Author: Fondation Singer-Polignac. Colloque international
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 812
Book Description
Boèce, Ou La Chaîne Des Savoirs
Author: Fondation Singer-Polignac. Colloque international
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 812
Book Description
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 812
Book Description
From Number Theory to Physics
Author: Michel Waldschmidt
Publisher: Springer Science & Business Media
ISBN: 3662028387
Category : Science
Languages : en
Pages : 702
Book Description
The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.
Publisher: Springer Science & Business Media
ISBN: 3662028387
Category : Science
Languages : en
Pages : 702
Book Description
The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.
Conflicts Between Generalization, Rigor, and Intuition
Author: Gert Schubring
Publisher: Springer Science & Business Media
ISBN: 0387282734
Category : Mathematics
Languages : en
Pages : 689
Book Description
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
Publisher: Springer Science & Business Media
ISBN: 0387282734
Category : Mathematics
Languages : en
Pages : 689
Book Description
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
Advances In The History Of Mathematics Education
Author: Alexander Karp
Publisher: Springer Nature
ISBN: 3030952355
Category : Education
Languages : en
Pages : 262
Book Description
This book is a collection of scholarly studies in the history of mathematics education, very abbreviated versions of which were presented at the ICMI Congress in 2021. The book discusses issues in education in Brazil and Belgium, in Poland and Spain, in Russia and the United States. Probably the main factor that unifies the chapters of the book is their attention to key moments in the formation of the field of mathematics education. Topics discussed in the book include the formation and development of mathematics education for women; the role of the research mathematician in the formation of standards for writing textbooks; the formation of curricula and the most active figures in this formation during the New Math period; the formation of certain distinctive features of curricula in Poland; the formation of the views of David Eugene Smith and the influence of European mathematics education on him; the formation of the American mathematics community; and the creation of such forms of student assessment as entrance exams to higher educational institutions. The book is of interest not only to historians of mathematics education, but also to wide segments of specialists in other areas of mathematics education.
Publisher: Springer Nature
ISBN: 3030952355
Category : Education
Languages : en
Pages : 262
Book Description
This book is a collection of scholarly studies in the history of mathematics education, very abbreviated versions of which were presented at the ICMI Congress in 2021. The book discusses issues in education in Brazil and Belgium, in Poland and Spain, in Russia and the United States. Probably the main factor that unifies the chapters of the book is their attention to key moments in the formation of the field of mathematics education. Topics discussed in the book include the formation and development of mathematics education for women; the role of the research mathematician in the formation of standards for writing textbooks; the formation of curricula and the most active figures in this formation during the New Math period; the formation of certain distinctive features of curricula in Poland; the formation of the views of David Eugene Smith and the influence of European mathematics education on him; the formation of the American mathematics community; and the creation of such forms of student assessment as entrance exams to higher educational institutions. The book is of interest not only to historians of mathematics education, but also to wide segments of specialists in other areas of mathematics education.
The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae
Author: Catherine Goldstein
Publisher: Springer Science & Business Media
ISBN: 3540347208
Category : Mathematics
Languages : en
Pages : 579
Book Description
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Publisher: Springer Science & Business Media
ISBN: 3540347208
Category : Mathematics
Languages : en
Pages : 579
Book Description
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Report of the Superintendent of Public Instruction of the Province of Quebec for the Year ...
Author: Québec (Province). Department of Public Instruction
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 270
Book Description
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 270
Book Description
Histoire Des Sciences Mathématiques Et Physiques: D'Euler à Lagrange. 1886
Author: Maximilien Marie
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 278
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 278
Book Description
The Legacy of Mario Pieri in Geometry and Arithmetic
Author: Elena Anne Marchisotto
Publisher: Springer Science & Business Media
ISBN: 0817646035
Category : Mathematics
Languages : en
Pages : 508
Book Description
This book is the first in a series of three volumes that comprehensively examine Mario Pieri’s life, mathematical work and influence. The book introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations — one in arithmetic and one in geometry. The book combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index. And yet the book requires no specialized experience in mathematical logic or the foundations of geometry.
Publisher: Springer Science & Business Media
ISBN: 0817646035
Category : Mathematics
Languages : en
Pages : 508
Book Description
This book is the first in a series of three volumes that comprehensively examine Mario Pieri’s life, mathematical work and influence. The book introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations — one in arithmetic and one in geometry. The book combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index. And yet the book requires no specialized experience in mathematical logic or the foundations of geometry.
Approaches to Algebra
Author: N. Bednarz
Publisher: Springer Science & Business Media
ISBN: 9400917325
Category : Education
Languages : en
Pages : 342
Book Description
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Publisher: Springer Science & Business Media
ISBN: 9400917325
Category : Education
Languages : en
Pages : 342
Book Description
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Philosophy, Phenomenology, Sciences
Author: Carlo Ierna
Publisher: Springer Science & Business Media
ISBN: 9400700717
Category : Philosophy
Languages : en
Pages : 731
Book Description
The present volume contains many of the papers presented at a four-day conference held by the Husserl-Archives in Leuven in April 2009 to c- memorate the one hundred and ?ftieth anniversary of Edmund Husserl’s birth. The conference was organized to facilitate the critical evaluation of Husserl’s philosophical project from various perspectives and in light of the current philosophical and scienti?c climate. Still today, the characteristic tension between Husserl’s concrete and detailed descriptions of consciousness, on the one hand, and his radical philosophical claim to ultimate truth and certainty in thinking, feeling, and acting, on the other, calls for a sustained re?ection on the relation between a Husserlian phenomenological philosophy and philosophy in general. What can phenomenological re?ection contribute to the ongoing discussion of certain perennial philosophical questions and which phi- sophical problems are raised by a phenomenological philosophy itself? In addition to addressing the question of the relation between p- nomenology and philosophy in general, phenomenology today cannot avoid addressing the nature of its relation to the methods and results of the natural and human sciences. In fact, for Husserl, phenomenology is not just one among many philosophical methods and entirely unrelated to the sciences. Rather, according to Husserl, phenomenology should be a “?rst philosophy” and should aim to become the standard for all true science.
Publisher: Springer Science & Business Media
ISBN: 9400700717
Category : Philosophy
Languages : en
Pages : 731
Book Description
The present volume contains many of the papers presented at a four-day conference held by the Husserl-Archives in Leuven in April 2009 to c- memorate the one hundred and ?ftieth anniversary of Edmund Husserl’s birth. The conference was organized to facilitate the critical evaluation of Husserl’s philosophical project from various perspectives and in light of the current philosophical and scienti?c climate. Still today, the characteristic tension between Husserl’s concrete and detailed descriptions of consciousness, on the one hand, and his radical philosophical claim to ultimate truth and certainty in thinking, feeling, and acting, on the other, calls for a sustained re?ection on the relation between a Husserlian phenomenological philosophy and philosophy in general. What can phenomenological re?ection contribute to the ongoing discussion of certain perennial philosophical questions and which phi- sophical problems are raised by a phenomenological philosophy itself? In addition to addressing the question of the relation between p- nomenology and philosophy in general, phenomenology today cannot avoid addressing the nature of its relation to the methods and results of the natural and human sciences. In fact, for Husserl, phenomenology is not just one among many philosophical methods and entirely unrelated to the sciences. Rather, according to Husserl, phenomenology should be a “?rst philosophy” and should aim to become the standard for all true science.