Mathematics
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NIM; includes arithmetic, geometry, calculus; differentiate from STATISTICS |
Mathematics Categories.
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Algorithms - A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. |
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Finite Element Analysis - A computer based method of simulating or analyzing the behavior of structures or components. |
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Fourier Analysis - Analysis based on the mathematical function first formulated by Jean-Baptiste-Joseph Fourier in 1807. The function, known as the Fourier transform, describes the sinusoidal pattern of any fluctuating pattern in the physical world in terms of its amplitude and its phase. It has broad applications in biomedicine, e.g., analysis of the x-ray crystallography data pivotal in identifying the double helical nature of DNA and in analysis of other molecules, including viruses, and the modified back-projection algorithm universally used in computerized tomography imaging, etc. (From Segen, The Dictionary of Modern Medicine, 1992) |
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Fractals - Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time. |
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Game Theory - Theoretical construct used in applied mathematics to analyze certain situations in which there is an interplay between parties that may have similar, opposed, or mixed interests. In a typical game, decision-making "players," who each have their own goals, try to gain advantage over the other parties by anticipating each other's decisions; the game is finally resolved as a consequence of the players' decisions. |
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Mathematical Computing - Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem. |
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Nonlinear Dynamics - The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos. |
Mathematics Definitions and Terms
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