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Parallelizations in Weihrauch Reducibility and Constructive Reverse Mathematics [PDF]
Lecture Notes in Computer Science, 2020 Makoto Fujiwara
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Instance reducibility and Weihrauch degrees [PDF]
Logical Methods in Computer Science, 2022 We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in reverse constructive
Andrej Bauer
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Misconceptions about Numbers and Operations–A Case Study of Preschoolers [PDF]
Educational Process: International Journal, 2023 Background/purpose – Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs.
Artemis Eleftheriadi, Konstantinos Lavidas, Gerasimos Koustourakis, Stamatis Papadakis
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Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We propose a new model of computation based on nonstandard analysis. Intuitively, the role of "algorithm" is played by a new notion of finite procedure, called Omega-invariance and inspired by physics, from nonstandard analysis.
Sam Sanders
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The Brouwer invariance theorems in reverse mathematics
Forum of Mathematics, Sigma, 2020 In [12], John Stillwell wrote, ‘finding the exact strength of the Brouwer invariance theorems seems to me one of the most interesting open problems in reverse mathematics.’ In this article, we solve Stillwell’s problem by showing that (some forms of) the
Takayuki Kihara
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COVID Learning Loss: A Call to Action
Numeracy, 2023 The COVID-19 pandemic and policy responses designed to mitigate transmission have caused deep and persistent mathematics learning loss among K–12 students.
Nathan Grawe
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The computational content of Nonstandard Analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs.
Sam Sanders
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The Digital and the Real Universe Foundations of Natural Philosophy and Computational Physics
Philosophies, 2019 In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts.
Klaus Mainzer
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Reverse Mathematics in Bishop’s Constructive Mathematics
Philosophia Scientiæ, 2006 We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.
Hajime Ishihara
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Foundations of Online Structure Theory II: The Operator Approach [PDF]
Logical Methods in Computer Science, 2021 We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory.
Rod Downey +2 more
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