Mathematical Intuition
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Mathematical Intuition
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Author : R.L. Tieszen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Intuition written by R.L. Tieszen 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 2012-12-06 with Philosophy categories.
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
The Nature Of Mathematical Knowledge
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Author : San Diego Philip Kitcher Professor of Philosophy University of California
language : en
Publisher: Oxford University Press, USA
Release Date : 1983-04-21
The Nature Of Mathematical Knowledge written by San Diego Philip Kitcher Professor of Philosophy University of California and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-04-21 with Mathematics categories.
This book argues against the view that mathematical knowledge is a priori, contending that mathematics is an empirical science and develops historically, just as natural sciences do. Kitcher presents a complete, systematic, and richly detailed account of the nature of mathematical knowledge and its historical development, focusing on such neglected issues as how and why mathematical language changes, why certain questions assume overriding importance, and how standards of proof are modified.
Mathematical Thought And Its Objects
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Author : Charles Parsons
language : en
Publisher: Cambridge University Press
Release Date : 2007-12-24
Mathematical Thought And Its Objects written by Charles Parsons 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 2007-12-24 with Science categories.
Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
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.
Philosophy Of Mathematics In The Twentieth Century
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Author : Charles Parsons
language : en
Publisher: Harvard University Press
Release Date : 2014-03-10
Philosophy Of Mathematics In The Twentieth Century written by Charles Parsons and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-10 with Philosophy categories.
In these selected essays, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the past century: Brouwer, Hilbert, Bernays, Weyl, Gödel, Russell, Quine, Putnam, Wang, and Tait.
Math In Motion Dynamic Techniques For A Changing World
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-08-12
Math In Motion Dynamic Techniques For A Changing World written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-12 with Mathematics categories.
In a world awash with information, mathematics has emerged as the ultimate tool for making sense of complex data and solving real-world problems. From the intricate patterns of nature to the cutting-edge technologies that shape our lives, mathematics is the language that unlocks the secrets of the universe. This comprehensive guide to mathematics is designed for students of all levels, from those just beginning their mathematical journey to those seeking to deepen their understanding of more advanced concepts. With clear and engaging explanations, the book covers a wide range of topics, including: * The basics of mathematical language and problem-solving * Algebra, geometry, trigonometry, calculus, and statistics * Applications of mathematics in science, engineering, business, finance, and everyday life Written by a team of experienced educators, this book is packed with examples, exercises, and practice problems to help readers master the material. Whether you're a student, a professional, or simply someone who wants to expand their mathematical knowledge, this book is the perfect resource. Discover the power and beauty of mathematics and unlock the secrets of the universe! Mathematics is not just a collection of abstract concepts; it is a living, breathing language that is constantly evolving. New mathematical discoveries are being made all the time, and these discoveries are changing the way we understand the world. This book is just a starting point on your mathematical journey. Once you have mastered the basics, you will be ready to explore the many other fascinating branches of mathematics. Who knows, you might even make a few discoveries of your own! If you like this book, write a review!
Understanding And Teaching The Intuitive Mind
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Author : Bruce Torff
language : en
Publisher: Routledge
Release Date : 2001
Understanding And Teaching The Intuitive Mind written by Bruce Torff and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Education categories.
Pulls together diverse theoretical & methodological approaches to the origin, structure, function, & development of intuitive conceptions; explores these in a diversity of academic disciplines; explicitly links theory & research to educ. implications.
Mathematics
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Author : Douglas M. Campbell
language : en
Publisher: Taylor & Francis
Release Date : 1984
Mathematics written by Douglas M. Campbell and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Based upon the principle that graph design should be a science, this book presents the principles of graph construction. The orientation of the material is toward graphs in technical writings, such as journal articles and technical reports. But much of the material is relevant for graphs shown in talks and for graphs in nontechnical publications. -- from back cover.
Phenomenology And Mathematics
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Author : Michael Roubach
language : en
Publisher: Cambridge University Press
Release Date : 2023-12-06
Phenomenology And Mathematics written by Michael Roubach 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 2023-12-06 with Science categories.
This Element explores the relationship between phenomenology and mathematics. Its focus is the mathematical thought of Edmund Husserl, founder of phenomenology, but other phenomenologists and phenomenologically-oriented mathematicians, including Weyl, Becker, Gödel, and Rota, are also discussed. After outlining the basic notions of Husserl's phenomenology, the author traces Husserl's journey from his early mathematical studies. Phenomenology's core concepts, such as intention and intuition, each contributed to the emergence of a phenomenological approach to mathematics. This Element examines the phenomenological conceptions of natural number, the continuum, geometry, formal systems, and the applicability of mathematics. It also situates the phenomenological approach in relation to other schools in the philosophy of mathematics-logicism, formalism, intuitionism, Platonism, the French epistemological school, and the philosophy of mathematical practice.
Modeling Students Mathematical Modeling Competencies
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Author : Richard Lesh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-17
Modeling Students Mathematical Modeling Competencies written by Richard Lesh 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 2013-03-17 with Education categories.
Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.