Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. Analysts in the field of engineering look at requirements, structures, mechanisms, systems and dimensions.
The field of intelligence employs analysts to break down and understand a wide array of questions. Linguistics look at individual languages and language in general. Literary criticism is the analysis of literature.
The focus can be as diverse as the analysis of Homer or Freud. Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. 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. 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. 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.