Download or read book Platonism and Anti Platonism in Mathematics written by Mark Balaguer and published by . This book was released on 2001 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Download or read book Marvelous Math written by Lee Bennett Hopkins and published by Turtleback. This book was released on 2001-08-01 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each poem is about mathematics, numbers, and having fun. Barbour's vibrant artwork makes each page sing.

Download or read book The Best Writing on Mathematics 2018 written by Mircea Pitici and published by Princeton University Press. This book was released on 2018-12-04 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today’s hottest mathematical debates. James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there’s much, much more. In addition to presenting the year’s most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.

Download or read book Mathematics Matters in Education written by Yeping Li and published by Springer. This book was released on 2017-10-03 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange.

Download or read book An Introduction to Mathematical Cognition written by Camilla Gilmore and published by Routledge. This book was released on 2018-06-13 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Download or read book EBOOK TEACHING THE PRIMARY CURRICULUM written by Jane Johnston and published by McGraw-Hill Education (UK). This book was released on 2002-01-16 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: * What is good teaching and learning in the primary school? * How can teachers manage the whole curriculum and still educate the whole child and raise standards? * How can teachers be in critical dialogue with each other and with the curriculum in their search for improvement? * What is the role of the teacher in the new primary curriculum? This wide ranging book seeks to address these questions and to provide a comprehensive overview of the whole primary curriculum. It aims to develop teaching throughout primary education and to support teachers in the effective delivery of the curriculum. There is a particular focus on recent changes in primary education. The contributors consider how teaching methodologies need to adapt to these changes to meet the needs of children and raise standards in school. Throughout the book, emphasis is placed on effective teaching and learning methodologies, the importance of quality interaction in the classroom, the role of the teacher in teaching and learning and the experience of the child. Exemplars of good teaching are provided in each chapter, as well as thought provoking ideas for good practice.

Download or read book Naturalizing Logico Mathematical Knowledge written by Sorin Bangu and published by Routledge. This book was released on 2018-02-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Download or read book The Princeton Companion to Mathematics written by Timothy Gowers and published by Princeton University Press. This book was released on 2010-07-18 with total page 1057 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger

Download or read book The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara written by John Dee and published by BoD – Books on Demand. This book was released on 2020-07-17 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reproduction of the original: The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara by John Dee

Download or read book EBOOK Teaching Adult Numeracy Principles Practice written by Graham Griffiths and published by McGraw-Hill Education (UK). This book was released on 2013-09-16 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers friendly guidance on how to work with adult learners to develop their numeracy and mathematics skills. It brings together current research and practice on teaching adult numeracy into one handy volume and covers the major issues faced by teachers of adult numeracy such as current policy perspectives and implications for teaching practice. There are reflective tasks throughout, which encourage you to develop and apply your theoretical knowledge to your own experiences. Key features include: Reviews of existing policy and research and implications for practice Reflective tasks with commentary, encouraging you to develop and apply your knowledge Case studies of real student experiences Practical activities and ideas to support the planning, teaching and assessment of adult numeracy Drawing on the substantial experience of the contributors, who have a wealth of experience as practitioners and researchers in the field, this book is an essential resource for trainee and practising teachers of adult numeracy and mathematics. It is also an ideal textbook to support teacher training courses leading to a subject specific qualification in teaching numeracy to adults. Contributors: Jackie Ashton, John Barton, Carolyn Brooks, Martyn Edwards, Janette Gibney, David Holloway, David Kaye, Beth Kelly, Barbara Newmarch, Helen Oughton, David Prinn, Diana Spurr, Rebecca Woolley "This is a quite unique book about teaching adult numeracy, which will be invaluable to the many practitioners in this field. The chapters, contributed by a group of experienced and successful lecturers and practitioners, include all aspects of this field, from methods of teaching specific mathematical topics to more general explorations of dyscalculia and emotional factors in adult learners. Each chapter includes research findings and thoughtful presentation of ideas with practical ideas for teaching, and tasks for the reader. This is a market which has not been served well in the past, so it is good to see the gap filled at last." Margaret Brown, Emeritus Professor of Mathematics Education, King's College London, UK "The editors of this book set out to produce a text that would support teacher-education programmes for adult numeracy, and their book does that and more. The content covers different types of learners, different settings, different understandings of what numeracy actually is; and ranges from commentary on research through case studies to "how to" hints and tips for teaching. Chapters 7 (on provoking mathematical thinking) and 8 (attitudes, beliefs and teaching) should be a required read for any adult numeracy teacher. The book would be at home on any numeracy teacher's desk, and would make an excellent set text for numeracy teacher training courses." Carol Randall, course co-ordinator for numeracy in the department of Lifelong Learning Teacher Education, University of Greenwich, UK "This book is a welcome addition to the growing literature on adult numeracy. It should be essential reading for trainee and practising adult numeracy educators. It brings together relevant research and professional wisdom on a wide variety of aspects of adult numeracy teaching and learning in an accessible way, with well-focussed tasks for readers to extend their knowledge and understanding. While the book is born out of UK concerns and issues, it is also relevant to international readers. Highly recommended." Professor Diana Coben PhD, Director, National Centre of Literacy & Numeracy for Adults, University of Waikato, New Zealand, and Hon. Trustee, Adults Learning Mathematics - A Research Forum (ALM -- www.alm-online.net/)

Download or read book Carnap Tarski and Quine at Harvard written by Greg Frost-Arnold and published by Open Court. This book was released on 2013-08-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction of the lines of argument used by Carnap, Tarski, and Quine, highlighting their historical significance and contemporary relevance based on Carnap's own notes from his conversations of the time.During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. 'Carnap, Tarski, and Quine at Harvard' allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap's notes cover a wide range of topics, but surprisingly, the most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to anabiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine's attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine's break from Carnap),and relates them when possible to contemporary treatments of these issues.

Download or read book EBOOK Promoting Children s Learning from Birth to Five written by Angela Anning and published by McGraw-Hill Education (UK). This book was released on 2006-03-16 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews of the first edition “At a time of constant and rapid change in education, this book will inform and reassure early childhood professionals.” Practical Pre-School “Besides advice on the most helpful ways to develop learning in areas such as maths and literacy, there are suggestions and comments about further reading at the end of each chapter, and examples of the thoughts and responses of real children are never far from the page.” TES “Innovative, resourceful and thoroughly researched… a challenge to existing and emerging early childhood professionals.” Contemporary Issues in Early Childhood Promoting Children's Learning from Birth to Five supports early years professionals as they develop new practices to promote young children’s learning. This second edition fully reflects the enormous changes in early childhood education and care since the publication of the first edition. Retaining its successful focus on literacy and mathematical development as key exemplars of promoting young children's learning, the book considers new ways of working with parents, promoting inter-professional collaboration, and achieving sustainable, systematic change in children's services. The second edition: Draws on current research in early literacy and mathematical thinking Focuses on multiprofessional practice, showing how practitioners who work from evidence across professional boundaries are able to give strong, interactive and sensitive support to young children and their parents Takes into account policies and practices such as Every Child Matters, the Primary Strategy and Children's Centres Includes updated material on aspects of leadership, and on the role of the Senior Practitioner in developing innovative services for children and their families Explores the importance of personal, social and emotional development in the curriculum for under-fives Working from the basis that children learn most readily in contexts where parents and professionals are keen to learn, the authors help early childhood professionals to meet the challenges of reshaping children's services. This is key reading for all early childhood professionals and students.

Download or read book Encyclopedia of Mathematics and Society written by Sarah J. Greenwald and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents articles showing the math behind our daily lives. Explains how and why math works, and allows readers to better understand how disciplines such as algebra, geometry, calculus, and others affect what we do every day.

Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics And The Natural Sciences The Physical Singularity Of Life written by Giuseppe Longo and published by World Scientific. This book was released on 2011-03-04 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book identifies the organizing concepts of physical and biological phenomena by an analysis of the foundations of mathematics and physics. Our aim is to propose a dialog between different conceptual universes and thus to provide a unification of phenomena. The role of “order” and symmetries in the foundations of mathematics is linked to the main invariants and principles, among them the geodesic principle (a consequence of symmetries), which govern and confer unity to various physical theories. Moreover, an attempt is made to understand causal structures, a central element of physical intelligibility, in terms of both symmetries and symmetry breakings. A distinction between the principles of (conceptual) construction and of proofs, both in physics and in mathematics, guides most of the work.The importance of mathematical tools is also highlighted to clarify differences in the models for physics and biology that are proposed by continuous and discrete mathematics, such as computational simulations.Since biology is particularly complex and not as well understood at a theoretical level, we propose a “unification by concepts” which in any case should precede mathematization. This constitutes an outline for unification also based on highlighting conceptual differences, complex points of passage and technical irreducibilities of one field to another. Indeed, we suppose here a very common monist point of view, namely the view that living objects are “big bags of molecules”. The main question though is to understand which “theory” can help better understand these bags of molecules. They are, indeed, rather “singular”, from the physical point of view. Technically, we express this singularity through the concept of “extended criticality”, which provides a logical extension of the critical transitions that are known in physics. The presentation is mostly kept at an informal and conceptual level./a

Download or read book Methods of Mathematics Applied to Calculus Probability and Statistics written by Richard W. Hamming and published by Courier Corporation. This book was released on 2012-06-28 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.