The Emergence Of Number

Author : John N. Crossley
Publisher : World Scientific
Page : 240 pages
File Size : 53,5 Mb
Release : 1987
Category : Mathematics
ISBN : 9971504146

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The Emergence of Number by John N. Crossley Pdf

This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of G”del's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.

Author : John N. Crossley
Publisher : World Scientific Publishing Company Incorporated
Page : 222 pages
File Size : 53,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9971504138

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The Emergence of Number by John N. Crossley Pdf

Author : John Newsome Crossley
Publisher : World Scientific
Page : 238 pages
File Size : 45,6 Mb
Release : 1987-11-01
Category : Mathematics
ISBN : 9789814507745

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The Emergence Of Number by John Newsome Crossley Pdf

This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.

Author : Kay Owens,Glen Lean,Patricia Paraide,Charly Muke
Publisher : Springer
Page : 461 pages
File Size : 55,9 Mb
Release : 2017-10-24
Category : Education
ISBN : 9783319454832

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History of Number by Kay Owens,Glen Lean,Patricia Paraide,Charly Muke Pdf

This unique volume presents an ecocultural and embodied perspective on understanding numbers and their history in indigenous communities. The book focuses on research carried out in Papua New Guinea and Oceania, and will help educators understand humanity's use of numbers, and their development and change. The authors focus on indigenous mathematics education in the early years and shine light on the unique processes and number systems of non-European styled cultural classrooms. This new perspective for mathematics education challenges educators who have not heard about the history of number outside of Western traditions, and can help them develop a rich cultural competence in their own practice and a new vision of foundational number concepts such as large numbers, groups, and systems. Featured in this invaluable resource are some data and analyses that chief researcher Glendon Angove Lean collected while living in Papua New Guinea before his death in 1995. Among the topics covered: The diversity of counting system cycles, where they were established, and how they may have developed. A detailed exploration of number systems other than base 10 systems including: 2-cycle, 5-cycle, 4- and 6-cycle systems, and body-part tally systems. Research collected from major studies such as Geoff Smith's and Sue Holzknecht’s studies of Morobe Province's multiple counting systems, Charly Muke's study of counting in the Wahgi Valley in the Jiwaka Province, and Patricia Paraide's documentation of the number and measurement knowledge of her Tolai community. The implications of viewing early numeracy in the light of this book’s research, and ways of catering to diversity in mathematics education. In this volume Kay Owens draws on recent research from diverse fields such as linguistics and archaeology to present their exegesis on the history of number reaching back ten thousand years ago. Researchers and educators interested in the history of mathematical sciences will find History of Number: Evidence from Papua New Guinea and Oceania to be an invaluable resource.

Author : Ekkehard Kopp
Publisher : Open Book Publishers
Page : 280 pages
File Size : 46,5 Mb
Release : 2020-10-23
Category : Mathematics
ISBN : 9781800640979

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Making up Numbers: A History of Invention in Mathematics by Ekkehard Kopp Pdf

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Author : David Nirenberg,Ricardo L. Nirenberg
Publisher : University of Chicago Press
Page : 429 pages
File Size : 41,8 Mb
Release : 2024-05-09
Category : History
ISBN : 9780226828367

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Uncountable by David Nirenberg,Ricardo L. Nirenberg Pdf

Ranging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity. Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity? These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schrödinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.

Author : Gabriel Esmay
Publisher : Teacher Created Materials
Page : 32 pages
File Size : 54,9 Mb
Release : 2020-11-11
Category : Juvenile Nonfiction
ISBN : 9781087629728

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The History of Number Systems: Place Value: Read-along ebook by Gabriel Esmay Pdf

Learn the history of number systems with this engaging book! This text combines mathematics and literacy skills, and uses practical, real-world examples of problem solving to teach math and language arts content. Students will learn place value while reading about the number systems of the Egyptians and Romans, and also learn important vocabulary terms like cuneiform, binary systems, roman numerals, and more! The full-color images, math charts, and practice problems make learning math easy and fun. The table of contents, glossary, and index will further understanding of math and reading concepts. The Math Talk problems and Explore Math sidebars provide additional learning opportunities while developing students’ higher-order thinking skills.

Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662131572

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The Development of Prime Number Theory by Wladyslaw Narkiewicz Pdf

1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.

Author : Levi Leonard Conant
Publisher : Unknown
Page : 236 pages
File Size : 48,8 Mb
Release : 1896
Category : Number concept
ISBN : UOM:39015063588944

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The Number Concept by Levi Leonard Conant Pdf

Author : Leonard Eugene Dickson
Publisher : Legare Street Press
Page : 0 pages
File Size : 41,5 Mb
Release : 2023-07-22
Category : Electronic
ISBN : 1022888676

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History Of The Theory Of Numbers - I by Leonard Eugene Dickson Pdf

A landmark work in the field of mathematics, History of the Theory of Numbers - I traces the development of number theory from ancient civilizations to the early 20th century. Written by mathematician Leonard Eugene Dickson, this book is a comprehensive and accessible introduction to the history of one of the most fundamental branches of mathematics. 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 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. 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.

Author : Graham Flegg
Publisher : Courier Corporation
Page : 304 pages
File Size : 49,7 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486166513

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Numbers by Graham Flegg Pdf

Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Author : Caleb Everett
Publisher : Harvard University Press
Page : 308 pages
File Size : 42,5 Mb
Release : 2017-03-13
Category : Language Arts & Disciplines
ISBN : 9780674504431

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Numbers and the Making of Us by Caleb Everett Pdf

“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal

Author : Stephen Crain
Publisher : Cambridge University Press
Page : 307 pages
File Size : 47,5 Mb
Release : 2012-08-30
Category : Language Arts & Disciplines
ISBN : 9780521858090

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The Emergence of Meaning by Stephen Crain Pdf

An investigation into the underlying logic of human languages which looks at how children acquire English and Mandarin.

Author : Gabriel Esmay
Publisher : Teacher Created Materials
Page : 35 pages
File Size : 43,9 Mb
Release : 2017-06-01
Category : Juvenile Nonfiction
ISBN : 9781480757943

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The History of Number Systems: Place Value by Gabriel Esmay Pdf

Learn the history of number systems with this engaging book! This text combines mathematics and literacy skills, and uses practical, real-world examples of problem solving to teach math and language arts content. Students will learn place value while reading about the number systems of the Egyptians and Romans, and also learn important vocabulary terms like cuneiform, binary systems, roman numerals, and more! The full-color images, math charts, and practice problems make learning math easy and fun. The table of contents, glossary, and index will further understanding of math and reading concepts. The Math Talk problems and Explore Math sidebars provide additional learning opportunities while developing students’ higher-order thinking skills.

Author : Anonim
Publisher : Teacher Created Materials
Page : 35 pages
File Size : 40,9 Mb
Release : 2017-07-01
Category : Juvenile Nonfiction
ISBN : 9781480758179

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The History of Number Systems: Place Value 6-Pack by Anonim Pdf

This intriguing title teaches readers the history of number systems. From Egyptian times to the modern day, this title covers the number systems of the Roman Empire, the Maya Empire, the Inca Empire, Babylon, and India. These full-color books teach students about operations and algebraic reasoning, introducing them to new concepts and vocabulary terms like place value, rounded numbers, exact numbers, the binary system, and more. Primary sources like maps, images, and illustrations will engage students and make learning about math topics fun and enjoyable. Text features such as a glossary, index, bold print, and a table of contents increase understanding and build academic vocabulary. The DOK-leveled Math Talk section includes questions that facilitate mathematical discourse and activities that students can respond to at home or school. Let's Explore Math sidebars and the extensive Problem Solving section provide ample opportunities for students to practice what they have learned. This 6-Pack includes six copies of this title and a lesson plan.