sciences actually constitute a science. Methods of the formal sciences are, however, essential to the construction and testing of scientific models dealing with observable reality,[6] and major advances in formal sciences have often enabled major advances in the empirical sciences.

Logic[edit]

Main articles: Logic and Outline of logic

Logic (from Greek: λογική, logikḗ, 'possessed of reason, intellectual, dialectical, argumentative')[7][8][note 1] is the systematic study of valid rules of inference, i.e. the relations that lead to the acceptance of one proposition (the conclusion) on the basis of a set of other propositions (premises). More broadly, logic is the analysis and appraisal of arguments.[9]

It has traditionally included the classification of arguments; the systematic exposition of the logical forms; the validity and soundness of deductive reasoning; the strength of inductive reasoning; the study of formal proofs and inference (including paradoxes and fallacies); and the study of syntax and semantics.

Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century). More recently, logic has been studied in cognitive science, which draws on computer science, linguistics, philosophy and psychology, among other disciplines.

Mathematics[edit]

Main articles: Mathematics and Outline of mathematics

Mathematics, in the broadest sense, is just a synonym of formal science; but traditionally mathematics means more specifically the coalition of four areas: arithmetic, algebra, geometry, and analysis, which are, roughly speaking, the study of quantity, structure, space, and change respectively.

Statistics[edit]

Main articles: Statistics and Outline of statistics

Statistics is the study of the collection, organization, and interpretation of data.[10][11] It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.[10]

A statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained this experience through working in any of a wide number of fields. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

The word statistics, when referring to the scientific discipline, is singular, as in "Statistics is an art."[12] This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data,[13] whose plural is statistics ("this statistic seems wrong" or "these statistics are misleading").

Systems theory[edit]

Main article: Systems theory

Systems theory is the transdisciplinary study of systems in general, to elucidate principles that can be applied to all types of systems in all fields of research. The term does not yet have a well-established, precise meaning, but systems theory can reasonably be considered a specialization of systems thinking and a generalization of systems science. The term originates from Bertalanffy's General System Theory (GST) and is used in later efforts in other fields, such as the action theory of Talcott Parsons and the sociological autopoiesis of Niklas Luhmann.

In this context the word systems is used to refer specifically to self-regulating systems, i.e. that are self-correcting through feedback. Self-regulating systems are found in nature, including the physiological systems of our body, in local and global ecosystems, and climate.

Decision theory[edit]

Main article: Decision theory

Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent's choices.[14] Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do.

Decision theory is closely related to the field of game theory [15] and is an interdisciplinary topic, studied by economists, statisticians, psychologists, biologists,[16] political and other social scientists, philosophers,[17] and computer scientists.

Empirical applications of this rich theory are usually done with the help of statistical and econometric methods.

Theoretical computer science[edit]

Main article: Theoretical computer science

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.

It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description:[18]

TCS covers a wide variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic computation, quantum computation, automata theory, information theory, cryptography, program semantics and verification, machine learning, computational biology, computational economics, computational geometry, and computational number theory and algebra. Work in this field is often distinguished by its emphasis on mathematical technique and rigor.

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