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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 5 of 10

Werke
  • Volume 5
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1867
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 5, published in 1867, covers Gauss' work on mechanics and geomagnetism. It includes expositions of his principle of least constraint and the theory of capillarity. It also contains book reviews, and a description of the aurora borealis observed in January 1831.

Werke
  • Volume 8
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1900
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 8, published in 1900, supplements the first four volumes with further work on number theory, probability and differential geometry that was discovered posthumously among Gauss' papers. Gauss here engages with work by scholars including Lagrange, Legendre, Lobatschewsky and Möbius, and paves the way for non-Euclidean geometry.

Oeuvres complètes
  • Series 1
  • Volume 8
  • Augustin-Louis Cauchy
  • Published online:
    05 March 2012
    Print publication:
    20 July 2009
    First published in:
    1893
  • 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.

Werke
  • Volume 12
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1929
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 12, which appeared in 1929, contains a great variety of posthumous notes and fragments, scientific correspondence and even proposals for problems to be set at scientific competitions. The volume also includes a reproduction of Gauss' 1840 atlas of geomagnetism.

Werke
  • Volume 2
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1863
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 2, which appeared in 1863, supplements Volume 1 with additional articles on number theory. It also contains book reviews and posthumous papers, including an unfinished eighth chapter of the Disquisitiones arithmeticae.

Werke
  • Volume 10, Part 1
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1917
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. An invaluable source in tracing Gauss' development is his scientific diary, which was only discovered in 1898. Volume 10 Part I, published in 1917, contains a photographic reproduction of this manuscript and a detailed commentary, together with many letters about pure mathematics, and shorter works including a preface to Piazzi.

Werke
  • Volume 6
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1874
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. One of Gauss' key successes in astronomy was the prediction of the path of Ceres, leading to its rediscovery in 1801. The original reports about this dramatic course of events appear in Volume 6, published in 1874, which includes all of Gauss' publications on astronomy, book reviews and letters.

Werke
  • Volume 7
  • Carl Friedrich Gauss
  • Edited by Ernst Julius Schering
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1906
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 7, published in 1906, contains some of the most surprising material discovered among Gauss' papers: extensive calculations concerning the motion of Pallas. The volume also includes a reprint of Gauss' 1809 book on orbits, Theoria motus corporum coelestium, followed by his later updates and corrections.

Werke
  • Volume 11, Part 1
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1927
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 11 Part I, which appeared in 1927, supplements volumes 5 to 7 with additional material on physics (particularly magnetism) and both theoretical and practical astronomy. It also contains a substantial amount of scientific correspondence with scholars including Schumacher, Olbers and Bessel.

Werke
  • Volume 1
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1863
  • The genius of Carl Friedrich Gauss (1777–1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 1 reproduces the 1801 Disquisitiones arithmeticae, a masterpiece of mathematical rigour, in which Gauss drew together and greatly extended the number-theoretic knowledge of his time. The final chapter, on the criterion for the constructibility of a regular polygon, solved a problem that had been open since antiquity.

Scientific Papers
  • Volume 5, 1902–1910
  • John William Strutt
  • Published online:
    05 December 2011
    Print publication:
    20 July 2009
    First published in:
    1912
  • Lord Rayleigh served as President of Royal Society from 1905 to 1908, when he became Chancellor of the University of Cambridge. In 1904 he was awarded a Nobel Prize. He received the physics award while Ramsey, with whom he had conducted the research and announced the discovery of argon, received the Nobel Prize for chemistry. In 1906 he published his electron fluid model of the atom, a modification of Thomson's 'plum pudding' proposal. This was superseded by a series of other (also invalid) models, until Bohr's atomic theory of 1913. In 1907 Rayleigh published a detailed observational study on how humans can perceive sound and distinguish the directions of pure and complex tones. His interest in optics also continued, with a 1907 analysis of the theoretical basis for unusual banding patterns arising when polarised light was shone on diffraction gratings. This volume includes his papers from 1902 to 1910.

Scientific Papers
  • Volume 2, 1881–1887
  • John William Strutt
  • Published online:
    05 December 2011
    Print publication:
    20 July 2009
    First published in:
    1900
  • As Cavendish Professor of Experimental Physics at Cambridge University, Lord Rayleigh focussed his considerable energies on the study of electricity – building on the work of his illustrious predecessor, James Clerk Maxwell. This second volume of his papers, covering 1881–7, includes a series of four major contributions from 1881 and 1883 concerning the absolute determination of the ohm. Related reports include the measurement of current, and the electrical properties of various materials. A note from 1884 pessimistically predicts an absolute practical limit of less than 50 miles for a working telephone cable. In 1884, Rayleigh stepped down from his post as Cavendish Professor but continued his research work from his private laboratory. He proposed the existence of surface waves in a paper of 1885. These 'Rayleigh waves' roll along the surface of the earth and are responsible for producing most of the shaking experienced in an earthquake.

An Investigation of the Laws of Thought
  • On Which Are Founded the Mathematical Theories of Logic and Probabilities
  • George Boole
  • Published online:
    05 November 2011
    Print publication:
    20 July 2009
    First published in:
    1854
  • Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind.

The Collected Mathematical Papers
  • Volume 14, Index
  • Arthur Cayley
  • Published online:
    05 November 2011
    Print publication:
    20 July 2009
    First published in:
    1898
  • 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 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 a complete listing of all the papers, and a thorough index of persons and topics from Abel to Zornow.

The Collected Mathematical Papers
  • Volume 7
  • Arthur Cayley
  • Published online:
    05 November 2011
    Print publication:
    20 July 2009
    First published in:
    1894
  • 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 69 papers published mostly between 1866 and 1872.

The Collected Mathematical Papers
  • Volume 12
  • Arthur Cayley
  • Published online:
    07 October 2011
    Print publication:
    20 July 2009
    First published in:
    1897
  • 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 89 papers mostly published between 1883 and 1889.

The Collected Mathematical Papers
  • Volume 4
  • Arthur Cayley
  • Published online:
    07 October 2011
    Print publication:
    20 July 2009
    First published in:
    1891
  • 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 by his successor in the Sadleirian Chair. This volume contains 76 papers published between 1856 and 1862, plus one from 1891.

The Collected Mathematical Papers
  • Volume 3
  • Arthur Cayley
  • Published online:
    07 October 2011
    Print publication:
    20 July 2009
    First published in:
    1890
  • 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. Volume 3 contains 64 papers first published between 1857 and 1862.

Oeuvres complètes
  • Series 2
  • Volume 2
  • Augustin-Louis Cauchy
  • Published online:
    07 September 2011
    Print publication:
    20 July 2009
    First published in:
    1958
  • 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 2
  • Volume 6
  • Augustin-Louis Cauchy
  • Published online:
    07 September 2011
    Print publication:
    20 July 2009
    First published in:
    1887
  • 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.

Page 5 of 10