The Development of Arabic Mathematics: Between Arithmetic and Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 9401732744
Total Pages : 392 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis The Development of Arabic Mathematics: Between Arithmetic and Algebra by : R. Rashed

Download or read book The Development of Arabic Mathematics: Between Arithmetic and Algebra written by R. Rashed and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history. Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science.

Modern Mathematics

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Publisher : Springer Nature
ISBN 13 : 3031111664
Total Pages : 615 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Modern Mathematics by : Dirk De Bock

Download or read book Modern Mathematics written by Dirk De Bock and published by Springer Nature. This book was released on 2023-03-08 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels—kindergarten to college graduate—in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17, some of the effects became entrenched. This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) “Nicolas Bourbaki.” In the United States, there emerged, during the 1950s various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching “Sputnik,” the first satellite. Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final “epilogue” chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends.

Elements of Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 1475739761
Total Pages : 194 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Algebra by : John Stillwell

Download or read book Elements of Algebra written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

Emil Artin and Helmut Hasse

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Publisher : Springer Science & Business Media
ISBN 13 : 3034807155
Total Pages : 499 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Emil Artin and Helmut Hasse by : Günther Frei

Download or read book Emil Artin and Helmut Hasse written by Günther Frei and published by Springer Science & Business Media. This book was released on 2014-01-16 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.

Lectures in General Algebra

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Publisher : Elsevier
ISBN 13 : 1483149579
Total Pages : 375 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Lectures in General Algebra by : A. G. Kurosh

Download or read book Lectures in General Algebra written by A. G. Kurosh and published by Elsevier. This book was released on 2014-07-10 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

Arithmétique et algèbre modernes

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Publisher :
ISBN 13 :
Total Pages : 378 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Arithmétique et algèbre modernes by : Albert Châtelet

Download or read book Arithmétique et algèbre modernes written by Albert Châtelet and published by . This book was released on 1966 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Valuation Theory and Its Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821871393
Total Pages : 470 pages
Book Rating : 4.8/5 (713 download)

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Book Synopsis Valuation Theory and Its Applications by : Franz-Viktor Kuhlmann

Download or read book Valuation Theory and Its Applications written by Franz-Viktor Kuhlmann and published by American Mathematical Soc.. This book was released on 2002-01-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.

Algebraic Varieties

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Publisher : Springer Science & Business Media
ISBN 13 : 3642527612
Total Pages : 205 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Algebraic Varieties by : M. Baldassarri

Download or read book Algebraic Varieties written by M. Baldassarri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has always been an ec1ectic science, with its roots in algebra, function-theory and topology. Apart from early resear ches, now about a century old, this beautiful branch of mathematics has for many years been investigated chiefly by the Italian school which, by its pioneer work, based on algebro-geometric methods, has succeeded in building up an imposing body of knowledge. Quite apart from its intrinsic interest, this possesses high heuristic value since it represents an essential step towards the modern achievements. A certain lack of rigour in the c1assical methods, especially with regard to the foundations, is largely justified by the creative impulse revealed in the first stages of our subject; the same phenomenon can be observed, to a greater or less extent, in the historical development of any other science, mathematical or non-mathematical. In any case, within the c1assical domain itself, the foundations were later explored and consolidated, principally by SEVERI, on lines which have frequently inspired further investigations in the abstract field. About twenty-five years ago B. L. VAN DER WAERDEN and, later, O. ZARISKI and A. WEIL, together with their schools, established the methods of modern abstract algebraic geometry which, rejecting the c1assical restriction to the complex groundfield, gave up geometrical intuition and undertook arithmetisation under the growing influence of abstract algebra.

Algebra I

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540642435
Total Pages : 750 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Algebra I by : N. Bourbaki

Download or read book Algebra I written by N. Bourbaki and published by Springer Science & Business Media. This book was released on 1998-08-03 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, and the third investigatesalgebras, particularly tensor algebras.

Diophantine Equations Over Function Fields

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Publisher : Cambridge University Press
ISBN 13 : 9780521269834
Total Pages : 142 pages
Book Rating : 4.2/5 (698 download)

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Book Synopsis Diophantine Equations Over Function Fields by : R. C. Mason

Download or read book Diophantine Equations Over Function Fields written by R. C. Mason and published by Cambridge University Press. This book was released on 1984-04-26 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of a new approach to the subject.

Researching the History of Mathematics Education

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Publisher : Springer
ISBN 13 : 3319682946
Total Pages : 323 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Researching the History of Mathematics Education by : Fulvia Furinghetti

Download or read book Researching the History of Mathematics Education written by Fulvia Furinghetti and published by Springer. This book was released on 2017-12-04 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers insights into the history of mathematics education, covering both the current state of the art of research and the methodology of the field. History of mathematics education is treated in the book as a part of social history. This book grew out of the presentations delivered at the International Congress on Mathematics Education in Hamburg. Modern development and growing internationalization of mathematics education made it clear that many urgent questions benefit from a historical approach. The chapters present viewpoints from the following countries: Belgium, Brazil, Cambodia, China, Cyprus, Germany, Iceland, Italy, the Netherlands, Russia,Spain and Sweden. Each chapter represents significant directions of historical studies. The book is a valuable source for every historian of mathematics education and those interested in mathematics education and its development.

Field Arithmetic

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Publisher : Springer Nature
ISBN 13 : 3031280202
Total Pages : 839 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Field Arithmetic by : Michael D. Fried

Download or read book Field Arithmetic written by Michael D. Fried and published by Springer Nature. This book was released on 2023-07-14 with total page 839 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers.

Algebraic Geometry between Tradition and Future

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Publisher : Springer Nature
ISBN 13 : 9811982813
Total Pages : 371 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Algebraic Geometry between Tradition and Future by : Gilberto Bini

Download or read book Algebraic Geometry between Tradition and Future written by Gilberto Bini and published by Springer Nature. This book was released on 2023-05-05 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent influence on the evolution of complex algebraic geometry - both at the national and international levels - and still inspires modern research in the area. "Algebraic geometry in Italy between tradition and future" is a collection of contributions aiming at presenting some of these powerful ideas and their connection to contemporary and, if possible, future developments, such as Cremonian transformations, birational classification of high-dimensional varieties starting from Gino Fano, the life and works of Guido Castelnuovo, Francesco Severi's mathematical library, etc. The presentation is enriched by the viewpoint of various researchers of the history of mathematics, who describe the cultural milieu and tell about the bios of some of the most famous mathematicians of those times.

Nature

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Publisher :
ISBN 13 :
Total Pages : 692 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis Nature by : Sir Norman Lockyer

Download or read book Nature written by Sir Norman Lockyer and published by . This book was released on 1907 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics Teaching

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Publisher :
ISBN 13 :
Total Pages : 678 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematics Teaching by :

Download or read book Mathematics Teaching written by and published by . This book was released on 1964 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Subject- Catalogue of the Library of the College of New Jersey, at Princeton

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Publisher :
ISBN 13 :
Total Pages : 914 pages
Book Rating : 4.:/5 (45 download)

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Book Synopsis Subject- Catalogue of the Library of the College of New Jersey, at Princeton by :

Download or read book Subject- Catalogue of the Library of the College of New Jersey, at Princeton written by and published by . This book was released on 1884 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Revue Semestrielle Des Publications Mathématiques

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Publisher :
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis Revue Semestrielle Des Publications Mathématiques by :

Download or read book Revue Semestrielle Des Publications Mathématiques written by and published by . This book was released on 1910 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: