encompasses how products change under certain food processing techniques and ways either to enhance or to prevent them from happening. An example of enhancing a process would be to encourage fermentation of dairy products with microorganisms that convert lactose to lactic acid; an example of preventing a process would be stopping the browning on the surface of freshly cut apples using lemon juice or other acidulated water.
Financial statement analysis is the process of reviewing and analyzing a company's financial statements to make better economic decisions to earn income in future. These statements include the income statement, balance sheet, statement of cash flows, notes to accounts and a statement of changes in equity. Financial statement analysis is a method or process involving specific techniques for evaluating risks, performance, financial health, and future prospects of an organization.
Fundamental analysis, in accounting and finance, is the analysis of a business's financial statements ; health; and competitors and markets. It also considers the overall state of the economy and factors including interest rates, production, earnings, employment, GDP, housing, manufacturing and management. There are two basic approaches that can be used: bottom up analysis and top down analysis. These terms are used to distinguish such analysis from other types of investment analysis, such as quantitative and technical.
In finance, technical analysis is an analysis methodology for forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis use many of the same tools of technical analysis, which, being an aspect of active management, stands in contradiction to much of modern portfolio theory. The efficacy of both technical and fundamental analysis is disputed by the efficient-market hypothesis which states that stock market prices are essentially unpredictable.
Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions. Electrical engineers analyse systems in electronics. Life cycles and system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design.
The field of intelligence employs analysts to break down and understand a wide array of questions. Intelligence agencies may use heuristics, inductive and deductive reasoning, social network analysis, dynamic network analysis, link analysis, and brainstorming to sort through problems they face. Military intelligence may explore issues through the use of game theory, Red Teaming, and wargaming. Signals intelligence applies cryptanalysis and frequency analysis to break codes and ciphers. Business intelligence applies theories of competitive intelligence analysis and competitor analysis to resolve questions in the marketplace. Law enforcement intelligence applies a number of theories in crime analysis.
Linguistics looks at individual languages and language in general. It breaks language down and analyses its component parts: theory, sounds and their meaning, utterance usage, word origins, the history of words, the meaning of words and word combinations, sentence construction, basic construction beyond the sentence level, stylistics, and conversation. It examines the above using statistics and modeling, and semantics. It analyses language in context of anthropology, biology, evolution, geography, history, neurology, psychology, and sociology. It also takes the applied approach, looking at individual language development and clinical issues.
Literary criticism is the analysis of literature. The focus can be as diverse as the analysis of Homer or Freud. While not all literary-critical methods are primarily analytical in nature, the main approach to the teaching of literature in the west since the mid-twentieth century, literary formal analysis or close reading, is. This method, rooted in the academic movement labelled The New Criticism, approaches texts – chiefly short poems such as sonnets, which by virtue of their small size and significant complexity lend themselves well to this type of analysis – as units of discourse that can be understood in themselves, without reference to biographical or historical frameworks. This method of analysis breaks up the text linguistically in a study of prosody (the formal analysis of meter) and phonic effects such as alliteration and rhyme, and cognitively in examination of the interplay of syntactic structures, figurative language, and other elements of the poem that work to produce its larger effects.
Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.
Florian Cajori explains in A History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in [appended to] Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."
The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.
James Gow uses a similar argument as Cajori, with the following clarification, in his A Short History of Greek Mathematics (1884):
The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished theoretic from problematic analysis. A theoretic analysis is of the following kind. To prove that A is B, assume first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem.
In statistics, the term analysis may refer to any method used for data analysis. Among the many such methods, some are:
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
Data mining is the process of discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems. Data mining is an interdisciplinary subfield of computer science and statistics with an overall goal to extract information from a data set and transform the information into a comprehensible structure for further use. Data mining is the analysis step of the "knowledge discovery in databases" process, or KDD. Aside from the raw analysis step, it also involves database and data management aspects, data pre-processing, model and inference considerations, interestingness metrics, complexity considerations, post-processing of discovered structures, visualization, and online updating. The difference between data analysis and data mining is that data analysis is used to test models and hypotheses on the dataset, e.g., analyzing the effectiveness of a marketing campaign, regardless of the amount of data; in contrast, data mining uses machine-learning and statistical models to uncover clandestine or hidden patterns in a large volume of data.
Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, ecological, behavioral, and social systems. The field is broadly defined and includes foundations in biology, applied mathematics, statistics, biochemistry, chemistry, biophysics, molecular biology, genetics, genomics, computer science and evolution.
Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. One well known subject classification system for computer science is the ACM Computing Classification System devised by the Association for Computing Machinery.
Chemometrics is the science of extracting information from chemical systems by data-driven means. Chemometrics is inherently interdisciplinary, using methods frequently employed in core data-analytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to address problems in chemistry, biochemistry, medicine, biology and chemical engineering. In this way, it mirrors other interdisciplinary fields, such as psychometrics and econometrics.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.
Generally speaking, analytic refers to the "having the ability to analyze" or "division into elements or principles".
Network traffic simulation is a process used in telecommunications engineering to measure the efficiency of a communications network.
Data analysis is a process of inspecting, cleansing, transforming and modeling data with the goal of discovering useful information, informing conclusions and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.
Computational finance is a branch of applied computer science that deals with problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems.
Spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data.
Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modelling, and machine learning, that analyze current and historical facts to make predictions about future or otherwise unknown events.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
In computer science, a termination analysis is program analysis which attempts to determine whether the evaluation of a given program will definitely terminate. Because the halting problem is undecidable, termination analysis cannot be total. The aim is to find the answer "program does terminate" whenever this is possible. Without success the algorithm working on the termination analysis may answer with "maybe" or continue working infinitely long.
Visual analytics is an outgrowth of the fields of information visualization and scientific visualization that focuses on analytical reasoning facilitated by interactive visual interfaces.
Cross-impact analysis is a methodology developed by Theodore Gordon and Olaf Helmer in 1966 to help determine how relationships between events would impact resulting events and reduce uncertainty in the future. The Central Intelligence Agency (CIA) became interested in the methodology in the late 1960s and early 1970s as an analytic technique for predicting how different factors and variables would impact future decisions. In the mid-1970s, futurists began to use the methodology in larger numbers as a means to predict the probability of specific events and determine how related events impacted one another. By 2006, cross-impact analysis matured into a number of related methodologies with uses for businesses and communities as well as futurists and intelligence analysts.
The following outline is provided as an overview of and topical guide to formal science:
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