Download or read book The Numeratio The University Press written by Charles Pickering Bowditch and published by . This book was released on 1910 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numbers and the Making of Us written by Caleb Everett and published by Harvard University Press. This book was released on 2017-03-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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
Download or read book written by and published by . This book was released on 2007 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
Download or read book History of Number written by Kay Owens and published by Springer. This book was released on 2017-10-24 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Number Sense written by Stanislas Dehaene and published by OUP USA. This book was released on 2011-04-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Our understanding of how the human brain performs mathematical calculations is far from complete. In The Number Sense, Stanislas Dehaene offers readers an enlightening exploration of the mathematical mind. Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind"--Provided by publisher.
Download or read book Number Theory written by John J. Watkins and published by Princeton University Press. This book was released on 2013-12-26 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook with a unique historical approach to teaching number theory The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)
Download or read book The Oxford Handbook of Grammatical Number written by Patricia Cabredo Hofherr and published by Oxford University Press. This book was released on 2021 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers detailed accounts of current research in grammatical number in language. Following a detailed introduction, the chapters in the first three parts of the book explore the multiple research questions in the field and the complex problems surrounding the analysis of grammatical number: Part I presents the background and foundational notions, Part II the morphological, semantic, and syntactic aspects, and Part III the different means of expressing plurality in the event domain. The final part offers fifteen case studies that include in-depth discussion of grammatical number phenomena in a range of typologically diverse languages, written by - or in collaboration with - native speakers linguists or based on extensive fieldwork. The volume draws on work from a range of subdisciplines - including morphology, syntax, semantics, and psycholinguistics - and will be a valuable resource for students and scholars in all areas of theoretical, descriptive, and experimental linguistics.
Download or read book Learning to Teach Number written by Len Frobisher and published by Nelson Thornes. This book was released on 1999 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Organised into 21 independent modules covering number concepts and systems, the four number operations and pre-algebra, the book provides models for pupils' learning as well as seeking to develop the reader's own understanding of the subject"--Back cover.
Download or read book Number written by Midhat J. Gazalé and published by Princeton University Press. This book was released on 2000 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Mathematics Foundation Course written by and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Formal Languages Automata and Numeration Systems 1 written by Michel Rigo and published by John Wiley & Sons. This book was released on 2014-11-17 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.
Download or read book Formal Languages Automata and Numeration Systems 2 written by Michel Rigo and published by John Wiley & Sons. This book was released on 2014-11-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.
Download or read book When Languages Die written by K David Harrison and published by Oxford University Press. This book was released on 2008-07-21 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly agreed by linguists and anthropologists that the majority of languages spoken now around the globe will likely disappear within our lifetime. The phenomenon known as language death has started to accelerate as the world has grown smaller. This extinction of languages, and the knowledge therein, has no parallel in human history. K. David Harrison's book is the first to focus on the essential question, what is lost when a language dies? What forms of knowledge are embedded in a language's structure and vocabulary? And how harmful is it to humanity that such knowledge is lost forever? Harrison spans the globe from Siberia, to North America, to the Himalayas and elsewhere, to look at the human knowledge that is slowly being lost as the languages that express it fade from sight. He uses fascinating anecdotes and portraits of some of these languages' last remaining speakers, in order to demonstrate that this knowledge about ourselves and the world is inherently precious and once gone, will be lost forever. This knowledge is not only our cultural heritage (oral histories, poetry, stories, etc.) but very useful knowledge about plants, animals, the seasons, and other aspects of the natural world--not to mention our understanding of the capacities of the human mind. Harrison's book is a testament not only to the pressing issue of language death, but to the remarkable span of human knowledge and ingenuity. It will fascinate linguists, anthropologists, and general readers.
Download or read book Combinatorics Automata and Number Theory written by Valérie Berthé and published by Cambridge University Press. This book was released on 2010-08-12 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.
Download or read book Applied Algebra and Number Theory written by Gerhard Larcher and published by Cambridge University Press. This book was released on 2014-12-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains survey articles on modern topics related to the work of Harald Niederreiter, written by close colleagues and leading experts.
Download or read book A Possible Solution of the Number Series on Pages 51 to 58 of the Dresden Codex written by Carl Eugen Guthe and published by . This book was released on 1921 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Emerging Applications of Number Theory written by Dennis A. Hejhal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
