The Argument Of Mathematics
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The Argument Of Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Foundations Of Discrete Mathematics
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Author : K. D. Joshi
language : en
Publisher: New Age International
Release Date : 1989
Foundations Of Discrete Mathematics written by K. D. Joshi and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.
An Historical Introduction To The Philosophy Of Mathematics A Reader
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Author : Russell Marcus
language : en
Publisher: Bloomsbury Publishing
Release Date : 2016-02-11
An Historical Introduction To The Philosophy Of Mathematics A Reader written by Russell Marcus and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Philosophy categories.
A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
Mathematics Formative Assessment Volume 2
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Author : Page Keeley
language : en
Publisher: Corwin Press
Release Date : 2016-12-08
Mathematics Formative Assessment Volume 2 written by Page Keeley and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Education categories.
Everything you need to promote mathematical thinking and learning! Good math teachers have a robust repertoire of strategies to move students’ learning forward. This new volume from award-winning author Page Keeley and mathematics expert Cheryl Rose Tobey helps you improve student outcomes with 50 all-new formative assessment classroom techniques (FACTS) that are embedded throughout a cycle of instruction. Descriptions of how the FACTs promote learning and inform teaching, including illustrative examples, support the inextricable link between instruction and learning. Useful across disciplines, Keeley and Tobey’s purposeful assessment techniques help K-12 math teachers: Promote conceptual understanding Link techniques to core ideas and practices Modify instruction for diverse learners Seamlessly embed formative assessment throughout the stages of instruction Focus on learning targets and feedback Instead of a one-size fits all approach, you can build a bridge between your students’ initial ideas and correct mathematical thinking with this one-of-a-kind resource!
Mathematics Mathematics Education Searching For Common Ground
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Author : Michael N. Fried
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29
Mathematics Mathematics Education Searching For Common Ground written by Michael N. Fried and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Education categories.
This book is the fruit of a symposium in honor of Ted Eisenberg concerning the growing divide between the mathematics community and the mathematics education community, a divide that is clearly unhealthy for both. The work confronts this disturbing gap by considering the nature of the relationship between mathematics education and mathematics, and by examining areas of commonality as well as disagreement. It seeks to provide insight into the mutual benefit both stand to gain by building bridges based on the natural bonds between them.
The Sage Encyclopedia Of Theory In Science Technology Engineering And Mathematics
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Author : James Mattingly
language : en
Publisher: SAGE Publications
Release Date : 2022-10-28
The Sage Encyclopedia Of Theory In Science Technology Engineering And Mathematics written by James Mattingly and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-28 with Reference categories.
Project Description: Theories are part and parcel of every human activity that involves knowing about the world and our place in it. In all areas of inquiry from the most commonplace to the most scholarly and esoteric, theorizing plays a fundamental role. The SAGE Encyclopedia of Theory in Science, Technology, Engineering, and Mathematics focuses on the ways that various STEM disciplines theorize about their subject matter. How is thinking about the subject organized? What methods are used in moving a novice in given field into the position of a competent student of that subject? Within the pages of this landmark work, readers will learn about the complex decisions that are made when framing a theory, what goes into constructing a powerful theory, why some theories change or fail, how STEM theories reflect socio-historical moments in time and how – at their best – they form the foundations for exploring and unlocking the mysteries of the world around us. Featuring more than 200 authoritative articles written by experts in their respective fields, the encyclopedia includes a Reader’s Guide that organizes entries by broad themes; lists of Further Readings and cross-references that conclude each article; and a Resource Guide listing classic books in the field, leading journals, associations, and key websites.
Conceptions And Consequences Of Mathematical Argumentation Justification And Proof
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Author : Kristen N. Bieda
language : en
Publisher: Springer Nature
Release Date : 2022-03-03
Conceptions And Consequences Of Mathematical Argumentation Justification And Proof written by Kristen N. Bieda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Education categories.
This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.
Crc Concise Encyclopedia Of Mathematics
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Author : Eric W. Weisstein
language : en
Publisher: CRC Press
Release Date : 2002-12-12
Crc Concise Encyclopedia Of Mathematics written by Eric W. Weisstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-12 with Mathematics categories.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Philosophy Of Mathematics
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press
Release Date : 1997-08-07
Philosophy Of Mathematics written by Stewart Shapiro 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 1997-08-07 with Mathematics categories.
Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic.As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences.Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Mathematics And Reality
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Author : Mary Leng
language : en
Publisher: OUP Oxford
Release Date : 2010-04-22
Mathematics And Reality written by Mary Leng and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Philosophy categories.
Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.