Understanding The Generality Of Mathematical Statements
DOWNLOAD
Download Understanding The Generality Of Mathematical Statements PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Understanding The Generality Of Mathematical Statements book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Understanding The Generality Of Mathematical Statements
DOWNLOAD
Author : Milena Damrau
language : en
Publisher: Springer Nature
Release Date :
Understanding The Generality Of Mathematical Statements written by Milena Damrau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Oxford Handbook Of Generality In Mathematics And The Sciences
DOWNLOAD
Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016-07-07
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-07 with Mathematics categories.
Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.
The Oxford Handbook Of Generality In Mathematics And The Sciences
DOWNLOAD
Author : Karine Chemla
language : en
Publisher: Oxford University Press
Release Date : 2016-08-25
The Oxford Handbook Of Generality In Mathematics And The Sciences written by Karine Chemla and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-25 with Mathematics categories.
Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how collectives have valued generality and how they have worked with specific types of "general" entities, procedures, and arguments. The books connects history and philosophy of mathematics and the sciences at the intersection of two of the most fruitful contemporary lines of research: historical epistemology, in which values (e.g. "objectivity", "accuracy") are studied from a historical viewpoint; and the philosophy of scientific practice, in which conceptual developments are seen as embedded in networks of social, instrumental, and textual practices. Each chapter provides a self-contained case-study, with a clear exposition of the scientific content at stake. The collection covers a wide range of scientific domains - with an emphasis on mathematics - and historical periods. It thus allows a comparative perspective which suggests a non-linear pattern for a history of generality. The introductory chapter spells out the key issues and points to the connections between the chapters.
Functions And Generality Of Logic
DOWNLOAD
Author : Hourya Benis-Sinaceur
language : en
Publisher: Springer
Release Date : 2015-06-24
Functions And Generality Of Logic written by Hourya Benis-Sinaceur and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Philosophy categories.
This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.
Teaching Secondary Mathematics
DOWNLOAD
Author : Gregory Hine
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-15
Teaching Secondary Mathematics written by Gregory Hine and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-15 with Education categories.
A valuable resource for pre-service teachers who wish to integrate contemporary technology into teaching key mathematical concepts.
Mathematical Thinking And Problem Solving
DOWNLOAD
Author : Alan H. Schoenfeld
language : en
Publisher: Routledge
Release Date : 2016-05-06
Mathematical Thinking And Problem Solving written by Alan H. Schoenfeld and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-06 with Education categories.
In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed to establish a base for communication. In those conferences, interdisciplinary teams reviewed major topic areas and put together distillations of what was known about them.* A more recent conference -- upon which this volume is based -- offered a forum in which various people involved in education reform would present their work, and members of the broad communities gathered would comment on it. The focus was primarily on college mathematics, informed by developments in K-12 mathematics. The main issues of the conference were mathematical thinking and problem solving.
Philosophy Of Logic
DOWNLOAD
Author :
language : en
Publisher: Elsevier
Release Date : 2006-11-29
Philosophy Of Logic written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-29 with Mathematics categories.
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter
New Mathematics Education Research And Practice
DOWNLOAD
Author :
language : en
Publisher: BRILL
Release Date : 2006-01-01
New Mathematics Education Research And Practice written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Education categories.
Mathematics education research has blossomed into many different areas which we can see in the programmes of the ICME conferences as well as in the various survey articles in the Handbooks. However, all of these lines of research are trying to grapple with a common problem, the complexity of the process of learning mathematics.
Mathematics Classrooms That Promote Understanding
DOWNLOAD
Author : Elizabeth Fennema
language : en
Publisher: Routledge
Release Date : 1999-04-01
Mathematics Classrooms That Promote Understanding written by Elizabeth Fennema and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-01 with Education categories.
Mathematics Classrooms That Promote Understanding synthesizes the implications of research done by the National Center for Research in Mathematical Sciences on integrating two somewhat diverse bodies of scholarly inquiry: the study of teaching and the study of learning mathematics. This research was organized around content domains and/or continuing issues of education, such as equity and assessment of learning, and was guided by two common goals--defining the mathematics content of the K-12 curriculum in light of the changing mathematical needs of citizens for the 21st century, and identifying common components of classrooms that enable students to learn the redefined mathematics with understanding. To accomplish these goals, classrooms in which instruction facilitated the growth of understanding were established and/or studied. This volume reports and discusses the findings which grew out of this research, and subsequent papers and discussions among the scholars engaged in the endeavor. Section I, "Setting the Stage," focuses on three major threads: What mathematics should be taught; how we should define and increase students' understanding of that mathematics; and how learning with understanding can be facilitated for all students. Section II, "Classrooms That Promote Understanding," includes vignettes from diverse classrooms that illustrate classroom discourse, student work, and student engagement in the mathematics described in Chapter 1 as well as the mental activities described in Chapter 2. These chapters also illustrate how teachers deal with the equity concerns described in Chapter 3. Section III addresses "Developing Classrooms That Promote Understanding." The knowledge of the teaching/learning process gained from the research reported in this volume is a necessary prerequisite for implementing the revisions called for in the current reform movement. The classrooms described show that innovative reform in teaching and learning mathematics is possible. Unlike many volumes reporting research, this book is written at a level appropriate for master's degree students. Very few references are included in the chapters themselves; instead, each chapter includes a short annotated list of articles for expanded reading which provides the scholarly basis and research substantiation for this volume.
Interpreting Carnap
DOWNLOAD
Author : Alan Richardson
language : en
Publisher: Cambridge University Press
Release Date : 2024-01-31
Interpreting Carnap written by Alan Richardson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-31 with Philosophy categories.
Rudolf Carnap (1891–1970), one of the most important philosophers of the twentieth century, helped found logical positivism, was one of the originators of the field of philosophy of science, and was a leading contributor to semantics and inductive logic. This volume of new essays, written by leading international experts, places Carnap in his philosophical context and studies his topics, his interests, and the major stages of his thought. The essays reassess Carnap's place in the history of analytic philosophy through his approach to metaphysics, values, politics, epistemology and philosophy of science. They delve into important topics of Carnap's mature thought, namely explication, naturalism, and his defence of analyticity; and they recover the logical and the linguistic components of philosophy and how they unfolded in the syntax-semantics relation, induction, and language-planning. The resulting interpretation of Carnap will be illuminating for both current and future research.