The Mathematics Of Coordinated Inference

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The Mathematics of Coordinated Inference

Author : Christopher S. Hardin
Publisher : Springer Science & Business Media
ISBN 13 : 3319013335
Total Pages : 114 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Mathematics of Coordinated Inference by : Christopher S. Hardin

Download or read book The Mathematics of Coordinated Inference written by Christopher S. Hardin and published by Springer Science & Business Media. This book was released on 2013-10-17 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads; each hat is either red or green. The two prisoners must simultaneously submit a guess of their own hat color, and they both go free if at least one of them guesses correctly. While no communication is allowed once the hats have been placed, they will, however, be allowed to have a strategy session before being brought to the room. Is there a strategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a “hat problem.” This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points. Topics range from hat problems that are accessible to everyone willing to think hard, to some advanced topics in set theory and infinitary combinatorics. For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense. The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any graduate student in mathematics. The broad range of readership includes researchers, postdocs, and graduate students in the fields of set theory, mathematical logic, and combinatorics. The hope is that this book will bring together mathematicians from different areas to think about set theory via a very broad array of coordinated inference problems.

Game-Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
Publisher : John Wiley & Sons
ISBN 13 : 0470903058
Total Pages : 480 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Game-Theoretic Foundations for Probability and Finance by : Glenn Shafer

Download or read book Game-Theoretic Foundations for Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2019-05-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

The Universal Coefficient Theorem and Quantum Field Theory

Author : Andrei-Tudor Patrascu
Publisher : Springer
ISBN 13 : 3319461435
Total Pages : 270 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Universal Coefficient Theorem and Quantum Field Theory by : Andrei-Tudor Patrascu

Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Coordination, Organizations, Institutions, and Norms in Agent Systems III

Author : Jaime Simão Sichman
Publisher : Springer
ISBN 13 : 3540790039
Total Pages : 331 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Coordination, Organizations, Institutions, and Norms in Agent Systems III by : Jaime Simão Sichman

Download or read book Coordination, Organizations, Institutions, and Norms in Agent Systems III written by Jaime Simão Sichman and published by Springer. This book was released on 2008-03-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-workshop proceedings of the International Workshop on Coordination, Organization, Institutions and Norms in Agent Systems, COIN 2007. The 23 papers in this volume were carefully selected from 38 initial submissions.

Thinking Practices in Mathematics and Science Learning

Author : James G. Greeno
Publisher : Routledge
ISBN 13 : 1136485260
Total Pages : 451 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis Thinking Practices in Mathematics and Science Learning by : James G. Greeno

Download or read book Thinking Practices in Mathematics and Science Learning written by James G. Greeno and published by Routledge. This book was released on 2013-04-03 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term used in the title of this volume--thinking practices--evokes questions that the authors of the chapters within it begin to answer: What are thinking practices? What would schools and other learning settings look like if they were organized for the learning of thinking practices? Are thinking practices general, or do they differ by disciplines? If there are differences, what implications do those differences have for how we organize teaching and learning? How do perspectives on learning, cognition, and culture affect the kinds of learning experiences children and adults have? This volume describes advances that have been made toward answering these questions. These advances involve several agendas, including increasing interdisciplinary communication and collaboration; reconciling research on cognition with research on teaching, learning, and school culture; and strengthening the connections between research and school practice. The term thinking practices is symbolic of a combination of theoretical perspectives that have contributed to the volume editors' understanding of how people learn, how they organize their thinking inside and across disciplines, and how school learning might be better organized. By touring through some of the perspectives on thinking and learning that have evolved into school learning designs, Greeno and Goldman begin to establish a frame for what they are calling thinking practices. This volume is a significant contribution to a topic that they believe will continue to emerge as a coherent body of scientific and educational research and practice.

Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles

Author : Daniel J. Velleman
Publisher : American Mathematical Soc.
ISBN 13 : 1470447592
Total Pages : 286 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles by : Daniel J. Velleman

Download or read book Bicycle or Unicycle?: A Collection of Intriguing Mathematical Puzzles written by Daniel J. Velleman and published by American Mathematical Soc.. This book was released on 2020-08-17 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bicycle or Unicycle? is a collection of 105 mathematical puzzles whose defining characteristic is the surprise encountered in their solutions. Solvers will be surprised, even occasionally shocked, at those solutions. The problems unfold into levels of depth and generality very unusual in the types of problems seen in contests. In contrast to contest problems, these are problems meant to be savored; many solutions, all beautifully explained, lead to unanswered research questions. At the same time, the mathematics necessary to understand the problems and their solutions is all at the undergraduate level. The puzzles will, nonetheless, appeal to professionals as well as to students and, in fact, to anyone who finds delight in an unexpected discovery. These problems were selected from the Macalester College Problem of the Week archive. The Macalester tradition of a weekly problem was started by Joseph Konhauser in 1968. In 1993 Stan Wagon assumed problem-generating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twenty-five years of the archive. The title problem in that collection was inspired by an error in logic made by Sherlock Holmes, who attempted to determine the direction of a bicycle from the tracks of its wheels. Here the title problem asks whether a bicycle track can always be distinguished from a unicycle track. You'll be surprised by the answer.

The Developmental Psychology of Reasoning and Decision-Making

Author : Henry Markovits
Publisher : Psychology Press
ISBN 13 : 1317931076
Total Pages : 200 pages
Book Rating : 4.3/5 (179 download)

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Book Synopsis The Developmental Psychology of Reasoning and Decision-Making by : Henry Markovits

Download or read book The Developmental Psychology of Reasoning and Decision-Making written by Henry Markovits and published by Psychology Press. This book was released on 2013-11-26 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects very strongly many of the major changes that have arisen in the field of thinking and reasoning research over recent years World class contributors to the book focus on the latest ideas concerning developmental aspects of causal and counterfactual thinking Strongly represents the way in which developmental studies have informed an understanding of dual-process theories of reasoning

Differential Geometry in Statistical Inference

Author : Shun'ichi Amari
Publisher : IMS
ISBN 13 : 9780940600126
Total Pages : 254 pages
Book Rating : 4.6/5 (1 download)

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Book Synopsis Differential Geometry in Statistical Inference by : Shun'ichi Amari

Download or read book Differential Geometry in Statistical Inference written by Shun'ichi Amari and published by IMS. This book was released on 1987 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Compendium for Early Career Researchers in Mathematics Education

Author : Gabriele Kaiser
Publisher : Springer
ISBN 13 : 3030156362
Total Pages : 532 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Compendium for Early Career Researchers in Mathematics Education by : Gabriele Kaiser

Download or read book Compendium for Early Career Researchers in Mathematics Education written by Gabriele Kaiser and published by Springer. This book was released on 2019-04-26 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Open Access compendium, written by experienced researchers in mathematics education, is to serve as a resource for early career researchers in furthering their knowledge of the state of the field and disseminating their research through publishing. To accomplish this, the book is split into four sections: Empirical Methods, Important Mathematics Education Themes, Academic Writing and Academic Publishing, and a section Looking Ahead. The chapters are based on workshops that were presented in the Early Career Researcher Day at the 13th International Congress on Mathematical Education (ICME-13). The combination of presentations on methodological approaches and theoretical perspectives shaping the field in mathematics education research, as well as the strong emphasis on academic writing and publishing, offered strong insight into the theoretical and empirical bases of research in mathematics education for early career researchers in this field. Based on these presentations, the book provides a state-of-the-art overview of important theories from mathematics education and the broad variety of empirical approaches currently widely used in mathematics education research. This compendium supports early career researchers in selecting adequate theoretical approaches and adopting the most appropriate methodological approaches for their own research. Furthermore, it helps early career researchers in mathematics education to avoid common pitfalls and problems while writing up their research and it provides them with an overview of the most important journals for research in mathematics education, helping them to select the right venue for publishing and disseminating their work.

Coordinating Mathematics Across the Primary School

Author : Tony Brown
Publisher : Routledge
ISBN 13 : 1135713189
Total Pages : 251 pages
Book Rating : 4.1/5 (357 download)

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Book Synopsis Coordinating Mathematics Across the Primary School by : Tony Brown

Download or read book Coordinating Mathematics Across the Primary School written by Tony Brown and published by Routledge. This book was released on 2003-10-04 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specifically designed for busy teachers who have responsibility for co-ordinating a subject area within their primary school. Each volume in the series conforms to a concise style, while providing a wealth of tips, case studies and photocopiable material that teachers can use immediately. There are special volumes dedicated to dealing with OFSTED, creating whole school policy and the demands of co-ordinating several subjects within a small school. The entire set of 16 volumes is available.

Invited Lectures from the 13th International Congress on Mathematical Education

Author : Gabriele Kaiser
Publisher : Springer
ISBN 13 : 3319721704
Total Pages : 786 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Invited Lectures from the 13th International Congress on Mathematical Education by : Gabriele Kaiser

Download or read book Invited Lectures from the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by Springer. This book was released on 2018-02-05 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the Invited Lectures given at 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 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Sketch-based Interfaces and Modeling

Author : Joaquim Jorge
Publisher : Springer Science & Business Media
ISBN 13 : 1848828128
Total Pages : 402 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Sketch-based Interfaces and Modeling by : Joaquim Jorge

Download or read book Sketch-based Interfaces and Modeling written by Joaquim Jorge and published by Springer Science & Business Media. This book was released on 2010-12-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of sketch-based interfaces and modeling (SBIM) is concerned with developing methods and techniques to enable users to interact with a computer through sketching - a simple, yet highly expressive medium. SBIM blends concepts from computer graphics, human-computer interaction, artificial intelligence, and machine learning. Recent improvements in hardware, coupled with new machine learning techniques for more accurate recognition, and more robust depth inferencing techniques for sketch-based modeling, have resulted in an explosion of both sketch-based interfaces and pen-based computing devices. Presenting the first coherent, unified overview of SBIM, this unique text/reference bridges the two complementary research areas of user interaction (sketch-based interfaces), and graphical modeling and construction (sketch-based modeling). The book discusses the state of the art of this rapidly evolving field, with contributions from an international selection of experts. Also covered are sketch-based systems that allow the user to manipulate and edit existing data - from text, images, 3D shapes, and video - as opposed to modeling from scratch. Topics and features: reviews pen/stylus interfaces to graphical applications that avoid reliance on user interface modes; describes systems for diagrammatic sketch recognition, mathematical sketching, and sketch-based retrieval of vector drawings; examines pen-based user interfaces for engineering and educational applications; presents a set of techniques for sketch recognition that rely strictly on spatial information; introduces the Teddy system; a pioneering sketching interface for designing free-form 3D models; investigates a range of advanced sketch-based systems for modeling and designing 3D objects, including complex contours, clothing, and hair-styles; explores methods for modeling from just a single sketch or using only a few strokes. This text is an essential resource for researchers, practitioners and graduate students involved in human-factors and user interfaces, interactive computer graphics, and intelligent user interfaces and AI.

Age of Inference

Author : Philip C. Short
Publisher : IAP
ISBN 13 : 1648027997
Total Pages : 487 pages
Book Rating : 4.6/5 (48 download)

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Book Synopsis Age of Inference by : Philip C. Short

Download or read book Age of Inference written by Philip C. Short and published by IAP. This book was released on 2021-12-01 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age where we are inundated with information, the ability to discern verifiable information to make proper decisions and solve problems is ever more critical. Modern science, which espouses a systematic approach to making “inferences,” requires a certain mindset that allows for a degree of comfort with uncertainty. This book offers inspirations and ideas for cultivating the proper mindset for the studying, teaching, and practicing of science that will be useful for those new to as well as familiar with the field. Although a paradigm shift from traditional instruction is suggested in the National Framework for K-12 science, this volume is intended to help educators develop a personal mental framework in which to transition from a teacher-centered, didactical approach to a student-centered, evidence-guided curriculum. While the topics of the book derive from currently published literature on STEM education as they relate to the National Framework for K-12 Science and the Three-Dimensional science instruction embedded in the Next Generation Science Standards, this book also examines these topics in the context of a new societal age posited as the “Age of Inference” and addresses how to make sense of the ever-increasing deluge of information that we are experiencing by having a scientific and properly discerning mindset. ENDORSEMENTS: "This volume takes on one of the thorniest existential problems of our time, the contradiction between the exponentially growing amount of information that individuals have access to, and the diminished capacity of those individuals to understand it. Its chapters provide the reader with an introduction to the relationship between knowledge, science, and inference; needed new approaches to learning science in our new data rich world; and a discussion of what we can and must do to reduce or eliminate the growing gap between the inference have’s and have nots. It is not too much to say that how we resolve the issues outlined in this volume will determine the future of our species on this planet." — Joseph L. Graves Jr., Professor of Biological Sciences North Carolina A&T State University, Fellow, American Association for the Advancement of Science: Biological Sciences, Author of: The Emperor’s New Clothes: Biological Theories of Race at the Millennium "Big data is not enough for addressing dangers to the environment or tackling threats to democracy; we need the ability to draw sound inferences from the data. Cultivating a scientific mindset requires fundamental changes to the way we teach and learn. This important and well -written volume shows how." — Ashok Goel, Professor of Computer Science and Human Centered Computing, Georgia Institute of Technology. Editor of AI Magazine Founding Editor of AAAI’s Interactive AI Magazine "If you are a science teacher concerned about the implications of information overload, analysis paralysis, and intellectual complacency on our health, economic future, and democracy, then I recommend this book." — Michael Svec, Professor for Physics and Astronomy Education, Furman University, Fulbright Scholar to Czech Republic

Epistemic Cognition and Development

Author : David Moshman
Publisher : Psychology Press
ISBN 13 : 1134650469
Total Pages : 201 pages
Book Rating : 4.1/5 (346 download)

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Book Synopsis Epistemic Cognition and Development by : David Moshman

Download or read book Epistemic Cognition and Development written by David Moshman and published by Psychology Press. This book was released on 2014-12-05 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epistemic cognition, the philosophical core of metacognition, concerns people’s knowledge about the justification and truth of beliefs. Multiple literatures in psychology and education address aspects of epistemic cognition. In the absence of a coherent conceptual framework, however, these literatures mostly fail to communicate with each other and often connect only loosely to genuine epistemology. This complicates any effort to achieve a systematic theoretical understanding of epistemic cognition and its development. Deanna Kuhn writes in her foreword, "Moshman is not the first to take on this challenge, but he fulfills it elegantly and, I think, the most comprehensively and astutely." After reviewing the basics of philosophical epistemology and cognitive psychology, Epistemic Cognition and Development provides a compelling account of developmental change across childhood and beyond in knowledge about knowledge, especially with regard to fundamental conceptions of objectivity, subjectivity, rationality, justification, and truth. This is followed by detailed consideration of domain-specific epistemologies of science, logic, morality, social convention, history, and identity, including associated forms of reasoning. The final section provides theoretical conclusions, educational and social applications, and suggestions for further research.

Models and Inferences in Science

Author : Emiliano Ippoliti
Publisher : Springer
ISBN 13 : 3319281631
Total Pages : 253 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Models and Inferences in Science by : Emiliano Ippoliti

Download or read book Models and Inferences in Science written by Emiliano Ippoliti and published by Springer. This book was released on 2016-01-27 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book answers long-standing questions on scientific modeling and inference across multiple perspectives and disciplines, including logic, mathematics, physics and medicine. The different chapters cover a variety of issues, such as the role models play in scientific practice; the way science shapes our concept of models; ways of modeling the pursuit of scientific knowledge; the relationship between our concept of models and our concept of science. The book also discusses models and scientific explanations; models in the semantic view of theories; the applicability of mathematical models to the real world and their effectiveness; the links between models and inferences; and models as a means for acquiring new knowledge. It analyzes different examples of models in physics, biology, mathematics and engineering. Written for researchers and graduate students, it provides a cross-disciplinary reference guide to the notion and the use of models and inferences in science.

Pattern Theory

Author : Ulf Grenander
Publisher : Oxford University Press
ISBN 13 : 0198505701
Total Pages : 633 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Pattern Theory by : Ulf Grenander

Download or read book Pattern Theory written by Ulf Grenander and published by Oxford University Press. This book was released on 2007 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Pattern Theory' provides a comprehensice & accessible overview of the modern challenges in signal, data & pattern analysis in speech recognition, computational linguistics, image analysis & computer vision. Aimed at graduate students the text includes numerous exercises & an extensive bibliography.

Measuring and Reasoning

Author : Fred L. Bookstein
Publisher : Cambridge University Press
ISBN 13 : 1107729203
Total Pages : 565 pages
Book Rating : 4.1/5 (77 download)

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Book Synopsis Measuring and Reasoning by : Fred L. Bookstein

Download or read book Measuring and Reasoning written by Fred L. Bookstein and published by Cambridge University Press. This book was released on 2014-02-28 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Measuring and Reasoning, Fred L. Bookstein examines the way ordinary arithmetic and numerical patterns are translated into scientific understanding, showing how the process relies on two carefully managed forms of argument: • Abduction: the generation of new hypotheses to accord with findings that were surprising on previous hypotheses, and • Consilience: the confirmation of numerical pattern claims by analogous findings at other levels of measurement. These profound principles include an understanding of the role of arithmetic and, more importantly, of how numerical patterns found in one study can relate to numbers found in others. More than 200 figures and diagrams illuminate the text. The book can be read with profit by any student of the empirical nature or social sciences and by anyone concerned with how scientists persuade those of us who are not scientists why we should credit the most important claims about scientific facts or theories.