The Mathematical Imagination
DOWNLOAD
Download The Mathematical Imagination PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Mathematical Imagination 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
The Mathematical Imagination
DOWNLOAD
Author : Matthew Handelman
language : en
Publisher: Fordham Univ Press
Release Date : 2019-03-05
The Mathematical Imagination written by Matthew Handelman and has been published by Fordham Univ Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-05 with Philosophy categories.
This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.
Mathematics And The Imagination
DOWNLOAD
Author : Edward Kasner
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Mathematics And The Imagination written by Edward Kasner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Mathematics For The Imagination
DOWNLOAD
Author : Peter Higgins
language : en
Publisher: OUP Oxford
Release Date : 2002-09-26
Mathematics For The Imagination written by Peter Higgins and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-26 with Mathematics categories.
Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems. A highly involving book which encourages the reader to enter into the spirit of mathematical exploration.
Geometry And The Imagination
DOWNLOAD
Author : D. Hilbert
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-03-17
Geometry And The Imagination written by D. Hilbert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Education categories.
This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in R 3 R3. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is “Projective Configurations”. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the “pantheon” of great mathematics books.
Poetic Logic And The Origins Of The Mathematical Imagination
DOWNLOAD
Author : Marcel Danesi
language : en
Publisher: Springer Nature
Release Date : 2023-09-02
Poetic Logic And The Origins Of The Mathematical Imagination written by Marcel Danesi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-02 with Mathematics categories.
This book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics. The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization. The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Understanding Imagination
DOWNLOAD
Author : Dennis L Sepper
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-13
Understanding Imagination written by Dennis L Sepper 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 2013-05-13 with Science categories.
This book discusses that imagination is as important to thinking and reasoning as it is to making and acting. By reexamining our philosophical and psychological heritage, it traces a framework, a conceptual topology, that underlies the most disparate theories: a framework that presents imagination as founded in the placement of appearances. It shows how this framework was progressively developed by thinkers like Plato, Aristotle, Descartes, and Kant, and how it is reflected in more recent developments in theorists as different as Peirce, Saussure, Wittgenstein, Benjamin, and Bachelard. The conceptual topology of imagination incorporates logic, mathematics, and science as well as production, play, and art. Recognizing this topology can move us past the confusions to a unifying view of imagination for the future.
Nature S Numbers
DOWNLOAD
Author : Ian Stewart
language : en
Publisher: Hachette UK
Release Date : 2014-03-20
Nature S Numbers written by Ian Stewart and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-20 with Mathematics categories.
A mathematical sightseeing tour of the natural world from the author of THE MAGICAL MAZE Why do many flowers have five or eight petals, but very few six or seven? Why do snowflakes have sixfold symmetry? Why do tigers have stripes but leopards have spots? Mathematics is to nature as Sherlock Holmes is to evidence. Mathematics can look at a single snowflake and deduce the atomic geometry of its crystals; it can start with a violin string and uncover the existence of radio waves. And mathematics still has the power to open our eyes to new and unsuspected regularities - the secret structure of a cloud or the hidden rhythms of the weather. There are patterns in the world we are now seeing for the first time - patterns at the frontier of science, yet patterns so simple that anybody can see them once they know where to look.
The Topological Imagination
DOWNLOAD
Author : Angus Fletcher
language : en
Publisher: Harvard University Press
Release Date : 2016-04-04
The Topological Imagination written by Angus Fletcher 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 2016-04-04 with Philosophy categories.
In a bold and boundary defining work, Angus Fletcher clears a space for an intellectual encounter with the shape of human imagining. Joining literature and topology—a branch of mathematics—he maps the ways the imagination’s contours are formed by the spherical earth’s patterns and cycles, and shows how the world we inhabit also inhabits us.
Matter Imagination And Geometry
DOWNLOAD
Author : Dmitriĭ Vladimirovich Nikulin
language : en
Publisher: Ashgate Publishing
Release Date : 2002
Matter Imagination And Geometry written by Dmitriĭ Vladimirovich Nikulin and has been published by Ashgate Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Philosophy categories.
"This book considers conditions of applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction of mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. The author explores questions in the history of philosophy and science, particularly in late antiquity and early modernity. The focus is on key thinkers Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved