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# analysis

[uh-nal-uh-sis]
analysis, branch of mathematics that utilizes the concepts and methods of the calculus. It includes not only basic calculus, but also advanced calculus, in which such underlying concepts as that of a limit are subjected to rigorous examination; differential and integral equations, in which the unknowns are functions rather than numbers, as in algebraic equations; complex variable analysis, in which the variables are of the form z=x+iy, where i is the imaginary unit; vector analysis and tensor analysis; differential geometry; and many other fields.
analysis, chemical: see chemical analysis.
Analysis (from Greek ἀνάλυσις, "a breaking up") is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development.

As a formal concept, the method has variously been ascribed by Ibn al-Haytham, Descartes (Discourse on the Method), Galileo, and Isaac Newton, as a practical method of physical discovery.

## Use in specific fields

### Chemistry

The field of chemistry uses analysis to break down chemical processes and examine chemical reactions between elements of matter. For example, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze 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 Measurement and Signature Intelligence (MASINT) capabilities.

#### Isotopes

Chemists can use isotopes 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.

### Engineering

Analysts in the field of engineering look at structures, mechanisms, systems and dimensions. Electrical engineers analyze systems in electronics. Life cycles and system failures are broken down and studied by engineers.

### Intelligence

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

Linguistics began with the analysis of Sanskrit; today it looks at individual languages and language in general. It breaks language down and analyzes 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 analyzes 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

• Analysis (Homer), an influential school of thought in Homeric scholarship in the 19th-20th centuries
• Psychocriticism, Charles Mauron's method based on Freud's own initial interpretations of literary works such as Hamlet

### Statistics

• Analysis of variance (ANOVA), a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
• Meta-analysis, combines the results of several studies that address a set of related research hypotheses
• Time-series analysis, methods that attempt to understand a sequence of data points spaced apart at uniform time intervals

### Other

• Aura analysis, a technique in which supporters of the method claim that the body's aura, or energy field is analysed
• Bowling analysis, a notation summarizing a cricket bowler's performance
• Lithic analysis, the analysis of stone tools using basic scientific techniques
• Protocol analysis, a means for extracting persons' thoughts while they are performing a task