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From its pre-historic roots in simple counting to the algorithms powering modern desktop computers, from the genius of Archimedes to the genius of Einstein, advances in mathematical understanding and numerical techniques have been directly responsible for creating the modern world as we know it. This series will provide a library of the most influential publications and writers on mathematics in its broadest sense. As such, it will show not only the deep roots from which modern science and technology have grown, but also the astonishing breadth of application of mathematical techniques in the humanities and social sciences and in everyday life.

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182 results in Cambridge Library Collection - Mathematics

Page 8 of 10

The Collected Mathematical Papers
  • Volume 11
  • Arthur Cayley
  • Published online:
    03 May 2011
    Print publication:
    20 July 2009
    First published in:
    1896
  • Arthur Cayley (1821–1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge and published three papers while still an undergraduate. He then qualified as a lawyer and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he took a significant salary cut to become the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death under the editorship of his successor in the Sadleirian Chair. This volume contains 93 papers mostly published between 1878 and 1883.

Essai sur la Théorie des Nombres
  • 2nd edition
  • Adrien Marie Legendre
  • Published online:
    03 May 2011
    Print publication:
    20 July 2009
    First published in:
    1798
  • Adrien-Marie Legendre (1752–1833), one of the great French mathematicians active in the Revolutionary period, made important contributions to number theory, statistics, mathematical analysis and algebra. He taught at the École Militaire, where he was a colleague of Laplace, and made his name with a paper on the trajectory of projectiles which won a prize of the Berlin Academy in 1782, and brought him to the attention of Lagrange. In 1794 he published Eléments de géométrie, which remained a textbook for over 100 years. The first edition of his Essai sur la théorie des nombres was published in 1798, and the much improved second edition, which is offered here, in 1808. In it Legendre had taken account of criticism by Gauss of the mathematical proofs in the first edition, though he was bitter at the manner in which his younger rival had claimed credit for some of his solutions.

The Collected Mathematical Papers
  • Volume 10
  • Arthur Cayley
  • Published online:
    03 May 2011
    Print publication:
    20 July 2009
    First published in:
    1896
  • Arthur Cayley (1821–1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge and published three papers while still an undergraduate. He then qualified as a lawyer and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he took a significant salary cut to become the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death under the editorship of his successor in the Sadleirian Chair. This volume contains 76 papers mostly published between 1876 and 1880.

The Collected Mathematical Papers
  • Volume 8
  • Arthur Cayley
  • Published online:
    03 May 2011
    Print publication:
    20 July 2009
    First published in:
    1895
  • Arthur Cayley (1821–1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge, qualified as a lawyer, and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he became the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death (while this volume was in the press) under the editorship of his successor in the Sadleirian Chair. This volume contains 70 papers published mostly between 1871 and 1873, as well as a 36-page obituary of the author.

The Collected Mathematical Papers
  • Volume 2
  • Arthur Cayley
  • Published online:
    03 May 2011
    Print publication:
    20 July 2009
    First published in:
    1889
  • Arthur Cayley (1821–1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge and published three papers while still an undergraduate. He then qualified as a lawyer and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he became the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death. This second volume contains 56 papers published between 1851 and 1860, plus two 1889 papers, and includes six of the Memoirs on Quantics.

Oeuvres complètes
  • Series 2
  • Volume 10
  • Augustin-Louis Cauchy
  • Published online:
    01 March 2011
    Print publication:
    20 July 2009
    First published in:
    1895
  • Augustin-Louis, Baron Cauchy (1789–1857) was the pre-eminent French mathematician of the nineteenth century. He began his career as a military engineer during the Napoleonic Wars, but even then was publishing significant mathematical papers, and was persuaded by Lagrange and Laplace to devote himself entirely to mathematics. His greatest contributions are considered to be the Cours d'analyse de l'École Royale Polytechnique (1821), Résumé des leçons sur le calcul infinitésimal (1823) and Leçons sur les applications du calcul infinitésimal à la géométrie (1826–8), and his pioneering work encompassed a huge range of topics, most significantly real analysis, the theory of functions of a complex variable, and theoretical mechanics. Twenty-six volumes of his collected papers were published between 1882 and 1958. The first series (volumes 1-12) consists of papers published by the Académie des Sciences de l'Institut de France; the second series (volumes 13-26) of papers published elsewhere.

Oeuvres complètes
  • Series 1
  • Volume 9
  • Augustin-Louis Cauchy
  • Published online:
    01 March 2011
    Print publication:
    20 July 2009
    First published in:
    1896
  • Augustin-Louis, Baron Cauchy (1789–1857) was the pre-eminent French mathematician of the nineteenth century. He began his career as a military engineer during the Napoleonic Wars, but even then was publishing significant mathematical papers, and was persuaded by Lagrange and Laplace to devote himself entirely to mathematics. His greatest contributions are considered to be the Cours d'analyse de l'École Royale Polytechnique (1821), Résumé des leçons sur le calcul infinitésimal (1823) and Leçons sur les applications du calcul infinitésimal à la géométrie (1826–8), and his pioneering work encompassed a huge range of topics, most significantly real analysis, the theory of functions of a complex variable, and theoretical mechanics. Twenty-six volumes of his collected papers were published between 1882 and 1958. The first series (volumes 1-12) consists of papers published by the Académie des Sciences de l'Institut de France; the second series (volumes 13-26) of papers published elsewhere.

Essai philosophique sur les probabilités
  • 5th edition
  • Pierre Simon Laplace
  • Published online:
    01 March 2011
    Print publication:
    20 July 2009
    First published in:
    1825
  • The work of the Marquis de Laplace (1749–1827) was enormously influential in the development of mathematical physics, astronomy and statistics. Educated in Normandy, he moved to Paris on obtaining a letter of introduction to d'Alembert, who acted as his mentor while he undertook teaching and independent research in probability, statistics and astronomy. Laplace survived the turmoil of the French Revolution, the rise of Napoleon and the restoration of the Bourbons by a series of manoeuvres which gave him a reputation for insincerity and hypocrisy even among his peers who could correctly assess his contributions to science. His Essai philosophique sur les probabilités, first published in 1814, and of which the fifth edition, revised by the author, is presented here, is a fundamental work which establishes six principles of probability in mathematical terms.

Oeuvres complètes
  • Series 1
  • Volume 11
  • Augustin-Louis Cauchy
  • Published online:
    01 March 2011
    Print publication:
    20 July 2009
    First published in:
    1899
  • Augustin-Louis, Baron Cauchy (1789–1857) was the pre-eminent French mathematician of the nineteenth century. He began his career as a military engineer during the Napoleonic Wars, but even then was publishing significant mathematical papers, and was persuaded by Lagrange and Laplace to devote himself entirely to mathematics. His greatest contributions are considered to be the Cours d'analyse de l'École Royale Polytechnique (1821), Résumé des leçons sur le calcul infinitésimal (1823) and Leçons sur les applications du calcul infinitésimal à la géométrie (1826–8), and his pioneering work encompassed a huge range of topics, most significantly real analysis, the theory of functions of a complex variable, and theoretical mechanics. Twenty-six volumes of his collected papers were published between 1882 and 1958. The first series (volumes 1-12) consists of papers published by the Académie des Sciences de l'Institut de France; the second series (volumes 13-26) of papers published elsewhere.

Exposition du systéme du monde
  • 2nd edition
  • Pierre-Simon Laplace
  • Published online:
    10 November 2010
    Print publication:
    20 July 2009
    First published in:
    1796
  • The work of the Marquis de Laplace (1749–1827) was enormously influential on the development of mathematical physics, astronomy and statistics. His Exposition du système du monde (first published in 1796) is often regarded as the most important book on mechanics after Newton's Principia Mathematica, and the elegance and clarity of its style won Laplace a seat in the Académie Française. The book, which was translated into English in 1809, was intended to 'offer a complete solution of the great mechanical problem presented by the solar system'. It was in this work that Laplace offered his nebular hypothesis, which proposed that the solar system originated from the contraction and cooling of a cloud of incandescent gas. The book, here in its second edition of 1799, is an introduction to Laplace's multi-volume masterpiece, the Traité de Mécanique Céleste, of which Mary Somerville's English version is also reissued in this series.

Problems of Cosmology and Stellar Dynamics
  • James Jeans
  • Published online:
    05 October 2010
    Print publication:
    20 July 2009
    First published in:
    1919
  • Problems of Cosmogony and Stellar Dynamics is a theoretical prelude to Jeans's later and more mature work on the subject, Astronomy and Cosmogony. The impetus for publishing his theories on the behaviour of rotating masses, and on general dynamical theory, was the 1917 Adams Prize on the 'rotating and gravitating fluid mass'. Jeans won the prize with the core text of this volume. Enlarging on that work, and utilising the burgeoning results of astronomy, as well as the author's bolder theoretical conjectures, this book became a solid foundation for substantial progress in cosmology.

The Collected Mathematical Papers
  • Volume 1
  • Arthur Cayley
  • Published online:
    05 October 2010
    Print publication:
    20 July 2009
    First published in:
    1889
  • Arthur Cayley (1821–1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge and published three papers while still an undergraduate. He then qualified as a lawyer and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he took a significant salary cut to become the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death under the editorship of his successor in the Sadleirian Chair. This first volume contains 100 papers published between 1841 and 1851.

The Works of Archimedes
  • Edited in Modern Notation with Introductory Chapters
  • Archimedes
  • Edited by Thomas L. Heath
  • Published online:
    07 September 2010
    Print publication:
    24 September 2009
    First published in:
    1897
  • Archimedes lived in the third century BC, and died in the siege of Syracuse. Together with Euclid and Apollonius, he was one of the three great mathematicians of the ancient world, credited with astonishing breadth of thought and brilliance of insight. His practical inventions included the water-screw for irrigation, catapults and grappling devices for military defence on land and sea, compound pulley systems for moving large masses, and a model for explaining solar eclipses. According to Plutarch however, Archimedes viewed his mechanical inventions merely as 'diversions of geometry at play'. His principal focus lay in mathematics, where his achievements in geometry, arithmetic and mechanics included work on spheres, cylinders and floating objects. This classic 1897 text celebrates Archimedes' achievements. Part 1 places Archimedes in his historical context and presents his mathematical methods and discoveries, while Part 2 contains translations of his complete known writings.

Elements of the Mathematical Theory of Electricity and Magnetism
  • 4th edition
  • John Joseph Thomson
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1895
  • The British physicist Sir Joseph John Thomson, the discoverer of the electron, published the first edition of his Elements of the Mathematical Theory of Electricity and Magnetism in 1895; this fourth edition was issued in 1909, three years after he was awarded the Nobel Prize in Physics for his theoretical and experimental investigations on the conduction of electricity by gases. In this book for students his intention is to give 'an account of the fundamental principles of the mathematical theory of electricity and magnetism and their more important applications, using only simple mathematics.' Starting at the basic level of describing electrical phenomena such as rubbing a stick of sealing wax with cloth to produce a charge, he guides the reader through electrostatics, induction, magnetism, thermoelectric currents and the theory of light. This textbook, by one of the greatest scientists of his day, is still a fascinating introduction to the topic.

Science and Music
  • James Jeans
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1937
  • Sir James Jeans has used his remarkable gifts of exposition to set out all that is relevant in the science of acoustics to the art of music. He offers a simple but precise account (illustrated with well-chosen photographs and diagrams) of the anatomical origin and workings of the human ear; the nature of sound vibrations; simple tones and complex sounds; the principles and operation of musical instruments; harmony and the musical scale; the effects of music on men and animals; and the practical problems of acoustical design. Scientists who appreciate music, musicians with an interest in science and laymen who care for both, will thoroughly enjoy this book.

Théorie Analytique de la Chaleur
  • Jean Baptiste Joseph Fourier
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1822
  • French mathematician Joseph Fourier's Théorie Analytique de la Chaleur was originally published in 1822. In this groundbreaking study, arguing that previous theories of mechanics advanced by such outstanding scientists as Archimedes, Galileo, Newton and their successors did not explain the laws of heat, Fourier set out to study the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids: this is now known as the 'Fourier Series'. His work paved the way for modern mathematical physics. This book will be especially useful for mathematicians who are interested in trigonometric series and their applications, and it is reissued simultaneously with Alexander Freeman's English translation, The Analytical Theory of Heat, of 1878.

Mathematical and Physical Papers
  • Volume 2
  • George Gabriel Stokes
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1883
  • Sir George Stokes (1819–1903) established the science of hydrodynamics with his law of viscosity describing the velocity of a small sphere through a viscous fluid. He published no books, but was a prolific lecturer and writer of papers for the Royal Society, the British Association for the Advancement of Science, the Victoria Institute and other mathematical and scientific institutions. These collected papers (issued between 1880 and 1905) are therefore the only readily available record of the work of an outstanding and influential mathematician, who was Lucasian Professor of Mathematics in Cambridge for over fifty years, Master of Pembroke College, President of the Royal Society (1885–1890), Associate Secretary of the Royal Commission on the University of Cambridge and a Member of Parliament for the University.

Babbage's Calculating Engines
  • Being a Collection of Papers Relating to them; their History and Construction
  • Charles Babbage
  • Edited by Henry P. Babbage
  • Published online:
    07 September 2010
    Print publication:
    20 May 2010
    First published in:
    1889
  • The famous and prolific nineteenth-century mathematician, engineer and inventor Charles Babbage (1791–1871) was an early pioneer of computing. He planned several calculating machines, but none was built in his lifetime. On his death his youngest son, Henry P. Babbage, was charged with the task of completing an unfinished volume of papers on the machines, which was finally published in 1889 and is reissued here. The papers, by a variety of authors, were collected from journals including The Philosophical Magazine, The Edinburgh Review and Scientific Memoirs. They relate to the construction and potential application of Charles Babbage's calculating engines, notably the Difference Engine and the more complex Analytical Engine, which was to be programmed using punched cards. The book also includes correspondence with members of scientific societies, as well as proceedings, catalogues and drawings. Included is a complete catalogue of the drawings of the Analytical Engine.

Mathematical and Physical Papers
  • Volume 4
  • George Gabriel Stokes
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1904
  • Sir George Stokes (1819–1903) established the science of hydrodynamics with his law of viscosity describing the velocity of a small sphere through a viscous fluid. He published no books, but was a prolific lecturer and writer of papers for the Royal Society, the British Association for the Advancement of Science, the Victoria Institute and other mathematical and scientific institutions. These collected papers (issued between 1880 and 1905) are therefore the only readily available record of the work of an outstanding and influential mathematician, who was Lucasian Professor of Mathematics in Cambridge for over fifty years, Master of Pembroke College, President of the Royal Society (1885–1890), Associate Secretary of the Royal Commission on the University of Cambridge and a Member of Parliament for the University.

Odd Numbers
  • Herbert McKay
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1940
  • Mathematics has a reputation of being dull and difficult. Here is an antidote. This lively exploration of arithmetic considers its basic processes and manipulations, demonstrating their value and power and justifying an enduring interest in the subject. With humour and insight, the author shows how basic mathematics relates to everyday life – as true now as when this book was originally published in 1940. The introductory treatment of millions, billions and even trillions could be profitably read by aspiring bankers, economists or politicians. H. G. Wells is gently teased for his mistake in applying the law of proportionality in a novel. McKay politely adjusts the astronomical scales selected by the eminent cosmologist Sir James Jeans. He confidently navigates the hazards of averages, approximations and units. For anyone interested in what numbers mean and how they can be used most effectively, this book will still educate and delight.

Page 8 of 10