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Simplicity Ideals Of Practice In Mathematics And The Arts

Author : Roman Kossak
language : en
Publisher: Springer
Release Date : 2017-06-28

Download Simplicity Ideals Of Practice In Mathematics And The Arts written by Roman Kossak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-28 with Mathematics categories.

To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice.

Imagine Math 3

Author : Michele Emmer
language : en
Publisher: Springer
Release Date : 2015-03-04

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Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This volume in the series “Imagine Math” casts light on what is new and interesting in the relationships between mathematics, imagination and culture. The book opens by examining the connections between modern and contemporary art and mathematics, including Linda D. Henderson’s contribution. Several further papers are devoted to mathematical models and their influence on modern and contemporary art, including the work of Henry Moore and Hiroshi Sugimoto. Among the many other interesting contributions are an homage to Benoît Mandelbrot with reference to the exhibition held in New York in 2013 and the thoughts of Jean-Pierre Bourguignon on the art and math exhibition at the Fondation Cartier in Paris. An interesting part is dedicated to the connections between math, computer science and theatre with the papers by C. Bardainne and A. Mondot. The topics are treated in a way that is rigorous but captivating, detailed but very evocative. This is an all-embracing look at the world of mathematics and culture.

Metamathematics Of First Order Arithmetic

Author : Petr Hájek
language : en
Publisher: Cambridge University Press
Release Date : 2017-03-02

Download Metamathematics Of First Order Arithmetic written by Petr Hájek 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 2017-03-02 with Mathematics categories.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

Turning Points In The History Of Mathematics

Author : Hardy Grant
language : en
Publisher: Birkhäuser
Release Date : 2016-04-15

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This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

The Laws Of Simplicity

Author : John Antonelli
language : en
Publisher: MIT Press
Release Date : 2006-07-07

Download The Laws Of Simplicity written by John Antonelli and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-07 with Design categories.

Finally, we are learning that simplicity equals sanity. We're rebelling against technology that's too complicated, DVD players with too many menus, and software accompanied by 75-megabyte "read me" manuals. The iPod's clean gadgetry has made simplicity hip. But sometimes we find ourselves caught up in the simplicity paradox: we want something that's simple and easy to use, but also does all the complex things we might ever want it to do. In The Laws of Simplicity, John Maeda offers ten laws for balancing simplicity and complexity in business, technology, and design -- guidelines for needing less and actually getting more.Maeda -- a professor in MIT's Media Lab and a world-renowned graphic designer -- explores the question of how we can redefine the notion of "improved" so that it doesn't always mean something more, something added on.Maeda's first law of simplicity is "Reduce." It's not necessarily beneficial to add technology features just because we can. And the features that we do have must be organized (Law 2) in a sensible hierarchy so users aren't distracted by features and functions they don't need. But simplicity is not less just for the sake of less. Skip ahead to Law 9: "Failure: Accept the fact that some things can never be made simple." Maeda's concise guide to simplicity in the digital age shows us how this idea can be a cornerstone of organizations and their products -- how it can drive both business and technology. We can learn to simplify without sacrificing comfort and meaning, and we can achieve the balance described in Law 10. This law, which Maeda calls "The One," tells us: "Simplicity is about subtracting the obvious, and adding the meaningful."

Accessible Mathematics

Author : Steve Leinwand
language : en
Publisher: Heinemann Educational Books
Release Date : 2009

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Raising students' math achievement doesn't mean ripping up your planning book and starting over. In Accessible Mathematics Steven Leinwand (author of Sensible Mathematics) shows how small shifts in the good teaching you already do can make a big difference in student learning. Steve focuses on the crucial issue of classroom instruction. He scours the research and visits highly effective classrooms for practical examples of small adjustments to your teaching that lead to deeper student learning in math. Some of his 10 classroom-tested teaching shifts may surprise you and others will validate your thinking. But all of them will improve your students' performance. Thoroughly practical and ever-aware of the limits of teachers' time, Steve gives you everything you need to put his commonsense ideas to use immediately. His extensive planning advice will help you streamline your teaching to get more from everything you do. Classroom examples from every grade level model teaching language and instructional moves. And his suggestions for professional learning help increase your effectiveness through the power of collaboration. Steven Leinwand shares your priority: raising the mathematical understanding and achievement of every one of your students. Read Accessible Mathematics, try his 10 suggestions in your practice, and discover how minor shifts in your teaching can put student learning into high gear.

Radical Simplicity

Author : Jim Merkel
language : en
Publisher: New Society Pub
Release Date : 2003

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Imagine you are first in line at a potluck buffet. The spread includes not just food and water, but all the materials needed for shelter, clothing, healthcare, and education. How do you know how much to take? How much is enough to leave for your neighbours behind you -- not just the six billion people, but the wildlife, and the as-yet-unborn? In the face of looming ecological disaster, many people feel the need to change their own lifestyles as a tangible way of transforming our unsustainable culture. Radical Simplicity is the first book that guides the reader to a personal sustainability goal, then offers a process to monitor progress to a lifestyle that is equitable amongst all people, species, and generations. Combining lyrical narrative, compassionate advocacy and absorbing science, Radical Simplicity is a practical, personal answer to 21st century challenges that will appeal as much to Cultural Creatives and students as to spiritual seekers, policy makers and sustainability professionals.