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6 produkter
6 produkter
218 kr
Skickas inom 5-8 vardagar
Reflections on the Foundations of Mathematics
Univalent Foundations, Set Theory and General Thoughts
Inbunden, Engelska, 2019
1 584 kr
Skickas inom 10-15 vardagar
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations.
Reflections on the Foundations of Mathematics
Univalent Foundations, Set Theory and General Thoughts
Häftad, Engelska, 2020
1 584 kr
Skickas inom 10-15 vardagar
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations.
1 281 kr
Skickas inom 10-15 vardagar
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis […] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever.In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionisticlogic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
1 281 kr
Skickas inom 10-15 vardagar
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis […] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever.In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionisticlogic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Problem Posing and Solving for Mathematically Gifted and Interested Students
Best Practices, Research and Enrichment
Häftad, Engelska, 2023
1 245 kr
Skickas inom 10-15 vardagar
Mathematics and mathematics education research have an ongoing interest in improving our understanding of mathematical problem posing and solving. This book focuses on problem posing in a context of mathematical giftedness. The contributions particularly address where such problems come from, what properties they should have, and which differences between school mathematics and more complex kinds of mathematics exist. These perspectives are examined internationally, allowing for cross-national insights.