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Analysis (pl.:analyses) is the process of breaking acomplex topic orsubstance into smaller parts in order to gain a betterunderstanding of it. The technique has been applied in the study ofmathematics andlogic since beforeAristotle (384–322 BC), thoughanalysis as a formal concept is a relatively recent development.[1]
The word comes from theAncient Greekἀνάλυσις (analysis, "a breaking-up" or "an untying" fromana- "up, throughout" andlysis "a loosening").[2] From it also comes the word's plural,analyses.
As a formal concept, the method has variously been ascribed toRené Descartes (Discourse on the Method), andGalileo Galilei. It has also been ascribed toIsaac Newton, in the form of a practical method of physical discovery (which he did not name).
The converse of analysis issynthesis: putting the pieces back together again in a new or different whole.
The field ofchemistry uses analysis in three ways: to identify the components of a particularchemical compound (qualitative analysis),[3] to identify the proportions of components in amixture (quantitative analysis),[4] and to break downchemical processes and examinechemical reactions betweenelements ofmatter.[5] For an example of its use, analysis of the concentration of elements is important in managing anuclear reactor, sonuclear scientists will analyzeneutron activation to develop discrete measurements within vast samples. Amatrix 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 adevice.
A) Qualitative Analysis: It is concerned with which components are in a given sample or compound.
Example: Precipitation reaction
B) Quantitative Analysis: It is to determine the quantity of individual component present in a given sample or compound.
Example: To find concentration by uv-spectrophotometer.
Chemists can useisotope analysis to assist analysts with issues inanthropology,archeology,food chemistry,forensics,geology, and a host of other questions ofphysical science. Analysts can discern the origins of natural and man-made isotopes in the study ofenvironmental radioactivity.
Analysts in the field ofengineering look atrequirements,structures, mechanisms,systems anddimensions.Electrical engineers analysesystems inelectronics.Life cycles andsystem failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design.
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 asreal numbers,complex variables,trigonometric functions, andalgorithms, or ofnon-classical concepts likeconstructivism,harmonics,infinity, andvectors.
Florian Cajori explains inA History of Mathematics (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The termssynthesis andanalysis 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 byEudoxus: "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 hisA 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 distinguishedtheoretic fromproblematic analysis. A theoretic analysis is of the following kind. Toprove 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 beconvertible, 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.
Instatistics, the termanalysis may refer to any method usedfordata analysis. Among the many such methods, some are:
The field ofintelligence employs analysts to break down and understand a wide array of questions.Intelligence agencies may useheuristics,inductive anddeductive reasoning,social network analysis,dynamic network analysis,link analysis, andbrainstorming to sort through problems they face.Military intelligence may explore issues through the use ofgame theory,Red Teaming, andwargaming.Signals intelligence appliescryptanalysis andfrequency analysis to breakcodes andciphers.Business intelligence applies theories ofcompetitive intelligence analysis andcompetitor analysis to resolve questions in themarketplace.Law enforcement intelligence applies a number of theories incrime analysis.
Linguistics explores individual languages andlanguage in general. It breaks language down and analyses its component parts:theory,sounds and their meaning,utterance usage,word origins, thehistory of words, the meaning ofwords andword combinations,sentence construction,basic construction beyond the sentence level,stylistics, andconversation. It examines the above usingstatistics and modeling, andsemantics. It analyses language in context ofanthropology,biology,evolution,geography,history,neurology,psychology, andsociology. It also takes theapplied approach, looking atindividual language development andclinical issues.
Literary criticism is the analysis ofliterature. The focus can be as diverse as the analysis ofHomer orFreud. 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 labelledThe New Criticism, approaches texts – chiefly short poems such assonnets, 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 ofprosody (the formal analysis of meter) and phonic effects such asalliteration andrhyme, 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.
