Mathematical Reasoning and Heuristics

Author: Carlo Cellucci,Donald Gillies

Publisher: Kings College Publications

ISBN: N.A

Category: Mathematics

Page: 212

View: 6873

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This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as the subject develops? What heuristics are involved in mathematical discovery, and do such heuristics constitute a logic of mathematical discovery? What new problems have been introduced by the development of mathematics since the 1930s? Other questions are concerned with the applications of mathematics both to physics and to the new field of computer science. Then there is the new question of whether the axiomatic method is really so essential to mathematics as is often supposed, and the question, which goes back to Wittgenstein, of the sense in which mathematical proofs are compelling. Taking these questions together they give part of an emerging agenda which is likely to carry philosophy of mathematics forward into the twenty first century.
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Heuristic Reasoning

Author: Emiliano Ippoliti

Publisher: Springer

ISBN: 331909159X

Category: Computers

Page: 191

View: 9511

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How can we advance knowledge? Which methods do we need in order to make new discoveries? How can we rationally evaluate, reconstruct and offer discoveries as a means of improving the ‘method’ of discovery itself? And how can we use findings about scientific discovery to boost funding policies, thus fostering a deeper impact of scientific discovery itself? The respective chapters in this book provide readers with answers to these questions. They focus on a set of issues that are essential to the development of types of reasoning for advancing knowledge, such as models for both revolutionary findings and paradigm shifts; ways of rationally addressing scientific disagreement, e.g. when a revolutionary discovery sparks considerable disagreement inside the scientific community; frameworks for both discovery and inference methods; and heuristics for economics and the social sciences.
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The Mathematics Enthusiast Issue

Volume 12 #13

Author: Bharath Sriraman

Publisher: IAP

ISBN: 1681232588

Category: Education

Page: 481

View: 3460

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The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. It is published on a print?on?demand basis by Information Age Publishing and the electronic version is hosted by the Department of Mathematical Sciences? University of Montana. The journal is not affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education? North America] through special issues on various research topics.
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Abstracts of The First Sourcebook on Asian Research in Mathematics Education

China, Korea, Singapore, Japan, Malaysia and India

Author: Bharath Sriraman,Jinfa Cai,Kyeonghwa Lee,Lianghuo Fan,Yoshinori Shimizu,Chap Sam Lim,K. Subramaniam

Publisher: IAP

ISBN: 1617358274

Category: Mathematics

Page: 269

View: 1006

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Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on underrepresented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.
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The Challenge of Developing Statistical Literacy, Reasoning and Thinking

Author: Dani Ben-Zvi,Joan Garfield

Publisher: Springer Science & Business Media

ISBN: 9781402022784

Category: Mathematics

Page: 423

View: 2476

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Unique in that it collects, presents, and synthesizes cutting edge research on different aspects of statistical reasoning and applies this research to the teaching of statistics to students at all educational levels, this volume will prove of great value to mathematics and statistics education researchers, statistics educators, statisticians, cognitive psychologists, mathematics teachers, mathematics and statistics curriculum developers, and quantitative literacy experts in education and government.
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Automated Reasoning and Mathematics

Essays in Memory of William W. McCune

Author: Maria Paola Bonacina,Mark E. Stickel

Publisher: Springer

ISBN: 3642366759

Category: Computers

Page: 259

View: 5539

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This Festschrift volume is published in memory of William W. McCune who passed away in 2011. William W. McCune was an accomplished computer scientist all around but especially a fantastic system builder and software engineer. The volume includes 13 full papers, which are presenting research in all aspects of automated reasoning and its applications to mathematics. These papers have been thoroughly reviewed and selected out of 15 submissions received in response to the call for paper issued in September 2011. The topics covered are: strategies, indexing, superposition-based theorem proving, model building, application of automated reasoning to mathematics, as well as to program verification, data mining, and computer formalized mathematics.
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Appraising Lakatos

Mathematics, Methodology, and the Man

Author: György Kampis,L. Kvasz,Michael Stöltzner

Publisher: Springer Science & Business Media

ISBN: 9401707693

Category: Science

Page: 382

View: 8710

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Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.
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Artificial Intelligence, Automated Reasoning, and Symbolic Computation

Joint International Conferences, AISC 2002 and Calculemus 2002 Marseille, France, July 1-5, 2002 Proceedings

Author: France) Calculemus (2002 Marseille,International Conference on Artificial Intelligence,Spain) International Conference AISC 2000 (2000 : Madrid

Publisher: Springer Science & Business Media

ISBN: 3540438653

Category: Computers

Page: 341

View: 9017

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This book constitutes the refereed proceedings of the joint International Conferences on Artificial Intelligence and Symbolic Computation, AISC 2002, and Calculemus 2002 held in Marseille, France, in July 2002. The 24 revised full papers presented together with 2 system descriptions were carefully reviewed and selected from 52 submissions. Among the topics covered are automated theorem proving, logical reasoning, mathematical modeling, algebraic computations, computational mathematics, and applications in engineering and industrial practice.
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