Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. The geometry component extends the functionality to such spectacular objects as dynamic fractals, and the software includes two major new components: physical simulation such as of mechanical objects, virtual electronic devices, and electromagnetic properties. Cinderella.2 Documentation offers complete instruction and techniques for using Cinderella.2.
Cinderella is a unique, technically very sophisticated teachware for geometry that will be used as a tool by students learning Euclidean, projective, spherical and hyperbolic geometry, as well as in geometric research. Moreover, it can also serve as an authors' tool to design web pages with interactive constructions or even complete geometry exercises.
This clearly explained layman's introduction to quantum physics is an accessible excursion into metaphysics and the meaning of reality. Herbert exposes the quantum world and the scientific and philosophical controversy about its interpretation.
This book explains the main problems related to digital preservation using examples based on a modern version of the well-known Cinderella fairy tale. Digital preservation is the endeavor to protect digital material against loss, corruption, hardware/software technology changes, and changes in the knowledge of the community. Τhe structure of the book is modular, with each chapter consisting of two parts: the episode and the technical background. The episodes narrate the story in chronological order, exactly as in a fairy tale. In addition to the story itself, each episode is related to one or more digital preservation problems, which are discussed in the technical background section of the chapter. To reveal a more general and abstract formulation of these problems, the notion of pattern is used. Each pattern has a name, a summary of the problem, a narrative describing an attempt to solve the problem, an explanation of what could have been done to avoid or alleviate this problem, some lessons learned, and lastly, links to related patterns discussed in other chapters. The book is intended for anyone wanting to understand the problems related to digital preservation, even if they lack the technical background. It explains the technical details at an introductory level, provides references to the main approaches (or solutions) currently available for tackling related problems, and is rounded out by questions and exercises appropriate for computer engineers and scientists. In addition, the book's website, maintained by the authors, presents the contents of Cinderella's “real USB stick,” and includes links to various tools and updates.
A Practical Guide to Teaching Mathematics in the Secondary School offers straightforward advice, inspiration and a wide range of tried and tested approaches to help you find success in the secondary mathematics classroom. Illustrated throughout, this fully updated second edition includes new chapters on using ICT in the classroom and promoting a positive learning environment, as well as fresh and easy to use ideas that can help you engage your pupils and inspire mathematical thinking. Covering all key aspects of mathematics teaching, it is an essential companion for all training and newly qualified mathematics teachers. Combining ideas and practical insights from experienced teachers with important lessons from educational research, this book covers key aspects of mathematics teaching, including: planning effective lessons using assessment to support learning encouraging mathematical activity integrating ICT into your teaching making lessons engaging building resilient learners. A Practical Guide to Teaching Mathematics in the Secondary School is an essential companion to the core textbook Learning to Teach Mathematics in the Secondary School. Written by expert practitioners, it will support you in developing imaginative and effective mathematics lessons for your pupils.
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.
Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers. A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions. The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
The 70 years from 1880 to 1950 witnessed the final ascent of humankind into the modern age. Historically, this period is characterized by deep political, social and economic crises. However, parallel to this and much less known in the public, rational scientific thinking also experienced the darkest and deepest crisis of its own history. All the great modern scientific discoveries like quantum theory, genetics and neurology are products of this. Ground-breaking discoveries, profound crises, revolutionary thoughts, refutation of previously unshakable beliefs - these years are marked by scientific achievements of numerous great minds, who overturned our understanding of the world, of space, time and infinity, of life, logic and calculability almost overnight. The "intuitive genius" of these pioneers still forms the foundation of today’s scientific thinking and technological progress. In fact, tackling and overcoming those deep scientific crises shaped our modern life like nothing else. The resulting reorientation of our understanding of nature and ourselves allowed ancient philosophical questions to appear in a new light: "What is reality?", "What can we know about the world?" or "What is man's place in nature?". The most exciting period in the history of science is retold here in an entertaining way.
This book constitutes the refereed proceedings of the 7th FIP WG 2.2 International Conference, TCS 2012, held in Amsterdam, The Netherlands, in September 2012. The 25 revised full papers presented, together with one invited talk, were carefully reviewed and selected from 48 submissions. New results of computation theory are presented and more broadly experts in theoretical computer science meet to share insights and ask questions about the future directions of the field.
