Mathematical Imagining

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The Mathematical Imagination

Matthew Handelman
The Mathematical Imagination Book PDF

Author : Matthew Handelman
Publisher : Fordham Univ Press
Page : 256 pages
File Size : 41,9 Mb
Release : 2019-03-05
Category : Philosophy
ISBN : 9780823283859

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The Mathematical Imagination by Matthew Handelman Pdf

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.

Mathematics for the Imagination

Peter Higgins
Mathematics for the Imagination Book PDF

Author : Peter Higgins
Publisher : OUP Oxford
Page : 238 pages
File Size : 51,7 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 9780191500534

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Mathematics for the Imagination by Peter Higgins Pdf

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.

Mathematics and the Imagination

Edward Kasner,James Newman
Mathematics and the Imagination Book PDF

Author : Edward Kasner,James Newman
Publisher : Courier Corporation
Page : 400 pages
File Size : 53,5 Mb
Release : 2013-04-22
Category : Mathematics
ISBN : 9780486320274

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Mathematics and the Imagination by Edward Kasner,James Newman Pdf

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 as Sign

Brian Rotman
Mathematics as Sign Book PDF

Author : Brian Rotman
Publisher : Stanford University Press
Page : 188 pages
File Size : 42,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0804736847

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Mathematics as Sign by Brian Rotman Pdf

In this book, Rotman argues that mathematics is a vast and unique man-made imagination machine controlled by writing. It addresses both aspects—mental and linguistic—of this machine. The essays in this volume offer an insight into Rotman's project, one that has been called "one of the most original and important recent contributions to the philosophy of mathematics."

Mathematical Imagining

Christof Weber
Mathematical Imagining Book PDF

Author : Christof Weber
Publisher : Taylor & Francis
Page : 255 pages
File Size : 42,5 Mb
Release : 2023-10-10
Category : Education
ISBN : 9781003839231

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Mathematical Imagining by Christof Weber Pdf

Imagine a plastic cup lying on the floor. Give the cup a nudge so that it begins to roll. What does the path it takes look like? So begins the journey that Christof Weber takes you on in Mathematical Imagining: A Routine for Secondary Classrooms . Along the way, he makes the case that the ability to imagine, manipulate, and explain mathematical images and situations is fundamental to all mathematics and particularly important to higher level study. Most importantly, drawing on years of experiments in his own classroom, Weber shows that mathematical imagining is a skill that can be taught efficiently and effectively. Mathematical Imagining describes an original routine that gives students space and time to imagine a mathematical situation and then revise, discuss, and act upon the mental images they create. You can use this creative routine to glimpse into your students' thinking and discover teaching opportunities, while empowering them to create their own mathematics.Inside you’ll find the following: An introduction to the routine including the rationale behind it, facilitation guidance, and classroom examples Modifications to implement the routine in your classroom, even with varying time constraints 37 exercises broken into four categories: constructions, problem-solving, reasoning, and paradoxes Discussions of the mathematics involved in each exercise, including possible follow-up questions Instructions on how to create your own exercises beyond the book This one-of-a-kind resource is for secondary teachers looking to inspire student creativity and curiosity, deepen their own subject matter knowledge and pedagogical content knowledge, and invite all students to access the power of their own mathematical imaginations.

Imagine Math 2

Michele Emmer
Imagine Math 2 Book PDF

Author : Michele Emmer
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 46,5 Mb
Release : 2013-10-04
Category : Mathematics
ISBN : 9788847028890

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Imagine Math 2 by Michele Emmer Pdf

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. The new volume in the series “Imagine Math” is intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture. The present book begins with the connections between mathematics, numbers, poetry and music, with the latest opera by Italian composer Claudio Ambrosini. Literature and narrative also play an important role here. There is cinema too, with the “erotic” mathematics films by Edward Frenkel, and the new short “Arithmétique “ by Munari and Rovazzani. The section on applications of mathematics features a study of ants, as well as the refined forms and surfaces generated by algorithms used in the performances by Adrien Mondot and Claire Bardainne. Last but not least, in honour of the hundredth anniversary of his birth, a mathematical, literary and theatrical homage to Alan Turing, one of the outstanding figures of the twentieth century.

Mathematical Imagining

Christof Weber
Mathematical Imagining Book PDF

Author : Christof Weber
Publisher : Unknown
Page : 257 pages
File Size : 52,8 Mb
Release : 2020
Category : Mathematics
ISBN : 9781625312778

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Mathematical Imagining by Christof Weber Pdf

"In Mathematical Imagining, the author makes the case that the ability to imagine, manipulate, and explain mathematical images and situations is fundamental to all mathematics and particularly important to higher level study. Most importantly, drawing on years of experiments in his own classroom, he shows that mathematical imagining is a skill that can be taught efficiently and effectively in secondary mathematics"--

Imagine Math 6

Michele Emmer,Marco Abate
Imagine Math 6 Book PDF

Author : Michele Emmer,Marco Abate
Publisher : Springer
Page : 327 pages
File Size : 40,9 Mb
Release : 2018-11-06
Category : Mathematics
ISBN : 9783319939490

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Imagine Math 6 by Michele Emmer,Marco Abate Pdf

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine combining music, art, poetry, literature, architecture and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics. This sixth volume in the series begins with a homage to the architect Zaha Hadid, who died on March 31st, 2016, a few weeks before the opening of a large exhibition of her works in Palazzo Franchetti in Venice, where all the Mathematics and Culture conferences have taken place in the last years. A large section of the book is dedicated to literature, narrative and mathematics including a contribution from Simon Singh. It discusses the role of media in mathematics, including museums of science, journals and movies. Mathematics and applications, including blood circulation and preventing crimes using earthquakes, is also addressed, while a section on mathematics and art examines the role of math in design. A large selection presents photos of mathematicians and mathematical objects by Vincent Moncorge. Discussing all topics in a way that is rigorous but captivating, detailed but full of evocations, it offers an all-embracing look at the world of mathematics and culture.

Einstein's Heroes

Robyn Arianrhod
Einstein s Heroes Book PDF

Author : Robyn Arianrhod
Publisher : Oxford University Press
Page : 340 pages
File Size : 55,8 Mb
Release : 2006
Category : Biography & Autobiography
ISBN : 0195308905

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Einstein's Heroes by Robyn Arianrhod Pdf

Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell.

Imagine Math 7

Michele Emmer,Marco Abate
Imagine Math 7 Book PDF

Author : Michele Emmer,Marco Abate
Publisher : Springer Nature
Page : 471 pages
File Size : 53,8 Mb
Release : 2020-10-07
Category : Mathematics
ISBN : 9783030426538

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Imagine Math 7 by Michele Emmer,Marco Abate Pdf

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine. This work is addressed to all those who have an interest in Mathematics.

Geometry and the Imagination

D. Hilbert,S. Cohn-Vossen
Geometry and the Imagination Book PDF

Author : D. Hilbert,S. Cohn-Vossen
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 48,9 Mb
Release : 2021-03-17
Category : Education
ISBN : 9781470463021

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Geometry and the Imagination by D. Hilbert,S. Cohn-Vossen Pdf

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.

Imagining Numbers

Barry Mazur
Imagining Numbers Book PDF

Author : Barry Mazur
Publisher : Penguin UK
Page : 288 pages
File Size : 46,8 Mb
Release : 2004-03-25
Category : Mathematics
ISBN : 9780141931708

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Imagining Numbers by Barry Mazur Pdf

The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

Poetic Logic and the Origins of the Mathematical Imagination

Marcel Danesi
Poetic Logic and the Origins of the Mathematical Imagination Book PDF

Author : Marcel Danesi
Publisher : Springer Nature
Page : 180 pages
File Size : 44,7 Mb
Release : 2023-09-02
Category : Mathematics
ISBN : 9783031315824

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Poetic Logic and the Origins of the Mathematical Imagination by Marcel Danesi Pdf

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.

Mathematics for Human Flourishing

Francis Su
Mathematics for Human Flourishing Book PDF

Author : Francis Su
Publisher : Yale University Press
Page : 287 pages
File Size : 51,5 Mb
Release : 2020-01-07
Category : Mathematics
ISBN : 9780300237139

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Mathematics for Human Flourishing by Francis Su Pdf

"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Mathematics for the Imagination

Peter Higgins
Mathematics for the Imagination Book PDF

Author : Peter Higgins
Publisher : Oxford University Press
Page : 238 pages
File Size : 40,5 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 9780198604600

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Mathematics for the Imagination by Peter Higgins Pdf

Explains the mathematical concepts behind everyday life using clear explanations and examples of how mathematics can be applied to history, geography, astronomy, and biography.