Global and local

Mathematical Intelligencer 36 (4) (2014)
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The global/local contrast is ubiquitous in mathematics. This paper explains it with straightforward examples. It is possible to build a circular staircase that is rising at any point (locally) but impossible to build one that rises at all points and comes back to where it started (a global restriction). Differential equations describe the local structure of a process; their solution describes the global structure that results. The interplay between global and local structure is one of the great themes of mathematics, but rarely discussed explicitly.



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James Franklin
University of New South Wales

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Discrete and continuous: a fundamental dichotomy in mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
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