Author: Ralph Abraham
Publisher:
ISBN:
Category : Social Science
Languages : en
Pages : 156

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Book Description

Author: Jessika Sobanski
Publisher: Learning Express (NY)
ISBN: 9781576854044
Category : Mathematics
Languages : en
Pages : 0

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Book Description
Visual Math has been designed to allow learners to "see" why math makes sense. By combining logical math concepts with pictures, previously unclear images will fade and math will suddenly click for you. Pictures, graphs, and diagrams help you understand math questions in the areas of number concepts and properties, fractions and decimals, ratios and proportions, percents, algebra, geometry, and much more. Designed especially for students who have difficulty with conventional math rules, this book gives you step-by step instructions with pictures to help you solve math problems.

Author: Claudi Alsina
Publisher: American Mathematical Soc.
ISBN: 1614441006
Category : Mathematics
Languages : en
Pages : 191

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Book Description
Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.

Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 9780198534464
Category : Mathematics
Languages : en
Pages : 620

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Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Author: P. Mancosu
Publisher: Springer Science & Business Media
ISBN: 1402033354
Category : Mathematics
Languages : en
Pages : 315

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Book Description
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

Author: Ralph M. Abraham
Publisher:
ISBN: 9780942344028
Category : Dynamics
Languages : en
Pages : 164

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Book Description

Author: Thomas G. West
Publisher: Prometheus Books
ISBN: 1615920390
Category : Computers
Languages : en
Pages : 521

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Book Description
This book is recognized as a classic in its field. It still stands alone as a compelling argument against popular myths of conventional intelligence and for the importance of visual thinking and visual technologies as powerful tools to aid and amplify the creative potential of many individuals with dyslexia or other learning difficulties.

Author: Steve Cunningham
Publisher: Springer Science & Business Media
ISBN: 3642772633
Category : Computers
Languages : en
Pages : 288

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Book Description
This book contains a selection of papers presented at the Computer Graphics and Education '91 Conference, held from 4th to 6th Apri11991, in Begur, Spain. The conference was organised under the auspices of the International Federation for Information Processing (IPIP) Working Group 5.10 on Computer Graphics. The goal of the organisers was to take a forward look at the impact on education of anticipated developments in graphics and related technologies, such as multimedia, in the next five years. We felt that at a time when many educational establishments are facing financial stringency and when major changes are taking place in patterns of education and training, this could be valuable for both educators and companies developing the technology: for educators, because they are often too bogged down in day-to-day problems to undertake adequate forward planning, and for companies, to see some of the problems faced by educators and to see what their future requirements might be.

Author: Günter Haag
Publisher: Springer Science & Business Media
ISBN: 3642488080
Category : Business & Economics
Languages : en
Pages : 424

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Book Description
The articles collected in this volume have two features in common: they wantto integrate economics, demography and geography, and they want to overcome the stationary approach in modelling in favour of a dynamic one. The book is subdivided into three parts, where Part I is focussing on economic evolution, Part II on geographical development and Part III is related to demographic change. The present volume aims at providing a new look at this triangle in view of the classical background of discussions by introducing new research ideas focussing in nonlinear dynamics and stochastic modelling. Thus the main purpose of this book is to make a contribution to the interdisciplinary work needed to integrate the effortsbetween these three research fields and to serve as a research source in demonstrating the current state of art in dynamic modelling. The book isaddressed to social scientists in general, and those in particular with a background in economics, geographics and demographics. It should also be of interest to mathematicians, physicists, and systems analysts interested in model building and applications of nonlinear dynamics.

Author: Clifford Alan Hooker
Publisher: SUNY Press
ISBN: 9780791422618
Category : Philosophy
Languages : en
Pages : 450

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Book Description
This book develops a new naturalist theory of reason and scientific knowledge from a synthesis of philosophy and the new sciences of complex adaptive systems. In particular, the theory of partially self-organizing regulatory systems is now emerging as central to all the life and social sciences, and this book shows how these ideas can be used to illuminate and satisfyingly reconstruct our basic philosophical concepts and principles. Evolutionary epistemology provides a unifying subject for the book. It is taken as proposing some important commonality between cognitive biological and cognitive epistemic processes. Here, that commonality is found by embedding both in a common model of complex adaptive system dynamics. New reconstructions are offered on the theories of Jean Piaget, Karl Popper, and Nicholas Rescher which show how their ideas are more deeply illuminated from this perspective in contrast to the formal rationalist interpretations standard among philosophers and scientists.