Download Free The Emergence Of Number Book in PDF and EPUB Free Download. You can read online The Emergence Of Number and write the review.

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.
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.
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
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.
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.
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.
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.
The 20th century was a time of great upheaval and great progress in mathematics. In order to get the overall picture of trends, developments, and results, it is illuminating to examine their manifestations locally, in the personal lives and work of mathematicians who were active during this time. The university archives of Gottingen harbor a wealth of papers, letters, and manuscripts from several generations of mathematicians--documents which tell the story of the historic developments from a local point of view. This book offers a number of essays based on documents from Gottingen and elsewhere--essays which have not yet been included in the author's collected works. These essays, independent from each other, are meant as contributions to the imposing mosaic of the history of number theory. They are written for mathematicians, but there are no special background requirements. The essays discuss the works of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grun, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether, Abraham Robinson, Ernst Steinitz, Hermann Weyl, and others.
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.
An investigation into the underlying logic of human languages which looks at how children acquire English and Mandarin.