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Making and Breaking Mathematical Sense : Histories and Philosophies of Mathematical Practice / / Roi Wagner
| Making and Breaking Mathematical Sense : Histories and Philosophies of Mathematical Practice / / Roi Wagner |
| Autore | Wagner Roi |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2017] |
| Descrizione fisica | 1 online resource (251 pages) |
| Disciplina | 510.1 |
| Soggetto topico |
Mathematics - Philosophy - History
Mathematics - History |
| Soggetto genere / forma |
History
Electronic books. |
| Soggetto non controllato |
Benedetto
Black-Scholes formula Eugene Wigner Friedrich W.J. Schelling George Lakoff Gilles Deleuze Hermann Cohen Hilary Putnam Johann G. Fichte Logic of Sensation Mark Steiner Rafael Nez Stanislas Dehaene Vincent Walsh Water J. Freeman III abbaco algebra arithmetic authority cognitive theory combinatorics conceptual freedom constraints economy gender role stereotypes generating functions geometry inferences infinities infinity mathematical cognition mathematical concepts mathematical cultures mathematical domains mathematical entities mathematical evolution mathematical interpretation mathematical language mathematical metaphor mathematical norms mathematical objects mathematical practice mathematical signs mathematical standards mathematical statements mathematics natural order natural sciences nature negative numbers number sense option pricing philosophy of mathematics reality reason relevance semiosis sexuality stable marriage problem |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title; Copyright; Dedication; Contents; Acknowledgments; Introduction; What Philosophy of Mathematics Is Today; What Else Philosophy of Mathematics Can Be; A Vignette: Option Pricing and the Black-Scholes Formula; Outline of This Book; Chapter 1: Histories of Philosophies of Mathematics; History 1: On What There Is, Which Is a Tension between Natural Order and Conceptual Freedom; History 2: The Kantian Matrix, Which Grants Mathematics a Constitutive Intermediary Epistemological Position; History 3: Monster Barring, Monster Taming, and Living with Mathematical Monsters.
History 4: Authority, or Who Gets to Decide What Mathematics Is AboutThe "Yes, Please!" Philosophy of Mathematics; Chapter 2: The New Entities of Abbacus and Renaissance Algebra; Abbacus and Renaissance Algebraists; The Emergence of the Sign of the Unknown; First Intermediary Reflection; The Arithmetic of Debited Values; Second Intermediary Reflection; False and Sophistic Entities; Final Reflection and Conclusion; Chapter 3: A Constraints-Based Philosophy of Mathematical Practice; Dismotivation; The Analytic A Posteriori; Consensus; Interpretation; Reality; Constraints; Relevance; Conclusion. Chapter 4: Two Case Studies of Semiosis in MathematicsAmbiguous Variables in Generating Functions; Between Formal Interpretations; Models and Applications; Openness to Interpretation; Gendered Signs in a Combinatorial Problem; The Problem; Gender Role Stereotypes and Mathematical Results; Mathematical Language and Its Reality; The Forking Paths of Mathematical Language; Chapter 5: Mathematics and Cognition; The Number Sense; Mathematical Metaphors; Some Challenges to the Theory of Mathematical Metaphors; Best Fit for Whom?; What Is a Conceptual Domain?; In Which Direction Does the Theory Go? So How Should We Think about Mathematical Metaphors?An Alternative Neural Picture; Another Vision of Mathematical Cognition; From Diagrams to Haptic Vision; Haptic Vision in Practice; Chapter 6: Mathematical Metaphors Gone Wild; What Passes between Algebra and Geometry; Piero della Francesca (Italy, Fifteenth Century); Omar Khayyam (Central Asia, Eleventh Century); Rene Descartes (France, Seventeenth Century); Rafael Bombelli (Italy, Sixteenth Century); Conclusion; A Garden of Infinities; Limits; Infinitesimals and Actual Infinities; Chapter 7: Making a World, Mathematically; Fichte. SchellingHermann Cohen; The Unreasonable Applicability of Mathematics; Bibliography; Index. |
| Record Nr. | UNINA-9910154298703321 |
Wagner Roi
|
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| Princeton, NJ : , : Princeton University Press, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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A primer on mapping class groups [[electronic resource] /] / Benson Farb and Dan Margalit
| A primer on mapping class groups [[electronic resource] /] / Benson Farb and Dan Margalit |
| Autore | Farb Benson |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2012 |
| Descrizione fisica | 1 online resource (489 p.) |
| Disciplina | 512.7/4 |
| Altri autori (Persone) | MargalitDan <1976-> |
| Collana | Princeton mathematical series |
| Soggetto topico |
Mappings (Mathematics)
Class groups (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| Soggetto non controllato |
3-manifold theory
Alexander method Birman exact sequence BirmanЈilden theorem Dehn twists DehnЌickorish theorem DehnЎielsenЂaer theorem Dennis Johnson Euler class FenchelЎielsen coordinates Gervais presentation Grtzsch's problem Johnson homomorphism Markov partitions Meyer signature cocycle Mod(S) Nielsen realization theorem NielsenДhurston classification theorem NielsenДhurston classification Riemann surface Teichmller mapping Teichmller metric Teichmller space Thurston compactification Torelli group Wajnryb presentation algebraic integers algebraic intersection number algebraic relations algebraic structure annulus aspherical manifold bigon criterion braid group branched cover capping homomorphism classifying space closed surface collar lemma compactness criterion complex of curves configuration space conjugacy class coordinates principle cutting homomorphism cyclic subgroup diffeomorphism disk existence theorem extended mapping class group finite index finite subgroup finite-order homeomorphism finite-order mapping class first homology group geodesic laminations geometric classification geometric group theory geometric intersection number geometric operation geometry harmonic maps holomorphic quadratic differential homeomorphism homological criterion homotopy hyperbolic geometry hyperbolic plane hyperbolic structure hyperbolic surface inclusion homomorphism infinity intersection number isotopy lantern relation low-dimensional homology mapping class group mapping torus measured foliation space measured foliations metric geometry moduli space orbifold orbit outer automorphism group pseudo-Anosov homeomorphism punctured disk quasi-isometry quasiconformal map second homology group simple closed curve simplicial complex stretch factors surface bundles surface homeomorphism surface symplectic representation topology torsion torus train track |
| ISBN |
1-283-22743-6
9786613227430 1-4008-3904-1 |
| Classificazione | SK 260 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory. |
| Record Nr. | UNINA-9910461382703321 |
|
Farb Benson
|
||
| Princeton, N.J., : Princeton University Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A primer on mapping class groups [[electronic resource] /] / Benson Farb and Dan Margalit
| A primer on mapping class groups [[electronic resource] /] / Benson Farb and Dan Margalit |
| Autore | Farb Benson |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2012 |
| Descrizione fisica | 1 online resource (489 p.) |
| Disciplina | 512.7/4 |
| Altri autori (Persone) | MargalitDan <1976-> |
| Collana | Princeton mathematical series |
| Soggetto topico |
Mappings (Mathematics)
Class groups (Mathematics) |
| Soggetto non controllato |
3-manifold theory
Alexander method Birman exact sequence BirmanЈilden theorem Dehn twists DehnЌickorish theorem DehnЎielsenЂaer theorem Dennis Johnson Euler class FenchelЎielsen coordinates Gervais presentation Grtzsch's problem Johnson homomorphism Markov partitions Meyer signature cocycle Mod(S) Nielsen realization theorem NielsenДhurston classification theorem NielsenДhurston classification Riemann surface Teichmller mapping Teichmller metric Teichmller space Thurston compactification Torelli group Wajnryb presentation algebraic integers algebraic intersection number algebraic relations algebraic structure annulus aspherical manifold bigon criterion braid group branched cover capping homomorphism classifying space closed surface collar lemma compactness criterion complex of curves configuration space conjugacy class coordinates principle cutting homomorphism cyclic subgroup diffeomorphism disk existence theorem extended mapping class group finite index finite subgroup finite-order homeomorphism finite-order mapping class first homology group geodesic laminations geometric classification geometric group theory geometric intersection number geometric operation geometry harmonic maps holomorphic quadratic differential homeomorphism homological criterion homotopy hyperbolic geometry hyperbolic plane hyperbolic structure hyperbolic surface inclusion homomorphism infinity intersection number isotopy lantern relation low-dimensional homology mapping class group mapping torus measured foliation space measured foliations metric geometry moduli space orbifold orbit outer automorphism group pseudo-Anosov homeomorphism punctured disk quasi-isometry quasiconformal map second homology group simple closed curve simplicial complex stretch factors surface bundles surface homeomorphism surface symplectic representation topology torsion torus train track |
| ISBN |
1-283-22743-6
9786613227430 1-4008-3904-1 |
| Classificazione | SK 260 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory. |
| Record Nr. | UNINA-9910789789803321 |
|
Farb Benson
|
||
| Princeton, N.J., : Princeton University Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||