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Although earlier philosophical principles which aim to ground scientific theory in some verifiable experience are found within the work of American pragmatist C.S. Peirce and that of French conventionalist Pierre Duhem, [4] who fostered instrumentalism, [5] the project of verificationism was launched by the logical positivists who, emerging from the Berlin Circle and the Vienna Circle in the ...
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology . [ 1 ]
In mathematics, graph theory is the study of graphs, ... and others. The study and the generalization of this problem by Tait, Heawood, ...
The Fréchet derivative defines the derivative for general normed vector spaces,.Briefly, a function :, where is an open subset of , is called Fréchet differentiable at if there exists a bounded linear operator: such that ‖ ‖ ‖ (+) ‖ ‖ ‖ =
In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. [1] In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a
Euler's theorem is a generalization of Fermat's little theorem: For any modulus n and any integer a coprime to n, one has (), where φ(n) denotes Euler's totient function (which counts the integers from 1 to n that are coprime to n).
Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general.
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring.The concept of module also generalizes the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.