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Título : Babylonian Mathematical Astronomy: Procedure Texts Tipo de documento: documento electrónico Autores: Ossendrijver, Mathieu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Colección: Sources and Studies in the History of Mathematics and Physical Sciences Número de páginas: XXVI, 618 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-3782-6 Idioma : Inglés (eng) Palabras clave: Mathematics History Oriental languages Semitic Astronomy Astrophysics Cosmology Observations, Astronomical Observations of Mathematical Sciences Astronomy, and Techniques Science Languages Clasificación: 51 Matemáticas Resumen: Babylonian Mathematical Astronomy: Procedure Texts contains a new analysis of the procedure texts of Babylonian mathematical astronomy. These cuneiform tablets, excavated in Babylon and Uruk and dating from 350?50 BCE, contain computational instructions that represent the earliest known form of mathematical astronomy of the ancient world. The targeted readership includes assyriologists, historians of science, astronomers and others with an interest in Babylonian astronomy. The book includes new translations of all 108 available tablets that are based on a modern approach incorporating recent insights from assyriology and translation science. All translations are accompanied by commentaries and photographs of the tablets. The preceding chapters are devoted to documentary, lexical, semantic, mathematical and astronomical aspects of the procedure texts. Special attention is given to issues of mathematical representation, a topic that had previously been largely ignored. Mathematical concepts are presented in a didactic fashion, setting out from the most elementary ones (numbers and elementary operations) to more complex ones (algorithms and computational systems). Chapters devoted to the planets and the Moon contain updated and expanded reconstructions and astronomical interpretations of the algorithms. The author intends to continue his study of Babylonian mathematical astronomy with a new publication devoted to the Tabular Texts—the end products of Babylonian mathematical astronomy, computed with algorithms that are formulated in the present volume. The upcoming volume will contain new editions and reconstructions of over 250 tabular texts and a new philological, astronomical, and mathematical analysis of these texts Nota de contenido: Preface -- Acknowledgements -- Abbreviations and symbols -- 1. Procedure texts -- 2. Mathematical concepts – from numbers to computational systems -- 3. Planets -- 4. Moon -- 5. Critical editions -- Appendices -- Glossary -- Bibliography -- Indices En línea: http://dx.doi.org/10.1007/978-1-4614-3782-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32819 Babylonian Mathematical Astronomy: Procedure Texts [documento electrónico] / Ossendrijver, Mathieu ; SpringerLink (Online service) . - New York, NY : Springer New York, 2012 . - XXVI, 618 p : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences) .
ISBN : 978-1-4614-3782-6
Idioma : Inglés (eng)
Palabras clave: Mathematics History Oriental languages Semitic Astronomy Astrophysics Cosmology Observations, Astronomical Observations of Mathematical Sciences Astronomy, and Techniques Science Languages Clasificación: 51 Matemáticas Resumen: Babylonian Mathematical Astronomy: Procedure Texts contains a new analysis of the procedure texts of Babylonian mathematical astronomy. These cuneiform tablets, excavated in Babylon and Uruk and dating from 350?50 BCE, contain computational instructions that represent the earliest known form of mathematical astronomy of the ancient world. The targeted readership includes assyriologists, historians of science, astronomers and others with an interest in Babylonian astronomy. The book includes new translations of all 108 available tablets that are based on a modern approach incorporating recent insights from assyriology and translation science. All translations are accompanied by commentaries and photographs of the tablets. The preceding chapters are devoted to documentary, lexical, semantic, mathematical and astronomical aspects of the procedure texts. Special attention is given to issues of mathematical representation, a topic that had previously been largely ignored. Mathematical concepts are presented in a didactic fashion, setting out from the most elementary ones (numbers and elementary operations) to more complex ones (algorithms and computational systems). Chapters devoted to the planets and the Moon contain updated and expanded reconstructions and astronomical interpretations of the algorithms. The author intends to continue his study of Babylonian mathematical astronomy with a new publication devoted to the Tabular Texts—the end products of Babylonian mathematical astronomy, computed with algorithms that are formulated in the present volume. The upcoming volume will contain new editions and reconstructions of over 250 tabular texts and a new philological, astronomical, and mathematical analysis of these texts Nota de contenido: Preface -- Acknowledgements -- Abbreviations and symbols -- 1. Procedure texts -- 2. Mathematical concepts – from numbers to computational systems -- 3. Planets -- 4. Moon -- 5. Critical editions -- Appendices -- Glossary -- Bibliography -- Indices En línea: http://dx.doi.org/10.1007/978-1-4614-3782-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32819 Ejemplares
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Título : Between Theory and Observations : Tobias Mayer's Explorations of Lunar Motion, 1751-1755 Tipo de documento: documento electrónico Autores: Wepster, Steven ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Sources and Studies in the History of Mathematics and Physical Sciences Número de páginas: XIV, 246 p. 54 illus Il.: online resource ISBN/ISSN/DL: 978-1-4419-1314-2 Idioma : Inglés (eng) Palabras clave: Mathematics History Astronomy Astrophysics Cosmology Physics of Mathematical Sciences and Philosophical Foundations Astronomy, Clasificación: 51 Matemáticas Resumen: In the 18th century purely scientific interests as well as the practical necessities of navigation motivated the development of new theories and techniques to accurately describe celestial and lunar motion. Tobias Mayer, a German mathematician and astronomer, was among the most notable scientists of the time in the area of lunar theory. "Between Theory and Observations" presents a detailed and rigorous account of Tobias Mayer’s work; his famous contribution is his extensive set of lunar tables, which were the most accurate of their time. This book gives a complete and accurate account, not to be found elsewhere in the literature, of Tobias Mayer's important contributions to the study of lunar motion. The book highlights and examines three of Mayer's major achievements: - The computational scheme embodied in Mayer's lunar tables is examined and traced back to the scheme of Newton's 1702 lunar theory with its decidedly non-dynamical characteristics. - Mayer's dynamical lunar theory is compared to Euler's work in celestial mechanics of the same period. Evidence is presented refuting the commonly held opinion that Mayer's lunar theory was simply a modification of Euler's theory. - Mayer's technique of adjusting the coefficients of his lunar tables to fit an extensive collection of observational data is examined in detail. The scale of Mayer's effort was unprecedented and preceded the invention of the least squares method by half a century. This volume is intended for historians of mathematics and/or astronomy as well as anyone interested in the historical development of the theory of lunar motion Nota de contenido: The Quest for Lunar Theory -- The Pioneer#x2019;s Work -- A Manual to the Tables -- Theoria Lunae -- The Horrocks Legacy -- Multisteps in -- #x2018;Hausbackene Combinationen#x2019; -- Further Aspects of Model Fitting -- Concluding Observations En línea: http://dx.doi.org/10.1007/978-1-4419-1314-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33589 Between Theory and Observations : Tobias Mayer's Explorations of Lunar Motion, 1751-1755 [documento electrónico] / Wepster, Steven ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XIV, 246 p. 54 illus : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences) .
ISBN : 978-1-4419-1314-2
Idioma : Inglés (eng)
Palabras clave: Mathematics History Astronomy Astrophysics Cosmology Physics of Mathematical Sciences and Philosophical Foundations Astronomy, Clasificación: 51 Matemáticas Resumen: In the 18th century purely scientific interests as well as the practical necessities of navigation motivated the development of new theories and techniques to accurately describe celestial and lunar motion. Tobias Mayer, a German mathematician and astronomer, was among the most notable scientists of the time in the area of lunar theory. "Between Theory and Observations" presents a detailed and rigorous account of Tobias Mayer’s work; his famous contribution is his extensive set of lunar tables, which were the most accurate of their time. This book gives a complete and accurate account, not to be found elsewhere in the literature, of Tobias Mayer's important contributions to the study of lunar motion. The book highlights and examines three of Mayer's major achievements: - The computational scheme embodied in Mayer's lunar tables is examined and traced back to the scheme of Newton's 1702 lunar theory with its decidedly non-dynamical characteristics. - Mayer's dynamical lunar theory is compared to Euler's work in celestial mechanics of the same period. Evidence is presented refuting the commonly held opinion that Mayer's lunar theory was simply a modification of Euler's theory. - Mayer's technique of adjusting the coefficients of his lunar tables to fit an extensive collection of observational data is examined in detail. The scale of Mayer's effort was unprecedented and preceded the invention of the least squares method by half a century. This volume is intended for historians of mathematics and/or astronomy as well as anyone interested in the historical development of the theory of lunar motion Nota de contenido: The Quest for Lunar Theory -- The Pioneer#x2019;s Work -- A Manual to the Tables -- Theoria Lunae -- The Horrocks Legacy -- Multisteps in -- #x2018;Hausbackene Combinationen#x2019; -- Further Aspects of Model Fitting -- Concluding Observations En línea: http://dx.doi.org/10.1007/978-1-4419-1314-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33589 Ejemplares
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Título : Cauchy’s Cours d’analyse : An Annotated Translation Tipo de documento: documento electrónico Autores: Bradley, Robert E ; SpringerLink (Online service) ; Sandifer, C. Edward Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Sources and Studies in the History of Mathematics and Physical Sciences Número de páginas: XX, 412 p. 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-0549-9 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History of Sciences Clasificación: 51 Matemáticas Resumen: This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the most influential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements. The authors' style mimics the look and feel of the second French edition. It is an essentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially "Euclidean architecture" in its careful ordering of definitions and theorems. It was the first book in analysis to do this. Cauchy's book is essentially a precalculus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of the volume. The basic audience is anyone interested in the history of mathematics, especially 19th century analysis. In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill to read. Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University Nota de contenido: On real functions. -- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases. -- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions. -- Determination of integer functions, when a certain number of particular values are known. Applications. -- Determination of continuous functions of a single variable that satisfy certain conditions. -- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series. -- On imaginary expressions and their moduli. -- On imaginary functions and variables. -- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series. -- On real or imaginary roots of algebraic equations for which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry. -- Decomposition of rational fractions. -- On recurrent series En línea: http://dx.doi.org/10.1007/978-1-4419-0549-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33970 Cauchy’s Cours d’analyse : An Annotated Translation [documento electrónico] / Bradley, Robert E ; SpringerLink (Online service) ; Sandifer, C. Edward . - New York, NY : Springer New York, 2009 . - XX, 412 p. 1 illus. in color : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences) .
ISBN : 978-1-4419-0549-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History of Sciences Clasificación: 51 Matemáticas Resumen: This is an annotated and indexed translation (from French into English) of Augustin Louis Cauchy's 1821 classic textbook Cours d'analyse. This is the first English translation of a landmark work in mathematics, one of the most influential texts in the history of mathematics. It belongs in every mathematics library, along with Newton's Principia and Euclid's Elements. The authors' style mimics the look and feel of the second French edition. It is an essentially modern textbook style, about 75% narrative and 25% theorems, proofs, corollaries. Despite the extensive narrative, it has an essentially "Euclidean architecture" in its careful ordering of definitions and theorems. It was the first book in analysis to do this. Cauchy's book is essentially a precalculus book, with a rigorous exposition of the topics necessary to learn calculus. Hence, any good quality calculus student can understand the content of the volume. The basic audience is anyone interested in the history of mathematics, especially 19th century analysis. In addition to being an important book, the Cours d'analyse is well-written, packed with unexpected gems, and, in general, a thrill to read. Robert E. Bradley is Professor of Mathematics at Adelphi University. C. Edward Sandifer is Professor of Mathematics at Western Connecticut State University Nota de contenido: On real functions. -- On infinitely small and infinitely large quantities, and on the continuity of functions. Singular values of functions in various particular cases. -- On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions. -- Determination of integer functions, when a certain number of particular values are known. Applications. -- Determination of continuous functions of a single variable that satisfy certain conditions. -- On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series. -- On imaginary expressions and their moduli. -- On imaginary functions and variables. -- On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series. -- On real or imaginary roots of algebraic equations for which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry. -- Decomposition of rational fractions. -- On recurrent series En línea: http://dx.doi.org/10.1007/978-1-4419-0549-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33970 Ejemplares
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Título : Conflicts between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17–19th Century France and Germany Tipo de documento: documento electrónico Autores: Schubring, Gert ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Colección: Sources and Studies in the History of Mathematics and Physical Sciences Número de páginas: XIV, 678 p. 22 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-28273-2 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History of Sciences Clasificación: 51 Matemáticas Resumen: Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there. This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries, with a detailed analysis of Lazare Carnot's and A. L. Cauchy's foundational ideas. By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. This approach permits a nuanced analysis of the meaning of mathematical ideas as conceived of by 18th and 19th century scientists, while illustrating the authors' actions within the context of their respective cultural and scientific communities. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics Nota de contenido: Question and Method -- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field -- Paths toward Algebraization — The Field of Limits: The Development of Infinitely Small Quantities -- Culmination of Algebraization and Retour du Refoulé -- Le Retour du Refoulé: From the Perspective of Mathematical Concepts -- Cauchy’s Compromise Concept -- Development of Pure Mathematics in Prussia/Germany -- Conflicts Between Confinement to Geometry and Algebraization in France -- Summary and Outlook En línea: http://dx.doi.org/10.1007/0-387-28273-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35140 Conflicts between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17–19th Century France and Germany [documento electrónico] / Schubring, Gert ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - XIV, 678 p. 22 illus : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences) .
ISBN : 978-0-387-28273-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History of Sciences Clasificación: 51 Matemáticas Resumen: Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there. This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries, with a detailed analysis of Lazare Carnot's and A. L. Cauchy's foundational ideas. By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. This approach permits a nuanced analysis of the meaning of mathematical ideas as conceived of by 18th and 19th century scientists, while illustrating the authors' actions within the context of their respective cultural and scientific communities. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics Nota de contenido: Question and Method -- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field -- Paths toward Algebraization — The Field of Limits: The Development of Infinitely Small Quantities -- Culmination of Algebraization and Retour du Refoulé -- Le Retour du Refoulé: From the Perspective of Mathematical Concepts -- Cauchy’s Compromise Concept -- Development of Pure Mathematics in Prussia/Germany -- Conflicts Between Confinement to Geometry and Algebraization in France -- Summary and Outlook En línea: http://dx.doi.org/10.1007/0-387-28273-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35140 Ejemplares
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Título : Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics : Translation and Commentary Tipo de documento: documento electrónico Autores: Fried, Michael N ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Sources and Studies in the History of Mathematics and Physical Sciences Número de páginas: X, 134 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-0146-9 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry History of Mathematical Sciences Clasificación: 51 Matemáticas Resumen: Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, four of which have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. Motivated by such questions as what role did Halley's reconstruction play in the mathematical world of the late 17th and early 18th century? and what did Halley see himself learning from engaging with mathematicians such as Apollonius?, Michael Fried’s work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. The volume also contains an introduction discussing aspects of Apollonius’s Conics, an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and appendices giving brief accounts of Apollonius’s approach to conic sections and his mathematical techniques. This book will be of great interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period. Nota de contenido: I. Introduction -- 1. Edmond Halley: Ancient and Modern -- 2. Apollonius’s Conics -- 3. The Path to Halley -- 4. Halley's General Strategy for Reconstructing Conics, Book VIII -- 5. Halley’s Dialogue with the Past.-6. A Note on the Translation-II. Apollonius of Perga’s On Conics: Book Eight Restored -- III.Synopsis and Appendices.-Synopsis of the Contents of Halley's Conics, Book VIII.-Appendix 1: Terminology and Notions from Greek Mathematics.-Appendix 2: Hippocrates' First Quadrature of a Lune.-References.-Index En línea: http://dx.doi.org/10.1007/978-1-4614-0146-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32734 Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics : Translation and Commentary [documento electrónico] / Fried, Michael N ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2012 . - X, 134 p : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences) .
ISBN : 978-1-4614-0146-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry History of Mathematical Sciences Clasificación: 51 Matemáticas Resumen: Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, four of which have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. Motivated by such questions as what role did Halley's reconstruction play in the mathematical world of the late 17th and early 18th century? and what did Halley see himself learning from engaging with mathematicians such as Apollonius?, Michael Fried’s work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. The volume also contains an introduction discussing aspects of Apollonius’s Conics, an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and appendices giving brief accounts of Apollonius’s approach to conic sections and his mathematical techniques. This book will be of great interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period. Nota de contenido: I. Introduction -- 1. Edmond Halley: Ancient and Modern -- 2. Apollonius’s Conics -- 3. The Path to Halley -- 4. Halley's General Strategy for Reconstructing Conics, Book VIII -- 5. Halley’s Dialogue with the Past.-6. A Note on the Translation-II. Apollonius of Perga’s On Conics: Book Eight Restored -- III.Synopsis and Appendices.-Synopsis of the Contents of Halley's Conics, Book VIII.-Appendix 1: Terminology and Notions from Greek Mathematics.-Appendix 2: Hippocrates' First Quadrature of a Lune.-References.-Index En línea: http://dx.doi.org/10.1007/978-1-4614-0146-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32734 Ejemplares
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