Proceedings Article10.1109/SYNASC.2012.79
What is an Equation
Solomon Marcus,Stephen M. Watt +1 more
- 26 Sep 2012
- pp 23-29
TL;DR: It may not be possible to decide into which of these cases a particular equality falls, although some languages make distinctions among ideas such equations that are always satisfied versus those that may be, or between equations with variables and relations without.
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Abstract: The equation concept is one of the most fundamental in mathematics, yet the word "equation" means different things to different people. It is used not only with various precise technical meanings, but also as a metaphor for complex situations. We review some of the history of the equation and its present meaning and use in a variety of settings. Although some languages make distinctions among ideas such equations that are always satisfied versus those that may not be, or between equations with variables and relations without, we observe that it may not be possible to decide into which of these cases a particular equality falls.
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Citations
Concrete Preliminary Damage Inspection by Classification of Terrestrial Laser Scanner Point Clouds through Systematic Threshold Definition
TL;DR: A novel approach for automatic, preliminary detection of damage in concrete structures using ground-based terrestrial laser scanners using a systematic point-wise defect classifier that automatically diagnoses the location of superficial damage on the investigated region.
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Solomon Marcus Contributions to Theoretical Computer Science and Applications
Cristian S. Calude,Gheorghe Paun +1 more
- 05 Apr 2021
TL;DR: This paper briefly presents his publications in theoretical computer science and related areas, which consist in almost ninety papers, and presents a selection of ten Marcus books in these areas.
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The Effort to Realize a Global Digital Mathematics Library
Patrick D. F. Ion
- 11 Jul 2016
TL;DR: A decade after a resolution in 2006 by the International Mathematical Union endorsing the notion of a global digital mathematics library, and following a thorough report on possibilities written under the auspices of the US National Research Council in 2012, an 8-person Working Group is still working toward implementations of some of the ideas.
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Ranking of Mathematical Equations within a Scientific Document
Jason Lin,Yi-Lun Lo +1 more
- 25 Sep 2023
TL;DR: An algorithm to rank mathematical equations within a scientific document based on their importance is presented. The algorithm considers the number of occurrences, density of mathematical objects, number of mathematical identifiers, and length of the equation. It tackles the issue of consecutive multiple identifiers and utilizes an aggregator to transform features into a single score. The results show an improvement over the baseline method.
References
Where mathematics comes from : how the embodied mind brings mathematics into being
George Lakoff,Rafael E. Núñez +1 more
TL;DR: The authors argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious, from arithmetic and algebra to sets and logic to infinity in all of its forms, and that abstract ideas for the most part arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world.
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A history of mathematical notations
Florian Cajori
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TL;DR: Volume I, Notations in Elementary Mathematics, just off the press, is sure to be an indispensable addition to every school and college library and will add greatly to the appreciation and understanding of elementary mathematics.
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Some undecidable problems involving elementary functions of a real variable
TL;DR: Let E be a set of expressions representing real, single valued, partially defined functions of one real variable and E * be the set of functions represented by expressions in E .
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On Canonical Forms and Simplification
TL;DR: It is shown that canonical forms do not exist for sufficiently rich classes of mathematical expressions, but with the aid of a nmnber- theoretic conjecture, a large subclass of the negative classes is shown to possess a canonical form.
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