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Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. [1] Specific mathematical techniques that are commonly used in statistics include mathematical analysis , linear algebra , stochastic analysis , differential equations , and ...
The concept has an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. [9] [10] All statistical analyses make use of at least some mathematics, and mathematical statistics ...
Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality. [1]
The concept has an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in "discrete" steps and ...
The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. [46] [47] Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. [48]
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