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In addition to John R. Anderson, Joshua Tenenbaum has been a contributor to the field of concept learning; he studied the computational basis of human learning and inference using behavioral testing of adults, children, and machines from Bayesian statistics and probability theory, but also from geometry, graph theory, and linear algebra ...
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. [1] The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change ...
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [ 1 ] [ 2 ] For example, { 3 x + 2 y − z = 1 2 x − 2 y + 4 z = − 2 − x + 1 2 y − z = 0 {\displaystyle {\begin{cases}3x+2y-z=1\\2x-2y+4z=-2\\-x+{\frac {1}{2}}y-z=0\end{cases}}}
In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
The term conceptual model refers to any model that is formed after a conceptualization or generalization process. [1] [2] Conceptual models are often abstractions of things in the real world, whether physical or social. Semantic studies are relevant to various stages of concept formation. Semantics is fundamentally a study of concepts, the ...
Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are L p spaces, which are Banach spaces, and especially the L 2 space of square integrable functions, which is the only Hilbert space among them. Functional ...
[1] A concept definition is similar to the usual notion of a definition in mathematics, with the distinction that it is personal to an individual: "a personal concept definition can differ from a formal concept definition, the latter being a concept definition which is accepted by the mathematical community at large." [1]