Analysis


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, though analysis as a formal concept is a relatively recent development.
The word comes from the Ancient Greek ἀνάλυσις. From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to René Descartes, and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery.
The converse of analysis is synthesis: putting the pieces back together again in a new or different whole.

Academic analysis

Academic analysis is a systematic, methodological approach to inquiry used across scholarly disciplines to deconstruct complex ideas, texts, data, or systems. Its primary aim is to foster a deeper, evidence-based understanding, challenge assumptions, and contribute to a body of knowledge through critical examination and rigorous argumentation. This form of analysis is foundational to higher education and research, distinguished by its adherence to disciplinary conventions, peer review, and the use of established theoretical or conceptual frameworks.
Methods vary significantly by field. In the humanities, it often involves hermeneutic or discourse analysis to interpret the meaning, context, and ideology within texts and artifacts. In the social sciences, analysis frequently employs qualitative methods and quantitative methods to examine human behavior and societal structures. In the natural and formal sciences, the analytical process is characterized by hypothesis testing, mathematical modeling, and the reproducible analysis of empirical data.
A cornerstone of academic analysis is reflexivity, where scholars critically examine their own role, potential biases, and the influence of their theoretical position on the analytical process. The product of academic analysis is typically a sustained argument presented in a format such as a monograph, journal article, or dissertation, which is subjected to peer evaluation for validity, originality, and contribution to the field.

Humanities and social sciences

Linguistics

is the scientific study of language. It involves the systematic analysis of the properties of specific languages as well as the universal characteristics of language in general, including its structure, use, and cognitive and social aspects. Linguistics explores individual languages and language in general by breaking language down into component parts for analysis. Core areas of analysis include theory, phonetics, phonology, morphology, the history of words and word origins, semantics, semantic analysis, syntax, pragmatics, discourse analysis, conversation, and stylistics and stylistics.
Theoretical linguistics is concerned with developing a general framework for understanding the fundamental nature of language. Linguistics also encompasses the study of language change over time, known as historical linguistics.
Linguistics examines these areas using a range of methods, including tools from computational linguistics that involve computational modelling, statistics, and modeling of natural language. The field also analyses language through interdisciplinary approaches that consider its context, including anthropological linguistics, biolinguistics and evolutionary linguistics or biolinguistics, geography, sociolinguistics, psycholinguistics, neurolinguistics and neurology, linguistic anthropology, and history, as well as related perspectives from anthropology, biology, evolution, psychology, and sociology.
The field takes applied approaches, utilizing scientific findings for practical purposes under the umbrella of applied linguistics. This includes understanding language acquisition and individual language development across the lifespan, from first language acquisition in children to second language learning in adults. Applied linguistics also addresses clinical issues in communication disorders and clinical issues, applying linguistic theory and methods to the study, diagnosis, and assessment of communication disorders. It also includes improving language education and other applied and interdisciplinary subfields such as computational linguistics, as well as areas such as stylistics.

Literature

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 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.

Music

  • Musical analysis – a process attempting to answer the question "How does this music work?"
  • *Musical Analysis is a study of how the composers use the notes together to compose music. Those studying music will find differences with each composer's musical analysis, which differs depending on the culture and history of music studied. An analysis of music is meant to simplify the music for you.
  • Schenkerian analysis
  • *Schenkerian analysis is a collection of music analysis that focuses on the production of the graphic representation. This includes both analytical procedure as well as the notational style. Simply put, it analyzes tonal music which includes all chords and tones within a composition.

    Philosophy

  • Philosophical analysis – a general term for the techniques used by philosophers
  • *Philosophical analysis refers to the clarification and composition of words put together and the entailed meaning behind them. Philosophical analysis dives deeper into the meaning of words and seeks to clarify that meaning by contrasting the various definitions. It is the study of reality, justification of claims, and the analysis of various concepts. Branches of philosophy include logic, justification, metaphysics, values and ethics. If questions can be answered empirically, meaning it can be answered by using the senses, then it is not considered philosophical. Non-philosophical questions also include events that happened in the past, or questions science or mathematics can answer.
  • Analysis is the name of a prominent journal in philosophy.

    Science and technology

Chemistry

The field of chemistry uses analysis in three ways: to identify the components of a particular chemical compound, to identify the proportions of components in a mixture, 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 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.

Types of Analysis

; Qualitative Analysis: It is concerned with which components are in a given sample or compound.
; Quantitative Analysis : It is to determine the quantity of individual component present in a given sample or compound.

Isotopes

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.

Computer science

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.

Mathematics

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 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 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 :

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.