Craig Fraser - Academia.edu (original) (raw)

Papers by Craig Fraser

Research paper thumbnail of Turbulent Times in Mathematics: The Life of J. C. Fields and the History of the Fields Medal

Research paper thumbnail of First Edition (1797)

In this volume, based upon his first teaching at the Ecole Polytechnique, Lagrange both popularis... more In this volume, based upon his first teaching at the Ecole Polytechnique, Lagrange both popularised and extended his view that the differential and integral calculus could be based solely on assuming the Taylor expansion of a function in an infinite power series and on al-gebraic manipulations thereafter. He also made some applications to problems in geometry and mechanics.

Research paper thumbnail of The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system

Research paper thumbnail of Mechanics in the Eighteenth Century

Oxford Handbooks Online, 2017

This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac New... more This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac Newton’s Mathematical Principles of Natural Philosophy has long been regarded as the event that ushered in the modern period in mathematical physics. The success and scope of the Principia heralded the arrival of mechanics as the model for the mathematical investigation of nature. This subject would be at the cutting edge of science for the next two centuries. This article first provides an overview of the fundamental principles and theorems of mechanics, including the principles of inertia and relativity, before discussing the dynamics of rigid bodies. It also considers the formulation of mechanics by Jean-Baptiste le Rond d’Alembert and Joseph-Louis Lagrange, the statics and dynamics of elastic bodies, and the mechanics of fluids. Finally, it describes major developments in celestial mechanics.

Research paper thumbnail of Sophie Germain: An Essay in the History of Elasticity

Research paper thumbnail of Euler at Three Hundred: An Appreciation. (Spectrum Series.)

Research paper thumbnail of Research in History and Philosophy of Mathematics

Research paper thumbnail of Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Glen Van Brummelen. Princeton University Press (2013), 208 pp

Research paper thumbnail of Mathematics in Library Subject Classification Systems

Insofar as library science is concerned, modern classification of mathematical subjects occurred ... more Insofar as library science is concerned, modern classification of mathematical subjects occurred within the larger framework of library classification, a vast project receiving sustained attention in the period from 1870 to 1920. The work of the library cataloguers was carried out against the background of a broad nineteenth-century interest in the classification of knowledge. We explore different views during this period concerning the position of mathematics in the overall scheme of knowledge, the scope of mathematics, and the internal organization of the different parts of mathematics. We examine how mathematical books were classified, from the most general level down to the level of particular subject areas in analysis. The focus is on the Library of Congress classification system in its various iterations from 1905 to the present.

Research paper thumbnail of Nonstandard Analysis, Infinitesimals, and the History of Calculus

Trends in the History of Science, 2015

Carl Boyer’s The Concepts of the Calculus; a Critical and Historical Discussion of the Derivative... more Carl Boyer’s The Concepts of the Calculus; a Critical and Historical Discussion of the Derivative and the Integral was published in 1939 and reprinted in several later editions.

Research paper thumbnail of The Princeton Companion to Mathematics, edited by Timothy Gowers (June Barrow-Green and Imre Leader, associate editors), Princeton University Press, 2008, 1008 pp

The Bulletin of Symbolic Logic, 2009

The Princeton Companion to Mathematics combines cultural, philosophical and historical perspectiv... more The Princeton Companion to Mathematics combines cultural, philosophical and historical perspectives on mathematics with substantial accounts of current mathematical subject areas. These accounts are written in enough detail to enable a reader with some universitylevel mathematics to obtain a sense of the character and leading problems of each subject area. The volume is divided into seven parts: nature of mathematics (Part I), historical origins (Part II), mathematical concepts, branches and results (Parts III, IV, V), biographies

Research paper thumbnail of Review††Edited by Adrian Rice and Scott WalterAll books, monographs, journal articles, and other publications (including films and other multisensory materials) relating to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of sel...

Historia Mathematica, 2006

Research paper thumbnail of The Background to and Early Emergence of Euler’S Analysis

Boston Studies in the Philosophy of Science, 1997

Research paper thumbnail of Die Genese der Variationsrechnung

Geschichte der Analysis, 1999

Research paper thumbnail of Introductory note to 1930c and 1931a

Ernst Zermelo - Collected Works/Gesammelte Werke II, 2013

The navigation problem treated in Zermelo 1930c and 1931a concerns a blimp or plane that moves wi... more The navigation problem treated in Zermelo 1930c and 1931a concerns a blimp or plane that moves with a given velocity relative to the air, travelling between two points on the earth. Because of the action of wind, the motion of the airship over land is modified. Suppose that the strength and direction of the wind are given as a function of position and time. The problem is to find the trajectory followed by the airship and the corresponding steering angle such that the airship completes its journey in the least time. Zermelo gives a mathematical formulation which leads to a “navigation formula” that essentially determines the “extremal motion”. He provides sufficient conditions for the existence of an extremum. The abstract 1930c considers the two-dimensional case, the paper 1931a is an extended and corrected version which also concerns the three-dimensional case.

Research paper thumbnail of D. König 1927b

Ernst Zermelo - Collected Works/Gesammelte Werke, 2010

Research paper thumbnail of Ernst Zermelo - Collected Works/Gesammelte Werke II

Research paper thumbnail of Calculus and analytical mechanics in the Age of Enlightenment

Page 1. Calculus and Analytical Mechanics in the Age of Enlightenment Craig G. Fraser, University... more Page 1. Calculus and Analytical Mechanics in the Age of Enlightenment Craig G. Fraser, University of Toronto, Canada Variorum Collected Studies Series: CS582 August 1997 224 x 150 mm 320 pages Hardback 978-0-86078-649-8 $150.00 ...

Research paper thumbnail of The History of Differential Equations, 1670--1950

Oberwolfach Reports, 2004

Differential equations have been a major branch of pure and applied mathematics since their inaug... more Differential equations have been a major branch of pure and applied mathematics since their inauguration in the mid 17th century. While their history has been well studied, it remains a vital field of on-going investigation, with the emergence of new connections with other parts of ...

Research paper thumbnail of Julian B. Barbour. Absolute or Relative Motion: A Study from a Machian Point of View of the Discovery and Structure of Dynamical Theories. Volume 1: The Discovery of Dynamics. Cambridge, Cambridge University Press, 1989. Pp. xv + 746. ISBN 0-521-32467X. £60.00, $95.00

The British Journal for the History of Science, 1990

Page 1. Book Reviews 349 look outside the circle of the sciences and see parallels and difference... more Page 1. Book Reviews 349 look outside the circle of the sciences and see parallels and differences. The book is not ordered enough to constitute 'the History of an Idea'; such a book might be well worth under-taking by a single ...

Research paper thumbnail of Turbulent Times in Mathematics: The Life of J. C. Fields and the History of the Fields Medal

Research paper thumbnail of First Edition (1797)

In this volume, based upon his first teaching at the Ecole Polytechnique, Lagrange both popularis... more In this volume, based upon his first teaching at the Ecole Polytechnique, Lagrange both popularised and extended his view that the differential and integral calculus could be based solely on assuming the Taylor expansion of a function in an infinite power series and on al-gebraic manipulations thereafter. He also made some applications to problems in geometry and mechanics.

Research paper thumbnail of The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system

Research paper thumbnail of Mechanics in the Eighteenth Century

Oxford Handbooks Online, 2017

This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac New... more This article focuses on mechanics in the eighteenth century. The publication in 1687 of Isaac Newton’s Mathematical Principles of Natural Philosophy has long been regarded as the event that ushered in the modern period in mathematical physics. The success and scope of the Principia heralded the arrival of mechanics as the model for the mathematical investigation of nature. This subject would be at the cutting edge of science for the next two centuries. This article first provides an overview of the fundamental principles and theorems of mechanics, including the principles of inertia and relativity, before discussing the dynamics of rigid bodies. It also considers the formulation of mechanics by Jean-Baptiste le Rond d’Alembert and Joseph-Louis Lagrange, the statics and dynamics of elastic bodies, and the mechanics of fluids. Finally, it describes major developments in celestial mechanics.

Research paper thumbnail of Sophie Germain: An Essay in the History of Elasticity

Research paper thumbnail of Euler at Three Hundred: An Appreciation. (Spectrum Series.)

Research paper thumbnail of Research in History and Philosophy of Mathematics

Research paper thumbnail of Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Glen Van Brummelen. Princeton University Press (2013), 208 pp

Research paper thumbnail of Mathematics in Library Subject Classification Systems

Insofar as library science is concerned, modern classification of mathematical subjects occurred ... more Insofar as library science is concerned, modern classification of mathematical subjects occurred within the larger framework of library classification, a vast project receiving sustained attention in the period from 1870 to 1920. The work of the library cataloguers was carried out against the background of a broad nineteenth-century interest in the classification of knowledge. We explore different views during this period concerning the position of mathematics in the overall scheme of knowledge, the scope of mathematics, and the internal organization of the different parts of mathematics. We examine how mathematical books were classified, from the most general level down to the level of particular subject areas in analysis. The focus is on the Library of Congress classification system in its various iterations from 1905 to the present.

Research paper thumbnail of Nonstandard Analysis, Infinitesimals, and the History of Calculus

Trends in the History of Science, 2015

Carl Boyer’s The Concepts of the Calculus; a Critical and Historical Discussion of the Derivative... more Carl Boyer’s The Concepts of the Calculus; a Critical and Historical Discussion of the Derivative and the Integral was published in 1939 and reprinted in several later editions.

Research paper thumbnail of The Princeton Companion to Mathematics, edited by Timothy Gowers (June Barrow-Green and Imre Leader, associate editors), Princeton University Press, 2008, 1008 pp

The Bulletin of Symbolic Logic, 2009

The Princeton Companion to Mathematics combines cultural, philosophical and historical perspectiv... more The Princeton Companion to Mathematics combines cultural, philosophical and historical perspectives on mathematics with substantial accounts of current mathematical subject areas. These accounts are written in enough detail to enable a reader with some universitylevel mathematics to obtain a sense of the character and leading problems of each subject area. The volume is divided into seven parts: nature of mathematics (Part I), historical origins (Part II), mathematical concepts, branches and results (Parts III, IV, V), biographies

Research paper thumbnail of Review††Edited by Adrian Rice and Scott WalterAll books, monographs, journal articles, and other publications (including films and other multisensory materials) relating to the history of mathematics are abstracted in the Abstracts Department. The Reviews Department prints extended reviews of sel...

Historia Mathematica, 2006

Research paper thumbnail of The Background to and Early Emergence of Euler’S Analysis

Boston Studies in the Philosophy of Science, 1997

Research paper thumbnail of Die Genese der Variationsrechnung

Geschichte der Analysis, 1999

Research paper thumbnail of Introductory note to 1930c and 1931a

Ernst Zermelo - Collected Works/Gesammelte Werke II, 2013

The navigation problem treated in Zermelo 1930c and 1931a concerns a blimp or plane that moves wi... more The navigation problem treated in Zermelo 1930c and 1931a concerns a blimp or plane that moves with a given velocity relative to the air, travelling between two points on the earth. Because of the action of wind, the motion of the airship over land is modified. Suppose that the strength and direction of the wind are given as a function of position and time. The problem is to find the trajectory followed by the airship and the corresponding steering angle such that the airship completes its journey in the least time. Zermelo gives a mathematical formulation which leads to a “navigation formula” that essentially determines the “extremal motion”. He provides sufficient conditions for the existence of an extremum. The abstract 1930c considers the two-dimensional case, the paper 1931a is an extended and corrected version which also concerns the three-dimensional case.

Research paper thumbnail of D. König 1927b

Ernst Zermelo - Collected Works/Gesammelte Werke, 2010

Research paper thumbnail of Ernst Zermelo - Collected Works/Gesammelte Werke II

Research paper thumbnail of Calculus and analytical mechanics in the Age of Enlightenment

Page 1. Calculus and Analytical Mechanics in the Age of Enlightenment Craig G. Fraser, University... more Page 1. Calculus and Analytical Mechanics in the Age of Enlightenment Craig G. Fraser, University of Toronto, Canada Variorum Collected Studies Series: CS582 August 1997 224 x 150 mm 320 pages Hardback 978-0-86078-649-8 $150.00 ...

Research paper thumbnail of The History of Differential Equations, 1670--1950

Oberwolfach Reports, 2004

Differential equations have been a major branch of pure and applied mathematics since their inaug... more Differential equations have been a major branch of pure and applied mathematics since their inauguration in the mid 17th century. While their history has been well studied, it remains a vital field of on-going investigation, with the emergence of new connections with other parts of ...

Research paper thumbnail of Julian B. Barbour. Absolute or Relative Motion: A Study from a Machian Point of View of the Discovery and Structure of Dynamical Theories. Volume 1: The Discovery of Dynamics. Cambridge, Cambridge University Press, 1989. Pp. xv + 746. ISBN 0-521-32467X. £60.00, $95.00

The British Journal for the History of Science, 1990

Page 1. Book Reviews 349 look outside the circle of the sciences and see parallels and difference... more Page 1. Book Reviews 349 look outside the circle of the sciences and see parallels and differences. The book is not ordered enough to constitute 'the History of an Idea'; such a book might be well worth under-taking by a single ...