funmath.be
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FunmathFunctional mathematicsMenu:Introduction Formalism History References Links EventsWhat is a function in mathematics? This question is answered in quite some detail (occasionally technical) in the paper Rekindling critical thinking: heeding major errors in current Introduction to Proof type textbooks. Note that this is only an initial version, prepared for MathFest 2015. All questions, comments and suggestions sent to raymond.boute@pandora.be would be much appreciated. Please note that, due to priorities, this site is maintained only very occasionally (last time was 5 years ago, and this entry is not counted as maintenance). IntroductionWhat is Funmath?Funmath stands for Functional mathematics (for other uses of the name, look here). The underlying principle consists in defining mathematical concepts as functions (hence the name) whenever doing so is appropriate. This turns out to be especially convenient where it has not yet become common practice. Funmath provides a simple and coherent framework for establishing more convenient mathematical conventions, styles of expression, exposition and (calculational) reasoning in most branches of pure and applied mathematics.Important remark From the preceding paragraph, it is clear that we are talking here about mathematical reasoning by humans (say, "pencil and paper") and communication among humans. In the current version of this website, we refer only occasionally to automated tools or mathematical software (e.g., when mentioning current and future work).What is its purpose?Funmath is designed to make the idea of letting the symbols do the work feasible and convenient in everyday mathematical practice. This idea is nicely captured by the logo (shown on the left)of the conference series on the Mathematics of Program Construction (MPC), which is oriented towards Computer Science. Making this idea work in a wider context, for every "working mathematician" (not "logicians only") and every engineer in classical as well as computer-related areas, requires a framework that is free of the many defects (ambiguities, abuses of notation, inconsistencies etc.) one encounters in common mathematical conventions, as discussed in a later subsection. Funmath provides such a defect-free framework, while also preserving the "look and feel" of familiar conventions to the largest extent possible without hampering the stated purpose. It is more expressive and convenient than traditional conventions, and is eminently suitable when working just with pencil and paper or on the blackboard.Where is it useful?Funmath is applicable at all levels of mathematical practice, starting from the most elementary ones. However, it is most useful at the higher levels and for the mathematical modeling of systems in all branches of engineering. In particular, in its design we paid special attention to bridging the methodological gap that has grown between classical engineering discipli
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