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Iconic Arithmetic Volume I
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Book Synopsis Iconic Arithmetic Volume I by : william bricken
Download or read book Iconic Arithmetic Volume I written by william bricken and published by Unary Press. This book was released on 2019-04-10 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic evolves. Iconic arithmetic is built from icons that look and feel like what they mean, rather than from strings of symbols that must be memorized. The book explores the formal structure of two types of postsymbolic boundary arithmetic. Ensemble arithmetic modernizes tallies to provide forms that add together by being placed together and multiply by being placed inside one another. James algebra defines the concepts and operations of arithmetic as different ways of arranging containers. Three simple axioms are sufficient. Features of iconic arithmetic include (1) a void with no representation and no properties instead of the symbol zero; (2) void-equivalent forms that can be freely deleted; (3) meaning based on existence of structure rather than truth or numerical value; (4) only one relation (containment) to represent all forms; and (5) construction and deletion to implement all transformations. Iconic forms and transformations can be represented as two and three dimensional structures that can be directly viewed, manipulated, and even inhabited. Many different spatial interactive dialects are described. The author explores this new kind of arithmetic from the perspectives of historical evolution, formal mathematics, computer science and mathematics education. The overall objective is to provide proof of principle that our current universal approach to the arithmetic of numbers is a design choice rather than a truth embedded in numbers themselves. Iconic Arithmetic recognizes that knowledge is embodied, multidimensional, sensual, simple. It helps us to transition into a postsymbolic world of interactive information.
Book Synopsis Iconic Arithmetic Volume III by : William Bricken
Download or read book Iconic Arithmetic Volume III written by William Bricken and published by . This book was released on 2021-02-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume III of this series applies the innovations of iconic arithmetic to several branches of elementary mathematics to yield new techniques and new insights that are not accessible to symbolic arithmetic. The rules of algebra are reduced to three simple patterns expressed as spatial containment relations. These patterns resurrect a discarded imaginary number that provides an additive foundation for the multiplicative i, replaces inverse operations by a single constant, and eliminates signed numbers by rendering polarity as an exponent. Postsymbolic arithmetic reduces trigonometry to reflection along a line, condenses calculus derivatives into a single generic pattern, and identifies and organizes infinite and indeterminate expressions. Other innovations include base-free logarithms, fractional polarity, bipolar numbers, and direct deletion of illusory structure introduced by typographic notation.The overall goal is to demonstrate a comprehensive formal system that can be interpreted as arithmetic but bears little resemblance to our current universally adopted symbolic arithmetic. Iconic Arithmetic provides a proof of concept that our understanding of arithmetic has been limited by the absence of formal techniques for sensory interaction with abstraction.
Book Synopsis Iconic Arithmetic Volume II by : william bricken
Download or read book Iconic Arithmetic Volume II written by william bricken and published by . This book was released on 2019-04-02 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of this series explores the unique structural characteristics of James algebra. The concepts of equality, substitution and concurrency are rendered from the perspective of void-based numeric form. Difference is more important than equality. Substitution is sufficient mechanism to define numeric operations. Non-linearity of representation encourages parallel numeric computation. Then boundary mathematics itself is examined without regard to numeric application. A central objective of Volume II is to place James algebra within the context of the formal structure of numbers developed by Hilbert, Frege and Peano at the turn of the twentieth century. Peano's axiomatic definition of numbers is substantively simplified. More recent weak models of arithmetic by Presburger, Robinson and Goodstein are restructured by removing the assumptions of string-based notation. The nature of formal systems and symbolic computation are then examined from a postsymbolic perspective, leading to the elimination of set theory, predicate and propositional logic, and functional thinking as necessities of formal structure. The James spatial forms are reexamined and new tools are introduced.
Book Synopsis Psychology and Mathematics Education by : Gila Hanna
Download or read book Psychology and Mathematics Education written by Gila Hanna and published by Frontiers Media SA. This book was released on 2023-09-05 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats. Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem. This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).
Book Synopsis Icons of Mathematics: An Exploration of Twenty Key Images by : Claudi Alsina
Download or read book Icons of Mathematics: An Exploration of Twenty Key Images written by Claudi Alsina and published by American Mathematical Soc.. This book was released on 2020-06-01 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.
Book Synopsis The Natural Arithmetic by : Isaac Oscar Winslow
Download or read book The Natural Arithmetic written by Isaac Oscar Winslow and published by . This book was released on 1901 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Number Theory, Analysis and Geometry by : Dorian Goldfeld
Download or read book Number Theory, Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-21 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
Book Synopsis Laws Of Form: A Fiftieth Anniversary by : Louis H Kauffman
Download or read book Laws Of Form: A Fiftieth Anniversary written by Louis H Kauffman and published by World Scientific. This book was released on 2023-01-09 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
Book Synopsis Arithmetic by : Edward Lee Thorndike
Download or read book Arithmetic written by Edward Lee Thorndike and published by . This book was released on 1917 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Everyday Arithmetic; by : Franklin Sherman Hoyt
Download or read book Everyday Arithmetic; written by Franklin Sherman Hoyt and published by Palala Press. This book was released on 2018-02-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Science and the Founding Fathers by : I. Bernard Cohen
Download or read book Science and the Founding Fathers written by I. Bernard Cohen and published by W. W. Norton & Company. This book was released on 1997 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thomas Jefferson was the only president who could read and understand Newton's Principia. Benjamin Franklin is credited with establishing the science of electricity. John Adams had the finest education in science that the new country could provide, including "Pnewmaticks, Hydrostaticks, Mechanicks, Staticks, Opticks." James Madison, chief architect of the Constitution, peppered his Federalist Papers with references to physics, chemistry, and the life sciences. For these men science was an integral part of life--including political life. This is the story of their scientific education and of how they employed that knowledge in shaping the political issues of the day, incorporating scientific reasoning into the Constitution.
Book Synopsis Enthusiastic Mathematics by : Bernie Lewin
Download or read book Enthusiastic Mathematics written by Bernie Lewin and published by . This book was released on 2018-11-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifty years ago, a small sparse book came out under the pretentious title Laws of Form. Its author might have once fallen in with the logical philosophers of Cambridge, including Russell and Wittgenstein. But only later, while designing primitive switching circuits for British Rail, did George Spencer Brown come upon the arithmetic underlying Boolean algebra. Laws of Form flips the reduction of mathematics to logic, revealing simple laws of being and knowing that only reflect what great mystics, East and West, have been saying all along. Enthusiastic Mathematics offers the first thorough, philosophical introduction to Laws of Form. With no presumption for logic or mathematics, the reader is delivered into its philosophical vision via a colourful journey through the history of science.
Book Synopsis The Natural Arithmetic by : Isaac Oscar Winslow
Download or read book The Natural Arithmetic written by Isaac Oscar Winslow and published by Palala Press. This book was released on 2016-05-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Madame Alexander: The Creator of the Iconic American Doll by : Susan Goldman Rubin
Download or read book Madame Alexander: The Creator of the Iconic American Doll written by Susan Goldman Rubin and published by . This book was released on 2022-10-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inspiring and uplifting picture book biography about Beatrice Alexander, founder of the iconic Madame Alexander doll.
Book Synopsis Durell's Arithmetic by : Fletcher Durell
Download or read book Durell's Arithmetic written by Fletcher Durell and published by Palala Press. This book was released on 2015-09 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis Arithmetic by : Edward Lee Thorndike
Download or read book Arithmetic written by Edward Lee Thorndike and published by . This book was released on 1920 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Benjamin Franklin's Numbers by : Paul C. Pasles
Download or read book Benjamin Franklin's Numbers written by Paul C. Pasles and published by Princeton University Press. This book was released on 2007-11-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few American lives have been as celebrated--or as closely scrutinized--as that of Benjamin Franklin. Yet until now Franklin's biographers have downplayed his interest in mathematics, at best portraying it as the idle musings of a brilliant and ever-restless mind. In Benjamin Franklin's Numbers, Paul Pasles reveals a side of the iconic statesman, scientist, and writer that few Americans know--his mathematical side. In fact, Franklin indulged in many areas of mathematics, including number theory, geometry, statistics, and economics. In this generously illustrated book, Pasles gives us the first mathematical biography of Benjamin Franklin. He draws upon previously unknown sources to illustrate Franklin's genius for numbers as never before. Magic squares and circles were a lifelong fascination of Franklin's. Here, for the first time, Pasles gathers every one of these marvelous creations together in one place. He explains the mathematics behind them and Franklin's hugely popular Poor Richard's Almanac, which featured such things as population estimates and a host of mathematical digressions. Pasles even includes optional math problems that challenge readers to match wits with the bespectacled Founding Father himself. Written for a general audience, this book assumes no technical skills beyond basic arithmetic. Benjamin Franklin's Numbers is a delightful blend of biography, history, and popular mathematics. If you think you already know Franklin's story, this entertaining and richly detailed book will make you think again.
