Titlebook: Mathematics as a Tool; Tracing New Roles of Johannes Lenhard,Martin Carrier Book 2017 Springer International Publishing AG 2017 Scientific

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Boon and Bane: On the Role of Adjustable Parameters in Simulation Modelsthey are boon and bane of simulation. They help to enlarge the scope of simulation far beyond what can be determined by theoretical knowledge, but at the same time undercut the epistemic value of simulation models.

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Systems Biology in the Light of Uncertainty: The Limits of Computationgmatic or investigative goals in mind, suggesting an important role for rationalizing uses of computation in systems biology and elsewhere as investigative tools. We discuss the concept of an “investigative tool”, and what insights it might offer our understanding of modern computational strategies and the bases for them.

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Object Oriented Models vs. Data Analysis – Is This the Right Alternative?ch theoretical guidance from other disciplines. This calls for new principles that are structural, abstract and independent of specific content. Mathematics then is no longer the tool of science, but becomes the science of tools.

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Shaping Mathematics as a Tool: The Search for a Mathematical Model for Quasi-crystalsations of different desiderata can take place. This framework is then illustrated by a case study of the early efforts to produce a mathematical model for quasi-crystals in the first two decades after Dan Shechtman’s discovery of this new phenomenon in 1984.

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The Vindication of Computer Simulationsify the circumstances under which simulations can be relied upon. With this in mind, this paper articulates a general perspective to better understand and compare the strengths and weaknesses of various error-analysis methods.

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Forcing Optimality and Brandt’s Principlewhat we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle.

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Trigonometry, Construction by Straightedge and Compass, and the Applied Mathematics of the ,es questions with regard to the comparative advantages of trigonometry over the older geometrical methods, and the particular emphasis that they received in the context of Greek mathematical astronomy.

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Barrister

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