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Mathematics, Education and History
This book includes 18 peer-reviewed papers from nine countries, originally presented in a shorter form at TSG 25 The Role of History of Mathematics in Mathematics Education, as part of ICME-13 during. It also features an introductory chapter, by its co-editors, on the structure and main points of the book with an outline of recent developments in exploring the role of history and epistemology in mathematics education. It serves as a valuable contribution in this domain, by making reports on recent developments in this field available to the international educational community, with a special focus on relevant research results since 2000. The 18 chapters of the book are divided into five inte...
The Geometry of Cubic Hypersurfaces
Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
The Bonn Handbook of Globality
This two-volume handbook provides readers with a comprehensive interpretation of globality through the multifaceted prism of the humanities and social sciences. Key concepts and symbolizations rooted in and shaped by European academic traditions are discussed and reinterpreted under the conditions of the global turn. Highlighting consistent anthropological features and socio-cultural realities, the handbook gathers coherently structured articles written by 110 professors in the humanities and social sciences at Bonn University, Germany, who initiate a global dialogue on meaningful and sustainable notions of human life in the age of globality. Volume 1 introduces readers to various interpretations of globality, and discusses notions of human development, communication and aesthetics. Volume 2 covers notions of technical meaning, of political and moral order, and reflections on the shaping of globality.
Local Analytic Geometry
Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.
Mixed Hodge Structures
This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.
Model Cases
We all know scientists study a predictable set of organisms when performing research, whether they be mice, fruit flies, or less commonly known but widely used species of snail or worm. But when we think of the so-called humanistic social sciences, we envision a different kind of research attuned to historical power relations or the unique experiences of a social group. In Model Cases, sociologist Monika Krause uncovers the ways the humanities and social sciences are shaped by and dependent on a set of canonical research objects of their own, often in unacknowledged ways. Krause shows that some research objects are studied repeatedly and shape the understanding of more general categories in ...
A History of Kinematics from Zeno to Einstein
This book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.
Proceedings of the 13th International Congress on Mathematical Education
This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German...
Fachkulturen in der Lehrerbildung
In den letzten Jahren hat die Lehrerbildung – Stichwort »Kompetenz- und Outputorientierung« – vielfältige bildungspolitische Steuerungsimpulse erfahren, während die universitären Wissenschaftsdisziplinen in den Hintergrund getreten sind. Der Band eruiert Möglichkeiten, Lehrerbildung wieder stärker aus den disziplinären Spezifika der Fächer heraus zu definieren. Denn fachwissenschaftliche, fachdidaktische, bildungswissenschaftliche und schulpraktische Studien- und Ausbildungselemente können erst im Zusammenwirken künftige Lehrerinnen und Lehrer auf ihr Berufsfeld vorbereiten. Eine Besonderheit des Bandes liegt darin, dass er nicht nur die universitäre Lehrerbildung in ihrer disziplinären Vielfalt vorstellt, sondern darüber hinaus auch die eng mit ihr kooperierende schulpraktische Lehrerausbildung berücksichtigt.
Erkundungen zum Eulerschen Polyedersatz
Mathematische Resultate werden häufig in einer Weise dargestellt, die kaum noch Einsicht in die Entdeckungsgeschichte der Resultate gewährt. Viele typische Vorgehensweisen, die beim Betreiben von Mathematik eine wichtige Rolle spielen, wie z.B. Analogiebildung, induktives Schließen oder das Aufspüren versteckter Annahmen, haben in der klassischen Anordnung des Wissens nach dem Schema „Definition, Satz, Beweis“ keinen Platz. Für das Lehren und Lernen von Mathematik als einer schöpferischen Tätigkeit kann eine Darstellung des Stoffes hilfreich sein, die stärker den Prozess des Entdeckens als das fertige Resultat betont. Stephan Berendonk liefert eine solche dem Entstehen von Mathematik zugewandte Darstellung für den Eulerschen Polyedersatz.
