Iconic Arithmetic Volume I

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Iconic Arithmetic Volume I

Author : william bricken
Publisher : Unary Press
ISBN 13 : 9781732485136
Total Pages : 446 pages
Book Rating : 4.4/5 (851 download)

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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.

Icons of Mathematics

Author : Claudi Alsina
Publisher : MAA
ISBN 13 : 0883853523
Total Pages : 348 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Icons of Mathematics by : Claudi Alsina

Download or read book Icons of Mathematics written by Claudi Alsina and published by MAA. This book was released on 2011-08-04 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.

Iconic Arithmetic Volume III

Author : William Bricken
Publisher :
ISBN 13 : 9781732485150
Total Pages : 418 pages
Book Rating : 4.4/5 (851 download)

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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.

Psychology and Mathematics Education

Author : Gila Hanna
Publisher : Frontiers Media SA
ISBN 13 : 2832529992
Total Pages : 552 pages
Book Rating : 4.8/5 (325 download)

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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).

Enthusiastic Mathematics

Author : Bernie Lewin
Publisher :
ISBN 13 : 9781982930523
Total Pages : 370 pages
Book Rating : 4.9/5 (35 download)

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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.

Laws Of Form: A Fiftieth Anniversary

Author : Louis H Kauffman
Publisher : World Scientific
ISBN 13 : 9811247447
Total Pages : 944 pages
Book Rating : 4.8/5 (112 download)

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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.

Finding Zero

Author : Amir D. Aczel
Publisher : Macmillan + ORM
ISBN 13 : 1466879106
Total Pages : 199 pages
Book Rating : 4.4/5 (668 download)

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Book Synopsis Finding Zero by : Amir D. Aczel

Download or read book Finding Zero written by Amir D. Aczel and published by Macmillan + ORM. This book was released on 2015-01-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A captivating story, not just an intellectual quest but a personal one . . . gripping [and] filled with the passion and wonder of numbers.” —The New York Times Virtually everything in our lives is digital, numerical, or quantified. But the story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is the saga of Amir Aczel’s lifelong obsession: to find the original sources of our numerals, perhaps the greatest abstraction the human mind has ever created. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross-examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride. The history begins with Babylonian cuneiform numbers, followed by Greek and Roman letter numerals. Then Aczel asks: Where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from. “A historical adventure that doubles as a surprisingly engaging math lesson . . . rip-roaring exploits and escapades.” —Publishers Weekly

Number Theory, Analysis and Geometry

Author : Dorian Goldfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1461412609
Total Pages : 715 pages
Book Rating : 4.4/5 (614 download)

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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.

Benjamin Franklin's Numbers

Author : Paul C. Pasles
Publisher : Princeton University Press
ISBN 13 : 9780691129563
Total Pages : 272 pages
Book Rating : 4.1/5 (295 download)

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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.

Harry and the Hot Lava

Author : Chris Robertson
Publisher : Xist Publishing
ISBN 13 : 1623955769
Total Pages : 20 pages
Book Rating : 4.6/5 (239 download)

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Book Synopsis Harry and the Hot Lava by : Chris Robertson

Download or read book Harry and the Hot Lava written by Chris Robertson and published by Xist Publishing. This book was released on 2014-07-15 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harry is a little boy with a big imagination. One day, a simple game of "don't step on the hot lava" turns into an adventure he'll never forget! This children's picture book features the iconic art of Chris Robertson and has fun simple text perfect for beginning readers and story time.

A Logical Foundation for Potentialist Set Theory

Author : Sharon Berry
Publisher : Cambridge University Press
ISBN 13 : 1108834310
Total Pages : 249 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis A Logical Foundation for Potentialist Set Theory by : Sharon Berry

Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.

Science and the Founding Fathers

Author : I. Bernard Cohen
Publisher : W. W. Norton & Company
ISBN 13 : 9780393315103
Total Pages : 378 pages
Book Rating : 4.3/5 (151 download)

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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.

Realizing Reason

Author : Danielle Macbeth
Publisher :
ISBN 13 : 0198704755
Total Pages : 507 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Realizing Reason by : Danielle Macbeth

Download or read book Realizing Reason written by Danielle Macbeth and published by . This book was released on 2014-03 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Danielle Macbeth offers a new account of mathematical practice as a mode of inquiry into objective truth, and argues that understanding the nature of mathematical practice provides us with the resources to develop a radically new conception of ourselves and our capacity for knowledge of objective truth.

Algebra

Author : Serge Lang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (65 download)

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Book Synopsis Algebra by : Serge Lang

Download or read book Algebra written by Serge Lang and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Math in Society

Author : David Lippman
Publisher :
ISBN 13 : 9781479276530
Total Pages : 0 pages
Book Rating : 4.2/5 (765 download)

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Book Synopsis Math in Society by : David Lippman

Download or read book Math in Society written by David Lippman and published by . This book was released on 2012-09-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

A Mathematician's Apology

Author : G. H. Hardy
Publisher : Cambridge University Press
ISBN 13 : 9780521427067
Total Pages : 158 pages
Book Rating : 4.4/5 (27 download)

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Book Synopsis A Mathematician's Apology by : G. H. Hardy

Download or read book A Mathematician's Apology written by G. H. Hardy and published by Cambridge University Press. This book was released on 1992-01-31 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

The History of Mathematical Proof in Ancient Traditions

Author : Karine Chemla
Publisher : Cambridge University Press
ISBN 13 : 1139510584
Total Pages : 522 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis The History of Mathematical Proof in Ancient Traditions by : Karine Chemla

Download or read book The History of Mathematical Proof in Ancient Traditions written by Karine Chemla and published by Cambridge University Press. This book was released on 2012-07-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.