Advertisement
| the nine chapters on the mathematical art: The Nine Chapters on the Mathematical Art Kangshen Shen, John N. Crossley, Anthony Wah-Cheung Lun, 1999 The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This volume contains the first complete English translation of the Nine Chapters, together with the illuminating commentary of Liu Hui written in the 3rd century AD and other early century commentaries and further insights provided by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation, while the Chinese commentators provide the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. This first, full-English translation gives us an idea of the distinctive style and important contributions that have been made by traditional Chinese mathematics. |
| the nine chapters on the mathematical art: A History of Chinese Mathematics Jean-Claude Martzloff, 2007-08-17 This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike. |
| the nine chapters on the mathematical art: Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth Joseph Needham, 1959 After two volumes mainly introductory, Dr Needham now embarks upon his systematic study of the development of the natural sciences in China. The Sciences of the Earth follow: geography and cartography, geology, seismology and mineralogy. Dr Needham distinguishes parallel traditions of scientific cartography and religious cosmography in East and West, discussing orbocentric wheel-maps, the origins of the rectangular grid system, sailing charts and relief maps, Chinese survey methods, and the impact of Renaissance cartography on the East. Finally-and here Dr Needham's work has no Western predecessors-there are full accounts of the Chinese contribution to geology and mineralogy. |
| the nine chapters on the mathematical art: The Suàn Shù Shū Christopher Cullen, 2004 |
| the nine chapters on the mathematical art: The Chinese Roots of Linear Algebra Roger Hart, 2011-01-01 A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West discovered in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By cross multiplying these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra. |
| the nine chapters on the mathematical art: The Gentle Art of Mathematics Dan Pedoe, 2012-12-27 This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more. |
| the nine chapters on the mathematical art: Crafting by Concepts sarah-marie belcastro, Carolyn Yackel, 2011-03-24 From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string art. Instructions are written as ordinary patterns, so the formatting and language will be familiar to crafters. |
| the nine chapters on the mathematical art: The development of mathematics in China and Japan Yoshio Mikami, 1913 |
| the nine chapters on the mathematical art: The Sea Island Mathematical Manual Frank J. Swetz, 1992 The Haidao Suanjing or Sea Island Mathematical Manual, is one of the Ten Classics of traditional Chinese mathematics, and its contents demonstrate the high standards of theoretical and mathematical sophistication present in early Chinese surveying theory. The Haidao composed in A.D. 263 by Liu Hui, established the mathematical procedures for much of East Asian surveying activity for the next one thousand years. The contents of the Haidao also testify to the ability of the Chinese to systematize mathematics and hint at the use of proof in Chinese mathematics, a concept usually associated with Greek mathematical thought. Frank Swetz provides an annotated translation of the Haidao and an analysis of its surveying problems. In particular, he details surveying techniques and undertakes a mathematical exposition of the Chinese chong cha solution procedures. The Haidao is a testimony to the ingenuity and skill of China's early surveyors and its author, Liu Hui. This study complements and extends the findings of Swetz's previous book, Was Pythagoras Chinese?An Examination of Right Triangle Theory in Ancient China. |
| the nine chapters on the mathematical art: Mathematics and the Imagination Edward Kasner, James Newman, 2013-04-22 With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures. |
| the nine chapters on the mathematical art: Linear Algebra and Linear Models Ravindra B. Bapat, 2008-01-18 This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians. |
| the nine chapters on the mathematical art: Methods and Applications of Longitudinal Data Analysis Xian Liu, 2015-09-01 Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include: - descriptive methods for delineating trends over time - linear mixed regression models with both fixed and random effects - covariance pattern models on correlated errors - generalized estimating equations - nonlinear regression models for categorical repeated measurements - techniques for analyzing longitudinal data with non-ignorable missing observations Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data. Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists. - From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis - Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection - Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples. |
| the nine chapters on the mathematical art: A History of Chinese Science and Technology Yongxiang Lu, 2014-10-14 A History of Chinese Science and Technology (Volumes 1, 2 & 3) presents 44 individual lectures, beginning with Ancient Chinese Science and Technology in the Process of Human Civilizations and an Overview of Chinese Science and Technology, and continuing with in-depth discussions of several issues in the History of Science and the Needham Puzzle, interspersed with topics on Astronomy, Arithmetic, Agriculture and Medicine, The Four Great Inventions, and various technological areas closely related to clothing, food, shelter and transportation. This book is the most authoritative work on the history of Chinese Science and Technology. It is the Winner of the China Book Award, the Shanghai Book Award (1st prize), and the Classical China International Publishing Project (GAPP, General Administration of Press and Publication of China) and offers an essential resource for academic researchers and non-experts alike. It originated with a series of 44 lectures presented to top Chinese leaders, which received very positive feedback. Written by top Chinese scholars in their respective fields from the Institute for the History of Natural Sciences, Chinese Academy of Sciences and many other respected Chinese organizations, the book is intended for scientists, researchers and postgraduate students working in the history of science, philosophy of science and technology, and related disciplines. Yongxiang Lu is a professor, former president and member of the Chinese Academy of Sciences (CAS) and Chinese Academy of Engineering (CAE), and Vice Chairman of the National Congress of China. |
| the nine chapters on the mathematical art: The Ellipse Arthur Mazer, 2011-09-26 Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse. The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics. |
| the nine chapters on the mathematical art: The History of Mathematical Proof in Ancient Traditions Karine Chemla, 2012-07-05 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. |
| the nine chapters on the mathematical art: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 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. |
| the nine chapters on the mathematical art: Our Mathematical Universe Max Tegmark, 2015-02-03 Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians. |
| the nine chapters on the mathematical art: Sacred Mathematics Fukagawa Hidetoshi, Tony Rothman, 2021-08-10 Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life--samurai, farmers, and merchants--inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. Sacred Mathematics is the first book published in the West to fully examine this tantalizing--and incredibly beautiful--mathematical tradition. Fukagawa Hidetoshi and Tony Rothman present for the first time in English excerpts from the travel diary of a nineteenth-century Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. The authors set this fascinating travel narrative--and almost everything else that is known about temple geometry--within the broader cultural and historical context of the period. They explain the sacred and devotional aspects of sangaku, and reveal how Japanese folk mathematicians discovered many well-known theorems independently of mathematicians in the West--and in some cases much earlier. The book is generously illustrated with photographs of the tablets and stunning artwork of the period. Then there are the geometry problems themselves, nearly two hundred of them, fully illustrated and ranging from the utterly simple to the virtually impossible. Solutions for most are provided. A unique book in every respect, Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries. |
| the nine chapters on the mathematical art: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| the nine chapters on the mathematical art: Fibonacci’s Liber Abaci Laurence Sigler, 2012-12-06 First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods. |
| the nine chapters on the mathematical art: Mathematical Models of Biological Systems Hugo van den Berg, 2010-11-25 This interdisciplinary textbook provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topics in turn to highlight key components in the art of modelling. |
| the nine chapters on the mathematical art: 5000 Years of Geometry Christoph J. Scriba, Peter Schreiber, 2015-04-22 The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) Five Thousand Years of Geometry - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague) |
| the nine chapters on the mathematical art: Single Digits Marc Chamberland, 2017-05-30 The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really six degrees of separation between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.--Jacket. |
| the nine chapters on the mathematical art: History in Mathematics Education John Fauvel, J.A. van Maanen, 2006-04-11 This ground-breaking book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. It draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. It includes a 300-item annotated bibliography of recent work in the field in eight languages. |
| the nine chapters on the mathematical art: Rome's Economic Revolution Philip Kay, 2014 Kay examines the economic change in Rome between the Second Punic War and the middle of the first century BC. He focuses on how the increased inflow of bullion and expansion of the availability of credit resulted in real per capita economic growth in the Italian peninsula, radically changing the composition and scale of the Roman economy. |
| the nine chapters on the mathematical art: Eco-Mathematics Education Nataly Chesky, Jack Milgram, 2021-10-18 Eco-Mathematics Education strives to show how everyone can experience the embedded connection between mathematics and the natural world. The authors’ sincere hope is that by doing so, we can radically change the way we come to understand mathematics, as well as humanity’s place in the ecosystem. The book hopes to accomplish this by providing in-depth lesson plans and resources for educators and anyone interested in teaching and learning mathematics through an ecological aesthetic perspective. All lessons are based on the inquiry method of teaching, aligned to standards, incorporate art projects inspired by famous artists, and utilize recycled and/or natural materials as much as possible. |
| the nine chapters on the mathematical art: The Math of Money Morton D. Davis, 2013-04-17 This lively and practical introduction to the mathematics of money invites us to take a fresh look at the numbers that underpin our financial decisions. Morton D. Davis talks about strategies to use when we are required to bet against the odds (purchasing auto insurance) or choose to bet against the odds (wagering in a casino or at the track). He considers the ways in which we can streamline and simplify the choices available to us in mortgages and other loans. And he helps us understand the real probabilities when we accept a tip on that one in a thousand stock, even when the tip comes from a successful day trader. With a wealth of entertaining and counterintuitive examples, The Math of Money delights as well as informs, and will help readers treat their financial resources more rationally. |
| the nine chapters on the mathematical art: Technology and Utopia Howard P. Segal, 2006 Segal examines the historical connection between technology and utopia, and shows how this connection is not just a contemporary western concept, but one that stretches back several centuries. |
| the nine chapters on the mathematical art: How to Guard an Art Gallery T.S. Michael, 2009-09-01 An “accessible and engaging” tool for understanding the branch of mathematics that is so crucial to modern computer science, using real-life problems (Mathematical Reviews). What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael’s gem of a book brings this vital but tough-to-teach subject to life using examples from the real world and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations. |
| the nine chapters on the mathematical art: What's Happening in the Mathematical Sciences Barry Cipra, Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers. |
| the nine chapters on the mathematical art: Classics of Mathematics Ronald Calinger, 1995 Appropriate for undergraduate and select graduate courses in the history of mathematics, and in the history of science. This edited volume of readings contains more than 130 selections from eminent mathematicians from A `h-mose' to Hilbert and Noether. The chapter introductions comprise a concise history of mathematics based on critical textual analysis and the latest scholarship. Each reading is preceded by a substantial biography of its author. |
| the nine chapters on the mathematical art: Experiential Learning David A. Kolb, 2015 Experiential learning is a powerful and proven approach to teaching and learning that is based on one incontrovertible reality: people learn best through experience. Now, in this extensively updated book, David A. Kolb offers a systematic and up-to-date statement of the theory of experiential learning and its modern applications to education, work, and adult development. Experiential Learning, Second Edition builds on the intellectual origins of experiential learning as defined by figures such as John Dewey, Kurt Lewin, Jean Piaget, and L.S. Vygotsky, while also reflecting three full decades of research and practice since the classic first edition. Kolb models the underlying structures of the learning process based on the latest insights in psychology, philosophy, and physiology. Building on his comprehensive structural model, he offers an exceptionally useful typology of individual learning styles and corresponding structures of knowledge in different academic disciplines and careers. Kolb also applies experiential learning to higher education and lifelong learning, especially with regard to adult education. This edition reviews recent applications and uses of experiential learning, updates Kolb's framework to address the current organizational and educational landscape, and features current examples of experiential learning both in the field and in the classroom. It will be an indispensable resource for everyone who wants to promote more effective learning: in higher education, training, organizational development, lifelong learning environments, and online. |
| the nine chapters on the mathematical art: Fleeting Footsteps Lay Yong Lam, Tian Se Ang, 2004 The Hindu-Arabic numeral system (1, 2, 3, ...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim. This book provides considerable evidence to show that the Hindu-Arabic numeral system, despite its commonly accepted name, has its origins in the Chinese rod numeral system. This system was widely used in China from antiquity till the 16th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetic operations, and also used by mathematicians to develop arithmetic and algebra. Based on this system, numerous mathematical treatises were written. Sun Zi suanjing (The Mathematical Classic of Sun Zi), written around 400 A.D., is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetic and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu-Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi suanjing. In this revised edition, Lam Lay Yong has included an edited text of her plenary lecture entitled Ancient Chinese Mathematics and Its Influence on World Mathematics, which was delivered at the International Congress of Mathematicians, Beijing 2002, after she received the prestigious Kenneth O. May Medal conferred by the International Commission on the History of Mathematics. This should serve as a useful and easy-to-comprehend introduction to the book. |
| the nine chapters on the mathematical art: Philosophy of Mathematics Øystein Linnebo, 2020-03-24 A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics. |
| the nine chapters on the mathematical art: The Math of Life and Death Kit Yates, 2021-04-27 Few of us really appreciate the full power of math--the extent to which its influence is not only in every office and every home, but also in every courtroom and hospital ward. In this ... book, Kit Yates explores the true stories of life-changing events in which the application--or misapplication--of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupted by faulty algorithms; innocent victims of miscarriages of justice; and the unwitting victims of software glitches--Publisher marketing. |
| the nine chapters on the mathematical art: Handbook of Mathematical Functions Milton Abramowitz, Irene A. Stegun, 1965-01-01 An extensive summary of mathematical functions that occur in physical and engineering problems |
| the nine chapters on the mathematical art: Euclid's Elements Euclid, Dana Densmore, 2002 The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary --from book jacket. |
| the nine chapters on the mathematical art: Nine Chapters on Mathematical Modernity Andrea Bréard, 2019-06-25 The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid portraits of a series of go-betweens (such as translators, educators, or state statisticians) based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. “While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous ‘Nine Chapters’ as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréard’s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!” (John Day, Boston University). |
| the nine chapters on the mathematical art: 99 Variations on a Proof Philip Ording, 2021-10-19 An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape. |
| the nine chapters on the mathematical art: Chinese Mathematics in the Thirteenth Century Ulrich Libbrecht, 2005-01-01 An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book. The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China. |
The Nine Chapters on the Mathematical Art - Wikipedia
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 1st century CE. This book is one of the earliest surviving mathematical texts from China, the others being the Suan shu shu (202 BCE – 186 BCE) and Zhoubi Suanjing (compiled throughout the Han until …
Jiu Zhang Suanshu 九章算衔 (Nine Chapters on the Mathematical Art…
(Nine Chapters on the Mathematical Art): An Overview Lam Lay Yong Table of Contents 1. The beginnings of our arithmetic 2. The beginnings of arithmetic in China 3. The Jiu zhang suanshu 3.1 Chapter One 3.1.1 The fundamental operations of arithmetic 3.1.2 The common fraction 3.1.3 Areas 3.2 Chapter Two 3.2.1 Rule of Three 3.2.2 Buying goods 3.3 ...
The Nine Chapters on the Mathematical Art: Companion and …
7 Oct 1999 · The Nine Chapters on the Mathematical Art is a classic text: the most important mathematical source in China during the past 2000 years, and comparable in significance to Euclid's Elements in the West. This volume contains the first complete English translation of the Nine Chapters, together with two commentaries written in the 3rd and 7th ...
Nine Chapters on the Mathematical Art - MacTutor History of Mathematics ...
The Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a practical handbook of mathematics consisting of 246 problems intended to provide methods to be used to solve everyday problems of engineering, surveying, trade, and taxation. It has played a fundamental role in the development of mathematics in China, not dissimilar to the role of Euclid's Elements …
The Nine Chapters on the Mathematical Art - Google Books
The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about …
The Nine Chapters on the History of Chinese Mathematics
The Nine Chapters on the Mathematical Art (ca. 1st century AD) is by far the most in°uential work: it would shape Chinese mathematics for centuries to come. Between the 3rd and the 11th century AD, Bud-dhist and Indian ideas got a flrm grip on China, yet curiously Chinese
A Chinese Classic: The Nine Chapters - California State …
A Chinese Classic: The Nine Chapters Math 330: History of Mathematics November 14, 2005. 1 Introduction The Jiuzhang suanshu, or Nine Chapters on the Mathematical Art was written for the training of civil servants in the Han dynasty (206 BC - AD 220). However, some of the material might have dates from as far back as 1000 BC.
The nine chapters on the mathematical art: companion and …
1 Aug 2016 · The nine chapters on the mathematical art: companion and commentary, by Shen Kangshen, John N. Crossley and Anthony W.-C. Lun. Pp. 596. £110. 1999. ISBN 0 19 853936 3 (Oxford University Press/Science Press, Beijing). - Volume 85 Issue 502
The Nine Chapters on the Mathematical Art - Wikisource
4 Mar 2021 · The Nine Chapters on the Mathematical Art (simplified Chinese: 九章算术; traditional Chinese: 九章算術; pinyin: Jiǔzhāng Suànshù) is a Chinese mathematics book, composed by several generations of scholars from the 10th century BCE to the 2nd century CE. It is among the earliest known Chinese mathematical texts.
The Nine Chapters on the Mathematical Art: Companion and …
31 Oct 2023 · The Chinese culture, between 200 BC and 100 BC, also approached matrices, as evidenced in the text "Nine Chapters on the Mathematical Art" [57].This text contains problems that lead to systems of ...
The Nine Chapters on the Mathematical Art - Wikipedia
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 1st …
Jiu Zhang Suanshu 九章算衔 (Nine Chapters on the Mathematical Art…
(Nine Chapters on the Mathematical Art): An Overview Lam Lay Yong Table of Contents 1. The beginnings of our arithmetic 2. The beginnings of arithmetic in China 3. The Jiu zhang suanshu …
The Nine Chapters on the Mathematical Art: Companion and …
7 Oct 1999 · The Nine Chapters on the Mathematical Art is a classic text: the most important mathematical source in China during the past 2000 years, and comparable in significance to …
Nine Chapters on the Mathematical Art - MacTutor History of Mathematics …
The Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a practical handbook of mathematics consisting of 246 problems intended to provide methods to be used to solve …
The Nine Chapters on the Mathematical Art - Google Books
The Nine Chapters on the Mathematical Art has been the most important mathematical source in China for the past 2000 years, comparable in significance to Euclid's Elements in the West. The …
The Nine Chapters on the History of Chinese Mathematics
The Nine Chapters on the Mathematical Art (ca. 1st century AD) is by far the most in°uential work: it would shape Chinese mathematics for centuries to come. Between the 3rd and the 11th century …
A Chinese Classic: The Nine Chapters - California State University …
A Chinese Classic: The Nine Chapters Math 330: History of Mathematics November 14, 2005. 1 Introduction The Jiuzhang suanshu, or Nine Chapters on the Mathematical Art was written for the …
The nine chapters on the mathematical art: companion and …
1 Aug 2016 · The nine chapters on the mathematical art: companion and commentary, by Shen Kangshen, John N. Crossley and Anthony W.-C. Lun. Pp. 596. £110. 1999. ISBN 0 19 853936 3 …
The Nine Chapters on the Mathematical Art - Wikisource
4 Mar 2021 · The Nine Chapters on the Mathematical Art (simplified Chinese: 九章算术; traditional Chinese: 九章算術; pinyin: Jiǔzhāng Suànshù) is a Chinese mathematics book, composed by …
The Nine Chapters on the Mathematical Art: Companion and …
31 Oct 2023 · The Chinese culture, between 200 BC and 100 BC, also approached matrices, as evidenced in the text "Nine Chapters on the Mathematical Art" [57].This text contains problems …
