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Distributivity Like Results In The Medieval Traditions Of Euclids Elements
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Book Synopsis Distributivity-like Results in the Medieval Traditions of Euclid's Elements by : Leo Corry
Download or read book Distributivity-like Results in the Medieval Traditions of Euclid's Elements written by Leo Corry and published by Springer Nature. This book was released on 2021-11-19 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a fresh view on an important and largely overlooked aspect of the Euclidean traditions in the medieval mathematical texts, particularly concerning the interrelations between geometry and arithmetic, and the rise of algebraic modes of thought. It appeals to anyone interested in the history of mathematics in general and in history of medieval and early modern science.
Book Synopsis British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) by : Leo Corry
Download or read book British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) written by Leo Corry and published by Springer Nature. This book was released on 2022-09-12 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century. Its focus is on Book II of the Elements and the ways in which algebraic symbolism and methods, especially as recently introduced by François Viète and his followers, took center stage as mediators between the two realms, and thus offered new avenues to work out that relationship in idiosyncratic ways not found in earlier editions of the Euclidean text. Texts examined include Robert Recorde's Pathway to Knowledge (1551), Henry Billingsley’s first English translation of the Elements (1570), Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot (both published in 1631), Isaac Barrow’s versions of the Elements (1660), and John Wallis Treatise of Algebra (1685), and the English translations of Claude Dechales’ French Euclidean Elements (1685). This book offers a completely new perspective of the topic and analyzes mostly unexplored material. It will be of interest to historians of mathematics, mathematicians with an interest in history and historians of renaissance science in general.
Book Synopsis Distributivity-like Results in the Medieval Traditions of Euclid's Elements by : Leo Corry
Download or read book Distributivity-like Results in the Medieval Traditions of Euclid's Elements written by Leo Corry and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a fresh view on an important and largely overlooked aspect of the Euclidean traditions in the medieval mathematical texts, particularly concerning the interrelations between geometry and arithmetic, and the rise of algebraic modes of thought. It appeals to anyone interested in the history of mathematics in general and in history of medieval and early modern science.
Book Synopsis Alfonso's Rectifying the Curved by : Ruth Glasner
Download or read book Alfonso's Rectifying the Curved written by Ruth Glasner and published by Springer Nature. This book was released on 2020-11-26 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a new English translation, introduction, and detailed commentary on Sefer Meyasher 'Aqov, (The Rectifying of the Curved), a 14th-century Hebrew treatise on the foundation of geometry. The book is a mixture of two genres: philosophical discussion and formal, Euclidean-type geometrical writing. A central issue is the use of motion and superposition in geometry, which is analyzed in depth through dialog with earlier Arab mathematicians. The author, Alfonso, was identified by Gita Gluskina (the editor of the 1983 Russian edition) as Alfonso of Valladolid, the converted Jew Abner of Burgos. Alfonso lived in Castile, rather far from the leading cultural centers of his time, but nonetheless at the crossroad of three cultures. He was raised in the Jewish tradition and like many Sephardic Jewish intellectuals was versed in Greek-Arabic philosophy and science. He also had connections with some Christian nobles and towards the end of his life converted to Christianity. Driven by his ambition to solve the problem of the quadrature of the circle, as well as other open geometrical problems, Alfonso acquired surprisingly wide knowledge and became familiar with several episodes in Greek and Arabic geometry that historians usually consider not to have been known in the West in the fourteenth century. Sefer Meyasher 'Aqov reflects his wide and deep erudition in mathematics and philosophy, and provides new evidence on cultural transmission around the Mediterranean.
Book Synopsis David Hilbert and the Axiomatization of Physics (1898–1918) by : L. Corry
Download or read book David Hilbert and the Axiomatization of Physics (1898–1918) written by L. Corry and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.
Book Synopsis A Concrete Introduction to Higher Algebra by : Lindsay N. Childs
Download or read book A Concrete Introduction to Higher Algebra written by Lindsay N. Childs and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.
Book Synopsis Elementary Number Theory in Nine Chapters by : James J. Tattersall
Download or read book Elementary Number Theory in Nine Chapters written by James J. Tattersall and published by Cambridge University Press. This book was released on 1999-10-14 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.
Book Synopsis Philosophy of Mathematics and Deductive Structure in Euclid's Elements by : Ian Mueller
Download or read book Philosophy of Mathematics and Deductive Structure in Euclid's Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Book Synopsis Geometry: Euclid and Beyond by : Robin Hartshorne
Download or read book Geometry: Euclid and Beyond written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Book Synopsis Infinity and the Mind by : Rudy Rucker
Download or read book Infinity and the Mind written by Rudy Rucker and published by Bantam Books. This book was released on 1983-01-01 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."
Book Synopsis A Concrete Introduction to Higher Algebra by : Lindsay Childs
Download or read book A Concrete Introduction to Higher Algebra written by Lindsay Childs and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.
Book Synopsis Modern Algebra and the Rise of Mathematical Structures by : Leo Corry
Download or read book Modern Algebra and the Rise of Mathematical Structures written by Leo Corry and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
Book Synopsis From Mathematics to Generic Programming by : Alexander A. Stepanov
Download or read book From Mathematics to Generic Programming written by Alexander A. Stepanov and published by Addison-Wesley Professional. This book was released on 2014-11-13 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful. If you’re a reasonably proficient programmer who can think logically, you have all the background you’ll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem. As you read this book, you’ll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You’ll also gain deep insight into the value of mathematics to programming—insight that will prove invaluable no matter what programming languages and paradigms you use. You will learn about How to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiency Ancient paradoxes, beautiful theorems, and the productive tension between continuous and discrete A simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on it Powerful mathematical approaches to abstraction How abstract algebra provides the idea at the heart of generic programming Axioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structures Surprising subtleties of simple programming tasks and what you can learn from them How practical implementations can exploit theoretical knowledge
Book Synopsis Mathematics of Choice by : Ivan Niven
Download or read book Mathematics of Choice written by Ivan Niven and published by MAA. This book was released on 1965 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reverse Mathematics by : John Stillwell
Download or read book Reverse Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2019-09-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Download or read book Logic written by Vern S. Poythress and published by Crossway. This book was released on 2013-02-28 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the well-rounded Christian looking to improve their critical thinking skills, here is an accessible introduction to the study of logic (parts 1 & 2) as well as an in-depth treatment of the discipline (parts 3 & 4) from a professor with 6 academic degrees and over 30 years experience teaching. Questions for further reflection are included at the end of each chapter as well as helpful diagrams and charts that are appropriate for use in high school, home school, college, and graduate-level classrooms. Overall, Vern Poythress has undertaken a radical recasting of the study of logic in this revolutionary work from a Christian worldview.
Book Synopsis The Art of the Infinite by : Robert Kaplan
Download or read book The Art of the Infinite written by Robert Kaplan and published by Bloomsbury Publishing USA. This book was released on 2014-02-04 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.
