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This is a list of mathematical theories. Almgren–Pitts min-max theory; ... Lie theory; M-theory; Measure theory; Model theory; Morse theory; Module theory;
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon.
The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, parts of computer science. Subsequent discoveries in the 20th century then stabilized the foundations of ...
(There are no theories whose models are exactly sets of cardinality N if N is an infinite subset of the integers.) The complete theories are the theories of sets of cardinality n for some finite n, and the theory of infinite sets. One special case of this is the inconsistent theory defined by the axiom ∃x ¬x = x. It is a perfectly good ...
Mathematical modeling of learning process were greatly developed in the 1950s as the behavioral learning theory was flourishing. One development is the stimulus sampling theory by Williams K. Estes , the other is linear operator models by Robert R. Bush, and Frederick Mosteller .
The learning theories of John Dewey, Maria Montessori, and David A. Kolb serve as the foundation of the application of constructivist learning theory in the classroom. [40] Constructivism has many varieties such as active learning , discovery learning , and knowledge building , but all versions promote a student's free exploration within a ...