Jonathan M. Borwein Livres

This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has five parts. The first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The fourth part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future: task and tool design and new forms of activity via connectivity and computer games.

A fully revised and expanded edition of the popular (over 50,000 copies sold) and authoritative Collins Dictionary of Mathematics, covering all mathematical fields from the mysteries of quantum theory to the practical use of probabibilty and statistics.

The world's top experts in mathematics multimedia development are presented with their most recent achievements in this book Includes supplementary material: sn. pub/extras

This collection features 25 papers published since the 1970s, focusing on pi and related areas in mathematics and computer science. It opens with a Foreword by Bruce Berndt, and each paper includes a brief summary and a keyword list that connects it to other contributions. The articles cover various topics, including actual computations of pi, mathematical inquiries such as the normality of pi, and innovative techniques for calculating its digits, like the “BBP” algorithm, which allows for the computation of arbitrary binary digits without prior digits. The volume also presents significant mathematical results related to pi and advanced graphical methods for analyzing its properties. It serves as a companion to a previous source book on pi, with its collection starting with two foundational papers from 1976 by Eugene Salamin and Richard Brent. These papers introduced “quadratically convergent” algorithms for pi and other functions, marking the onset of modern computational mathematics. This era coincides with the rise of high-performance computing, which has seen exponential growth in power. The book appeals to a diverse audience, offering advanced research insights for specialists while remaining accessible to undergraduate students in mathematics.

InhaltsverzeichnisInvited Talks.The Omega Number: Irreducible Complexity in Pure Math.Roles of Math Search in Mathematics.Contributed Papers.Structured Induction Proofs in Isabelle/Isar.Interpretation of Locales in Isabelle: Theories and Proof Contexts.A Dynamic Poincaré Principle.A Proof-Theoretic Approach to Tactics.A Formal Correspondence Between OMDoc with Alternative Proofs and the -Calculus.Proof Transformation by CERES.Synthesizing Proof Planning Methods and ?-Ants Agents from Mathematical Knowledge.Verifying and Invalidating Textbook Proofs Using Scunak.Capturing Abstract Matrices from Paper.Towards a Parser for Mathematical Formula Recognition.Stochastic Modelling of Scientific Terms Distribution in Publications.Capturing the Content of Physics: Systems, Observables, and Experiments.Communities of Practice in MKM: An Extensional Model.From Notation to Semantics: There and Back Again.Managing Informal Mathematical Knowledge: Techniques from Informal Logic.From Untyped to Polymorphically Typed Objects in Mathematical Web Services.Managing Automatically Formed Mathematical Theories.Authoring LeActiveMath Calculus Content.Information Retrieval and Rendering with MML Query.Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories.

Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.