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Author: Roger Hart
Publisher: JHU Press
ISBN: 0801899583
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: Roger Hart
Publisher: JHU Press
ISBN: 0801899583
Category : Mathematics
Languages : en
Pages : 304
Get Book Here
Book Description
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.
Author: Roger Hart
Publisher: JHU Press
ISBN: 1421407124
Category : Mathematics
Languages : en
Pages : 385
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Book Description
Roger Hart debunks the long-held belief that linear algebra developed independently in the West. Accounts of the seventeenth-century Jesuit Mission to China have often celebrated it as the great encounter of two civilizations. The Jesuits portrayed themselves as wise men from the West who used mathematics and science in service of their mission. Chinese literati-official Xu Guangqi (1562–1633), who collaborated with the Italian Jesuit Matteo Ricci (1552–1610) to translate Euclid’s Elements into Chinese, reportedly recognized the superiority of Western mathematics and science and converted to Christianity. Most narratives relegate Xu and the Chinese to subsidiary roles as the Jesuits' translators, followers, and converts. Imagined Civilizations tells the story from the Chinese point of view. Using Chinese primary sources, Roger Hart focuses in particular on Xu, who was in a position of considerable power over Ricci. The result is a perspective startlingly different from that found in previous studies. Hart analyzes Chinese mathematical treatises of the period, revealing that Xu and his collaborators could not have believed their declaration of the superiority of Western mathematics. Imagined Civilizations explains how Xu’s West served as a crucial resource. While the Jesuits claimed Xu as a convert, he presented the Jesuits as men from afar who had traveled from the West to China to serve the emperor.
Author: Jean-Claude Martzloff
Publisher: Springer
ISBN: 3540337830
Category : Mathematics
Languages : en
Pages : 491
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Book Description
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.
Author: Amy Shell-Gellasch
Publisher: JHU Press
ISBN: 1421417294
Category : Mathematics
Languages : en
Pages : 553
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Book Description
An engaging new approach to teaching algebra that takes students on a historical journey from its roots to modern times. This book’s unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life. Even those who have avoided mathematics for years will find the historical stories both inviting and gripping. The book’s lessons begin with the creation and spread of number systems, from the mathematical development of early civilizations in Babylonia, Greece, China, Rome, Egypt, and Central America to the advancement of mathematics over time and the roles of famous figures such as Descartes and Leonardo of Pisa (Fibonacci). Before long, it becomes clear that the simple origins of algebra evolved into modern problem solving. Along the way, the language of mathematics becomes familiar, and students are gradually introduced to more challenging problems. Paced perfectly, Amy Shell-Gellasch and J. B. Thoo’s chapters ease students from topic to topic until they reach the twenty-first century. By the end of Algebra in Context, students using this textbook will be comfortable with most algebra concepts, including • Different number bases • Algebraic notation • Methods of arithmetic calculation • Real numbers • Complex numbers • Divisors • Prime factorization • Variation • Factoring • Solving linear equations • False position • Solving quadratic equations • Solving cubic equations • nth roots • Set theory • One-to-one correspondence • Infinite sets • Figurate numbers • Logarithms • Exponential growth • Interest calculations
Author: Jonathan S. Golan
Publisher: Springer Science & Business Media
ISBN: 1402054955
Category : Mathematics
Languages : en
Pages : 443
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Book Description
This book rigorously deals with the abstract theory and, at the same time, devotes considerable space to the numerical and computational aspects of linear algebra. It features a large number of thumbnail portraits of researchers who have contributed to the development of linear algebra as we know it today and also includes over 1,000 exercises, many of which are very challenging. The book can be used as a self-study guide; a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or as a reference book.
Author: Sheldon Axler
Publisher: Springer Science & Business Media
ISBN: 9780387982595
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Author: Gilbert Strang
Publisher: Wellesley-Cambridge Press
ISBN: 9780980232790
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Author: Maurice Mignotte
Publisher: Springer Science & Business Media
ISBN: 1461391717
Category : Computers
Languages : en
Pages : 357
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Book Description
This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters.
Author: Roger Preston Hart
Publisher: JHU Press
ISBN: 1421406063
Category : History
Languages : en
Pages : 385
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Book Description
While the Jesuits claimed Xu as a convert, he presented the Jesuits as men from afar who had traveled from the West to China to serve the emperor.
Author: Yisong Yang
Publisher: Cambridge University Press
ISBN: 1107087511
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond.
