Theory and practice : a history of two centuries of Dutch mathematics education / / Harm Jan Smid

• Record Nr.: UNINA9910637740803321
• Autore: Smid Harm Jan
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783031218736; 9783031218729
• Descrizione fisica: 1 online resource (323 pages)
• Collana: International Studies in the History of Mathematics and Its Teaching
• Disciplina: 551.48
• Soggetti: Mathematics - Study and teaching; Ensenyament de la matemàtica; Llibres electrònics; Països Baixos
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- Contents -- Contents -- List of Abbreviations and Acronyms -- Chapter 1: Introduction -- 1.1 A Short Bibliography of the History of Dutch Mathematics Education -- Chapter 2: Prologue -- 2.1 Primary Schools -- 2.2 Latin Schools -- 2.3 French and Vocational Schools -- 2.4 Societies -- 2.5 Universities and Polytechnics Avant la Lettre -- 2.6 An Exceptional Country -- 2.7 On the Threshold of a New Era -- 2.8 Reform in a European Context -- 2.9 Conclusion -- Chapter 3: The Emergence of Mathematics as a School Topic -- 3.1 Latin Schools 1815-1826 -- 3.1.1 The Decree of 1815 -- 3.1.2 The Teachers -- 3.1.3 Content and Organisation -- 3.1.4 Lesson Plans -- 3.1.5 Textbooks -- 3.1.6 Jacob de Gelder -- 3.1.7 A Conflict at the Latin School of Leiden -- 3.1.8 Towards a Step Forward -- 3.2 Latin Schools 1826-1838 -- 3.2.1 The Decrees of 1826 and 1827 -- 3.2.2 Textbooks and Didactical Publications by Jacob de Gelder -- 3.2.3 The Effect of the Measures -- 3.2.4 Some More Details: Amsterdam, Leiden and Rotterdam -- 3.2.5 Teachers and Didactics -- 3.2.6 Some Form of Teacher Training -- 3.2.7 Conclusion -- 3.3 Latin Schools 1838-1876 -- 3.3.1 The Second Departments -- 3.3.2 The ; Curricula at the Gymnasia -- 3.3.3 Teachers -- 3.3.4 Textbooks -- 3.3.5 The State Exam and Afterwards -- 3.4 Mathematics Teaching at Other Schools -- 3.4.1 Primary Schools -- 3.4.2 French Schools -- 3.4.3 Vocational Schools -- 3.5 Summary and Analysis -- Chapter 4: The HBS and the New Gymnasia -- 4.1 The First Decades of the HBS -- 4.1.1 The Law on Secondary Education of 1863 -- 4.1.2 The Schools for Secondary Education -- 4.1.3 The Mathematics Curriculum at the HBS -- 4.1.4 Teachers -- 4.1.5 Textbooks -- 4.1.6 Jan Versluys -- 4.1.7 In a Wider Perspective -- 4.2 Reform of Latin Schools -- 4.2.1 The Curriculum -- 4.2.2 Teachers and Textbooks.; 4.3 Classical Versus Realistic Education -- 4.3.1 Gymnasia and HBS in a European Context -- 4.3.2 The Prussian Example -- Chapter 5: Stagnation and Reform: Curricula 1900-1968 -- 5.1 A Patchwork of Laws and Schools -- 5.1.1 Lycea -- 5.1.2 HBS-A -- 5.1.3 Extended Primary and Vocational Schools -- 5.1.4 Summary -- 5.2 HBS and Gymnasia in the First Decades of the Twentieth Century -- 5.2.1 Arithmetic -- 5.2.2 Algebra, Geometry and Trigonometry -- 5.2.3 Failed Reform in the HBS -- 5.2.4 Reform at the Gymnasia -- 5.3 The Third and Fourth Decade -- 5.3.1 Eduard Jan Dijksterhuis -- 5.3.2 The Beth-Dijksterhuis Proposals -- 5.3.3 The Reception of the Report -- 5.3.4 The Curriculum of 1937 -- 5.4 After the War -- 5.4.1 The Wimecos Curriculum -- 5.5 Extended Primary Schools and Vocational Schools -- 5.6 Summary and Analysis -- Chapter 6: Teachers, Textbooks and Didactics 1900-1968 -- 6.1 Teachers -- 6.1.1 Teacher Education -- 6.1.2 Teacher Organisations -- 6.1.3 Liwenagel -- 6.1.4 Wimecos -- 6.1.5 Other Organisations -- 6.1.6 An Outsider: The Wiskunde Werkgroep -- 6.2 Journals for Teachers -- 6.2.1 Wiskundig Tijdschrift -- 6.2.2 Euclides -- 6.3 Textbooks and Didactics -- 6.3.1 Pieter Wijdenes -- 6.3.2 Aside from the Mainstream -- 6.3.3 After the War -- Chapter 7: Modern Mathematics -- 7.1 Prelude -- 7.1.1 Van Dantzig -- 7.1.2 Modern Mathematics -- 7.1.3 The Dutch at Royaumont -- 7.2 The CMLW -- 7.2.1 Hans Freudenthal -- 7.2.2 The Early Years of the CMLW -- 7.2.3 A Complication: A New Law on Secondary Education -- 7.2.4 New Experts -- 7.2.5 Wiskobas -- 7.2.6 From CMLW to IOWO -- 7.3 New Curricula and Textbooks -- 7.3.1 The Problem of the Textbooks -- 7.3.2 The New Curricula and Exam Programs -- 7.3.3 Motivation and Criticism -- 7.4 After 1968 -- 7.4.1 Results and Effects of the New Curriculum -- 7.4.2 Didactical Activities -- 7.5 In Hindsight.; 7.5.1 Stagnation Versus Reform -- 7.5.2 The Role of Freudenthal -- Chapter 8: Realistic Mathematics Education -- 8.1 The IOWO and OW&amp -- OC -- 8.1.1 Realistic Mathematics Education (RME): Wiskobas -- 8.1.2 RME: Wiskivon -- 8.2 RME: Mathematics A -- 8.2.1 The Hewet Report -- 8.2.2 The Hewet Project -- Chapter 9: Epilogue -- 9.1 After Hewet -- 9.1.1 The W12-16 Project -- 9.1.2 The 'Profiles': New Exam Programs -- 9.2 Changing Times -- 9.2.1 Criticism of Arithmetic Skills -- 9.2.2 Criticism of Algebraic Skills -- 9.2.3 The Freudenthal Institute -- 9.3 The Success of Realistic Mathematics Education: An Analysis -- 9.3.1 A Tradition of Usability? -- 9.3.2 The Practical Character of the HBS -- 9.3.3 Officials, Experts and Professionals -- 9.4 In a Bird's-Eye View -- References -- Author Index -- Subject Index.

Quantization, Geometry and Noncommutative Structures in Mathematics and Physics / / edited by Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha, Andrés F. Reyes Lega

• Record Nr.: UNINA9910254593203321
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017
• ISBN: 3-319-65427-6
• Edizione: [1st ed. 2017.]
• Descrizione fisica: 1 online resource (X, 341 p. 6 illus.)
• Collana: Mathematical Physics Studies, , 0921-3767
• Disciplina: 530.143
• Soggetti: Quantum field theory; String theory; Mathematical physics; Algebraic geometry; Quantum Field Theories, String Theory; Mathematical Physics; Algebraic Geometry
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Quantization, Geometry and Noncommutative Structures in Mathematics and Physics (A. Cardona, H. Ocampo, P. Morales, S. Paycha, A.F. Reyes Lega (Eds.)) -- General Overview (Alexander Cardona, Sylvie Paycha and Andrés F. Reyes Lega) -- Introduction -- Poisson Geometry and Classical Dynamics -- Geometric and Deformation Quantization -- Noncommutative Geometry and Quantum Groups -- Deformation Quantization and Group Actions (Simone Gutt) -- What do we mean by quantization? -- Deformation Quantization -- Fedosov’s star products on a symplectic manifold -- Classification of Poisson deformations and star products -- Star products on Poisson manifolds and formality -- Group actions in deformation quantization -- Reduction in deformation quantization -- Some remarks about convergence -- . Principal fiber bundles in non-commutative geometry (Christian Kassel) -- Introduction -- Review of principal fiber bundles -- Basic ideas of non-commutative geometry -- From groups to Hopf ; algebras -- Quantum groups associated with SL2(C) -- Group actions in non-commutative geometry -- Hopf Galois extensions -- Flat deformations of Hopf algebras -- An Introduction to Nichols Algebras (Nicolás Andruskiewitsch) -- Preliminaries -- Braided tensor categories -- Nichols algebras -- Classes of Nichols algebras -- Quantum Field Theory in Curved Space-Time (Andrés F. Reyes Lega) -- Introduction -- Quantum Field Theory in Minkowski Space-Time -- Quantum Field Theory in Curved Space-Time -- Cosmology -- An Introduction to Pure Spinor Superstring Theory (Nathan Berkovits and Humberto Gomez) -- Introduction -- Particle and Superparticle -- Pure Spinor Superstring -- Appendix -- Introduction to Elliptic Fibrations (Mboyo Esole) -- Introduction -- Elliptic curves over C -- Elliptic fibrations -- Kodaira-Néron classification of singular fibers -- Miranda models -- Batalin–Vilkovisky formalism as a theory of integration for polyvectors (Pierre J. Clavier and Viet Dang Nguyen) -- Motivations and program -- BV integral -- Gauge fixing -- Master equations -- Conclusion -- Split Chern-Simons theory in the BV-BFV formalism (Alberto S. Cattaneo, Pavel Mnev, and Konstantin Wernli) -- Introduction -- Overview of the BV and BV-BFV formalisms -- Chern-Simons theory as a BF-like theory -- Split Chern-Simons theory on the solid torus -- Conclusions and outlook -- Weighted direct product of spectral triples (Kevin Falk) -- Introduction and motivation. -Weighted direct product of spectral triples -- Example of weighted direct product with Toeplitz operators -- Index.
• Sommario/riassunto: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity. An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples. This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.