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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 4 of 10

Reflections on the Decline of Science in England, and on Some of its Causes
  • Charles Babbage
  • Published online:
    05 August 2013
    Print publication:
    14 February 2013
    First published in:
    1830
  • The mathematician Charles Babbage (1791–1871) was one of the most original thinkers of the nineteenth century. In this influential 1830 publication, he criticises the continued failure of government to support science and scientists. In addition, he identifies the weaknesses of the then existing scientific societies, saving his most caustic remarks for the Royal Society. Asserting that the societies were operated largely by small groups of amateurs possessing only superficial interest and knowledge of science, Babbage explores the importance of the relationships between science, technology and society. Exposing the absence of a true scientific culture, he states, 'The pursuit of science does not, in England, constitute a distinct profession, as it does in other countries.' These concerns found favour with many, influencing reforms of the Royal Society and leading to the founding of the British Association.

Mathematical Tables
  • Containing the Common, Hyperbolic, and Logistic Logarithms
  • Charles Hutton, Olinthus Gregory
  • Published online:
    05 August 2013
    Print publication:
    11 October 2012
    First published in:
    1858
  • Prior to the advent of computers, no mathematician, physicist or engineer could do without a volume of tables of logarithmic and trigonometric functions. These tables made possible certain calculations which would otherwise be impossible. Unfortunately, carelessness and lazy plagiarism meant that the tables often contained serious errors. Those prepared by Charles Hutton (1737–1823) were notable for their reliability and remained the standard for a century. Hutton had risen, by mathematical ability, hard work and some luck, from humble beginnings to become a professor of mathematics at the Royal Military Academy. His mathematical work was distinguished by utility rather than originality, but his contributions to the teaching of the subject were substantial. This seventh edition was published in 1858 with additional material by Olinthus Gregory (1774–1841). The preliminary matter will be of interest to any modern-day reader who wishes to know how calculation was done before the electronic computer.

Oeuvres complètes de Niels Henrik Abel
  • Nouvelle édition
  • Volume 1
  • Niels Henrik Abel
  • Edited by L. Sylow, S. Lie
  • Published online:
    05 June 2013
    Print publication:
    02 August 2012
    First published in:
    1881
  • Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifth-degree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions - in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals.

G. Lejeune Dirichlet's Werke
  • Volume 1
  • Peter Gustav Lejeune Dirichlet
  • Edited by Leopold Kronecker
  • Published online:
    05 June 2013
    Print publication:
    14 June 2012
    First published in:
    1889
  • The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (1805–59) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and Göttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 1889–97, was compiled by Leopold Kronecker (1823–91). Volume 1 contains works published by Dirichlet up to 1843, together with a related 1846 essay.

Werke
  • Volume 9
  • Carl Friedrich Gauss
  • Published online:
    05 June 2013
    Print publication:
    03 November 2011
    First published in:
    1903
  • 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 9, which appeared in 1903, supplements the account in Volume 4 of geodesy, triangulation, and the geodesic survey of the Kingdom of Hanover. It includes both published work and previously unpublished notes found among Gauss' papers.

G. Lejeune Dirichlet's Werke
  • Volume 2
  • Peter Gustav Lejeune Dirichlet
  • Edited by Leopold Kronecker
  • Published online:
    05 June 2013
    Print publication:
    14 June 2012
    First published in:
    1897
  • The great nineteenth-century mathematician Peter Gustav Lejeune Dirichlet (1805–59) studied in Paris, coming under the influence of scholars including Fourier and Legendre. He then taught at Berlin and Göttingen universities, where he was the successor to Gauss and mentor to Riemann and Dedekind. His achievements include the first satisfactory proof of the convergence of Fourier series under appropriate conditions, and the theorem on primes in arithmetic progression which was, at the same time, the foundation of analytic number theory and one of its greatest achievements. He also did important work on Laplace's equation, the theory of series and many other topics. This two-volume collection of his works, published 1889–97, was compiled by Leopold Kronecker (1823–91). Volume 2 was completed by Lazarus Fuchs (1833–1902) and contains Dirichlet's publications from 1844 onwards, together with some unpublished papers and selected correspondence with Gauss, Alexander von Humboldt and Kronecker.

Theory of Groups of Finite Order
  • William Burnside
  • Published online:
    05 May 2013
    Print publication:
    07 June 2012
    First published in:
    1897
  • The British mathematician William Burnside (1852–1927) and Ferdinand Georg Frobenius (1849–1917), Professor at Zurich and Berlin universities, are considered to be the founders of the modern theory of finite groups. Not only did Burnside prove many important theorems, but he also laid down lines of research for the next hundred years: two Fields Medals have been awarded for work on problems suggested by him. The Theory of Groups of Finite Order, originally published in 1897, was the first major textbook on the subject. The 1911 second edition (reissued here) contains an account of Frobenius's character theory, and remained the standard reference for many years.

Niels-Henrik Abel
  • Tableau de sa vie et de son action scientifique
  • Carl Anton Bjerknes
  • Published online:
    05 May 2013
    Print publication:
    07 June 2012
    First published in:
    1885
  • Few men in modern mathematics have had as great an impact as the Norwegian Niels Henrik Abel (1802–29), whose discoveries paved the way for several new branches of nineteenth-century mathematics. Tragically, Abel's short life was dominated by poverty and his scientific achievements were not fully recognised until after his death. This work, written by Carl Anton Bjerknes (1825–1903), was the first full biography of Abel. Originally published in 1880 and translated into French in 1885, it became a valuable resource for later Abel biographers and scholars of the history of mathematics. With insight and understanding, Bjerknes charts the progress of the talented young mathematician and gives a detailed account of Abel's work and his correspondence with other contemporary mathematicians. In particular, he examines in depth (from Abel's point of view) the dispute between Abel and his rival Jacobi relating to their discoveries of elliptic functions in the 1820s.

Oeuvres complètes
  • Series 1
  • Volume 12
  • Augustin-Louis Cauchy
  • Published online:
    05 February 2013
    Print publication:
    20 July 2009
    First published in:
    1900
  • 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.

Œuvres de Charles Hermite
  • Volume 4
  • Charles Hermite
  • Published online:
    05 February 2013
    Print publication:
    20 July 2009
    First published in:
    1917
  • Charles Hermite (1822–1901) was a French mathematician who made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'. As a teacher at the École Polytechnique, the Faculté des Sciences de Paris and the École Normale Supérieure he was influential and inspiring to a new generation of scientists in many disciplines. The four volumes of his collected papers were published between 1905 and 1908.

Werke
  • Volume 3
  • Carl Friedrich Gauss
  • Published online:
    05 February 2013
    Print publication:
    03 November 2011
    First published in:
    1866
  • 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 3, which appeared in 1866, focuses on analysis. It includes Gauss' work on elliptic functions and on power series, for which he gave the first convergence criteria, as well as his first (1799) proof of the fundamental theorem of algebra, and reviews of works by contemporaries including Fourier.

Werke
  • Volume 10, Part 2
  • Carl Friedrich Gauss
  • Published online:
    05 June 2012
    Print publication:
    03 November 2011
    First published in:
    1922
  • 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. At the suggestion of Felix Klein, Gauss' twentieth-century successors planned a scientific biography consisting of essays covering the various areas in which he worked. Volume 10, Part II, (dated 1922–33) contains seven contributions, individually paginated and originally sold separately, relating to pure mathematics, probability and mechanics.

Oeuvres complètes
  • Series 1
  • Volume 6
  • Augustin-Louis Cauchy
  • Published online:
    05 May 2012
    Print publication:
    20 July 2009
    First published in:
    1888
  • 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 de Desargues
  • Volume 1
  • Gérard Desargues
  • Edited by Noël Germinal Poudra
  • Published online:
    05 April 2012
    Print publication:
    10 November 2011
    First published in:
    1864
  • The French mathematician and engineer Gérard Desargues (1591–1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and architecture. His important writings, which had been lost, were published in 1864 by the mathematician and scientific historian Noël-Germinal Poudra (1794–1894). Poudra's two-volume edition, republished here, reveals the major role played by Desargues in the scientific debates of the seventeenth century. It includes a biography of Desargues, in which Poudra discusses his role as architect, as well as his influence on famous scientists of his time including Pascal and Descartes. Volume 1 contains the majority of Desargues' treatises, including 'Perspective' (1636), followed by an analysis by Poudra, and the 'Traité des Coniques' (1639), with a lexicon of the scientific terms used.

The Algebra of Invariants
  • John Hilton Grace, Alfred Young
  • Published online:
    05 April 2012
    Print publication:
    31 October 2010
    First published in:
    1903
  • Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. John Hilton Grace (1873–1958) was a research mathematician specialising in algebra and geometry. He was elected a Fellow of the Royal Society in 1908. His co-author Dr Alfred Young (1873–1940) was also a research mathematician before being ordained in 1908; in 1934 he too was elected a Fellow of the Royal Society. Abstract algebra was one of the new fields of study within mathematics which developed out of geometry during the nineteenth century. It became a major area of research in the late nineteenth and early twentieth centuries. First published in 1903, this book introduced the work on invariant theory of the German mathematicians Alfred Clebsch and Paul Gordan into British mathematics. It was considered the standard work on the subject.

Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium
  • Carl Friedrich Gauss
  • Published online:
    05 April 2012
    Print publication:
    19 May 2011
    First published in:
    1809
  • Described by one reviewer as 'one of the most perfect books ever written on theoretical astronomy', this work in Latin by the German mathematician Carl Friedrich Gauss (1777–1855), the 'Prince of Mathematicians', derived from his attempt to solve an astronomical puzzle: where in the heavens would the dwarf planet Ceres, first sighted in 1801, reappear? Gauss' predicted position was correct to within half a degree, and this led him to develop a streamlined and sophisticated method of calculating the effect of the larger planets and the sun on the orbits of planetoids, which he published in 1809. As well as providing a tool for astronomers, Gauss' method also offered a way of reducing inaccuracy of calculations arising from measurement error; the primacy of this discovery was however disputed between him and the French mathematician Legendre, whose Essai sur la théorie des nombres is also reissued in this series.

Oeuvres de Desargues
  • Volume 2
  • Gérard Desargues
  • Edited by Noël Germinal Poudra
  • Published online:
    05 April 2012
    Print publication:
    10 November 2011
    First published in:
    1864
  • The French mathematician and engineer Gérard Desargues (1591–1661) was one of the founders of projective geometry. Desargues' theorem is named in the honour of this prolific writer of treatises on geometry and its application to the arts and architecture. His important writings, which had been lost, were published in 1864 by the mathematician and scientific historian Noël-Germinal Poudra (1794–1894). Poudra's two-volume edition, republished here, reveals the major role played by Desargues in the scientific debates of the seventeenth century. It includes a biography of Desargues, in which Poudra discusses his role as architect, as well as his influence on famous scientists of his time including Pascal and Descartes. Volume 2 contains Poudra's analysis of the works of the engraver Abraham Bosse (1603–76), which develop some of Desargues' ideas. It also reproduces some of the - often critical - responses to Desargues' work by his contemporaries.

Rapport historique sur les progrès des sciences mathématiques depuis 1789, et sur leur état actuel
  • Edited by Jean-Baptiste Joseph Delambre
  • Published online:
    05 April 2012
    Print publication:
    03 November 2011
    First published in:
    1810
  • In 1808, Napoleon I (1769–1821), emperor of the French from 1804 to 1815, commissioned a series of official reports on the progress of scientific research since 1789. First published in 1810, this report on the current state of mathematics was written by French mathematician and astronomer Jean-Baptiste Joseph Delambre (1749–1822). A Professor at the Collège de France and Director of the Paris Observatory, Delambre was appointed permanent secretary for the mathematical sciences of the Academy of Science in 1801. As such, he was charged with examining the state of mathematics in higher educational establishments, and with presenting an overview of the progress accomplished during Napoleon's reign in the fields of geometry, algebra, astronomy and geography. This report includes a chapter on the metric system, which Delambre was instrumental in determining via the measurement of the meridian between the north pole and the equator in 1792.

Werke
  • Volume 11, Part 2
  • Carl Friedrich Gauss
  • Published online:
    05 March 2012
    Print publication:
    03 November 2011
    First published in:
    1924
  • 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. At the suggestion of Felix Klein, Gauss' twentieth-century successors planned a scientific biography consisting of essays covering the various areas in which he worked. Volume 11, Part II (dated 1924–9) contains three contributions, individually paginated and originally sold separately, relating to geodesy, physics and astronomy.

Vollständige Anleitung zur Niedern und Höhern Algebra
  • Volume 3
  • Leonhard Euler
  • Published online:
    05 March 2012
    Print publication:
    20 July 2009
    First published in:
    1796
  • In 1770, one of the founders of pure mathematics, the Swiss-born mathematician Leonard Euler (1707–1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of this three-volume 1790s German edition. Volume 3 consists of the German translation of Lagrange's additional material, which the German publisher printed in a separate volume to enable those who already owned Euler's Algebra to obtain the supplementary material 'without incurring unnecessary expenditure'. The translator (the tutor to the sons of the Duke of Württemberg) added notes and further appendices of his own. This book provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.

Page 4 of 10