Mathesis Universalis, Computability and Proof / / edited by Stefania Centrone, Sara Negri, Deniz Sarikaya, Peter M. Schuster |
Edizione | [1st ed. 2019.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
Descrizione fisica | 1 online resource (375 pages) |
Disciplina | 511.3 |
Collana | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science |
Soggetto topico |
Logic
Mathematical logic Mathematical Logic and Foundations Mathematical Logic and Formal Languages |
ISBN | 3-030-20447-2 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | 1. Introduction: Mathesis Universalis, Proof and Computation (Stefania Centrone) -- 2. Diplomacy of Trust in the European Crisis (Enno Aufderheide) -- 3. Mathesis Universalis and Homotopy Type Theory (Steve Awodey) -- 4. Note on the Benefit of Proof Representations by Name (Matthias Baaz) -- 5. Constructive Proofs of Negated Statements (Josef Berger and Gregor Svindland) -- 6. Constructivism in Abstract Mathematics (Ulrich Berger) -- 7. Addressing Circular Definitions via Systems of Proofs (Riccardo Bruni) -- 8. The Monotone Completeness Theorem in Constructive Reverse Mathematics (Hajime Ishihara and Takako Nemoto) -- 9. From Mathesis Universalis to Fixed Points and Related Set-Theoretic Concepts (Gerhard Jäger and Silvia Steila) -- 10. Through an Inference Rule, Darkly (Roman Kuznets) -- 11. Objectivity and Truth in Mathematics: A Sober Non-Platonist Perspective (Godehard Link) -- 12. From Mathesis Universalis to Provability, Computability, and Constructivity (Klaus Mainzer) -- 13. Analytic Equational Proof Systems for Combinatory Logic and λ-Calculus: a Survey (Pierluigi Minari) -- 14. Computational Interpretations of Classical Reasoning: From the Epsilon Calculus to Stateful Programs (Thomas Powell) -- 15. The Concepts of Proof and Ground (Dag Prawitz) -- 16. On Relating Theories: Proof-Theoretical Reduction (Michael Rathjen and Michael Toppel) -- 17. Program Extraction from Proofs: the Fan Theorem for Uniformly Coconvex Bars (Helmut Schwichtenberg) -- 18. Counting and Numbers, from Pure Mathesis to Base Conversion Algorithms (Jan von Plato) -- 19. Point-Free Spectra of Linear Spreads (Daniel Wessel). . |
Record Nr. | UNINA-9910349539003321 |
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
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Lo trovi qui: Univ. Federico II | ||
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Problem posing and solving for mathematically gifted and interested students : best practices, research and enrichment / / Deniz Sarikaya, Lukas Baumanns, Karl Heuer, Benjamin Rott, editors |
Pubbl/distr/stampa | Wiesbaden : , : Springer Spektrum, , [2023] |
Descrizione fisica | 1 online resource (xii, 227 pages) : illustrations |
Disciplina | 510 |
Soggetto topico |
Mathematics - Study and teaching
Mathematics General Mathematics and Education General Mathematics |
ISBN |
3-658-41061-2
9783658410612 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | How to identify and foster mathematically gifted children in times of the pandemic, experiences from the PriSMa-project: Kinder der Primarstufe und Sekundarstufe auf verschiedenen Wegen zur Mathematik -- Problem Posing as a Central Criterion for the Support of Mathematically Highly Gifted Teenagers within the Program Pri(S)Ma -- Teaching problem solving – a problem-thread from the Pósa method. -- on excellence classes, title TBA -- Choosing problems by association. -- Differences and similarities between Open-start and Open-end mathematical tasks. (TBC) -- An enrichment course based on challenging problems – effects on students and teachers. -- Three articles by the WURM-Project: Workshops on Using Rich Mathematical Concepts for Educational Outreach and Advancement -- A story of multiple-year problem posing of a single problem for mathematics competition. -- Problem-posing processes: A comparison of structured and unstructured situations. -- Mathematics as a craft or how to train dimensions of problem variation: A illustrative William-Stern-Society – style example. |
Record Nr. | UNINA-9910746949803321 |
Wiesbaden : , : Springer Spektrum, , [2023] | ||
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Lo trovi qui: Univ. Federico II | ||
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Reflections on the Foundations of Mathematics : Univalent Foundations, Set Theory and General Thoughts / / edited by Stefania Centrone, Deborah Kant, Deniz Sarikaya |
Edizione | [1st ed. 2019.] |
Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
Descrizione fisica | 1 online resource (510 pages) |
Disciplina |
511.3
511.322 |
Collana | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science |
Soggetto topico |
Mathematics - Philosophy
Computer science - Mathematics Mathematical logic Mathematical physics Machine theory Philosophy of Mathematics Mathematics of Computing Mathematical Logic and Foundations Theoretical, Mathematical and Computational Physics Formal Languages and Automata Theory |
ISBN | 3-030-15655-9 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Part I: Current Challenges for the Set Theoretic Foundations -- 1. Neil Barton and Sy-David Friedman: Does set theory need an apology? -- 2. Laura Fontanella: The choice of new axioms in set theory -- 3. Michèle Friend: Pluralism in Foundations of Mathematics: Oxymoron, Paradox, Neither or Both? -- 4. Deborah Kant: A distinction between meta set theory and object set theory -- 5. Jan von Plato: The weaknesses of set theory -- 6. Claudio Ternullo: Multiversism and Naturalism -- 7. Philip Welch: Proving Theorems from Reflection: Global Reflection Theorems -- Part II: What are the Univalent Foundations? -- 8. Benedikt Ahrens and Paige North: Univalent foundations and the equivalence principle -- 9. Thorsten Altenkirch: A constructive justification of Homotopy Type Theory -- 10. Ulrik Buchholtz: Title: Higher structures in Homotopy Type Theory -- 11. Andrei Rodin: Models of HoTT and the Semantic View of Theories -- 12. Urs Schreiber: Modern Physics formalized in Modal Homotopy Type Theory -- 13. Vladimir Voevodsky: Multiple Concepts of Equality in the New Foundations of Mathematics -- Part III: Thoughts on the Foundations of Mathematics -- 14. Nathan Bowler: Foundations for the working mathematician, and for their computer -- 15. Merlin Carl: Formal and Natural Proof - A phenomenological approach -- 16. Stefania Centrone and Deniz Sarikaya: Thoughts on the Foundation of Mathematics: Logicism, Intuitionism and Formalism -- 17. Mirna Džamonja: A new foundational crisis in mathematics, is it really happening? -- 18. Penelope Maddy: What foundational jobs do we want done? -- 19. Giovanni Sambin: Dynamics in foundations: what does it mean in practice -- 20. Roy Wagner: Does mathematics need foundations?. |
Record Nr. | UNINA-9910357845703321 |
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
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Lo trovi qui: Univ. Federico II | ||
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