Mathematical generalization from the articulation of advanced mathematical thinking and knot theory
نویسندگان
چکیده
منابع مشابه
Reflections on APOS theory in Elementary and Advanced Mathematical Thinking
What are the processes by which we construct mathematical concepts? What is the nature of the cognitive entities constructed in this process? Based on the theories of cognitive construction developed by Piaget for younger children, Dubinsky proposed APOS theory to describe how act ions become interiorized into processes and then encapsulated as mental objects, which take their place in more sop...
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ion is the isolation of specific attributes of a concept so that they can be considered separately from the other attributes. Abstraction is often coupled with generalization. But the two are by no means synonymous. For instance, the solution of linear equations in two variables may be seen as a generalization to the process of solving linear equations in three variables. Although one may argue...
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A b st r a ct. The problem of how best to generalize from a given learning set of input-output examples is cent ral to the fields of neur al nets, statistics, approximation theory, and artificial intelligence. This series of pap ers inve stigates this problem from within an abst ract and mod elindepend ent fr amework and then test s some of the resultant concept s in real-world situations. In t...
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ژورنال
عنوان ژورنال: Acta Scientiae
سال: 2020
ISSN: 2178-7727
DOI: 10.17648/acta.scientiae.5667