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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 3 of 10

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 2
  • Carl Gustav Jacob Jacobi
  • Edited by Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1882
  • One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804–51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802–29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815–97), Volume 2 appeared in 1882.

Mathematische Werke
  • Herausgegeben unter Mitwirkung einer von der königlich preussischen Akademie der Wissenschaften eingesetzten Commission
  • Volume 7
  • Karl Weierstrass
  • Edited by Rudolf Rothe
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1927
  • The German mathematician Karl Weierstrass (1815–97) is generally considered to be the father of modern analysis. His clear eye for what was important is demonstrated by the publication, late in life, of his polynomial approximation theorem; suitably generalised as the Stone–Weierstrass theorem, it became a central tool for twentieth-century analysis. Furthermore, the Weierstrass nowhere-differentiable function is the seed from which springs the entire modern theory of mathematical finance. The best students in Europe came to Berlin to attend his lectures, and his rigorous style still dominates the first analysis course at any university. His seven-volume collected works in the original German contain not only published treatises but also records of many of his famous lecture courses. Edited by Rudolf Rothe (1873–1942), Volume 7 was published in 1927.

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Supplement
  • Carl Gustav Jacob Jacobi
  • Edited by Eduard Lottner, Alfred Clebsch
  • Foreword by Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1884
  • One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804–51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802–29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891, edited chiefly by Karl Weierstrass (1815–97). Published in 1884, this supplementary volume contains Jacobi's 1842–3 lectures on dynamics as compiled by Alfred Clebsch (1833–72) in the revised second edition by Eduard Lottner (1826–87).

Mathematische Werke
  • Herausgegeben unter Mitwirkung einer von der königlich preussischen Akademie der Wissenschaften eingesetzten Commission
  • Volume 4
  • Karl Weierstrass
  • Edited by Georg Hettner, Johannes Knoblauch
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1902
  • The German mathematician Karl Weierstrass (1815–97) is generally considered to be the father of modern analysis. His clear eye for what was important is demonstrated by the publication, late in life, of his polynomial approximation theorem; suitably generalised as the Stone–Weierstrass theorem, it became a central tool for twentieth-century analysis. Furthermore, the Weierstrass nowhere-differentiable function is the seed from which springs the entire modern theory of mathematical finance. The best students in Europe came to Berlin to attend his lectures, and his rigorous style still dominates the first analysis course at any university. His seven-volume collected works in the original German contain not only published treatises but also records of many of his famous lecture courses. Edited by Johannes Knoblauch (1885–1915) and Georg Hettner (1854–1914), Volume 4 was published in 1902.

Recherches sur la théorie des surfaces élastiques
  • Sophie Germain
  • Published online:
    05 April 2014
    Print publication:
    06 June 2013
    First published in:
    1821
  • Sophie Germain (1776–1831) was one of the first distinguished female mathematicians of the modern era. Largely self-taught, she won the admiration and friendship of Legendre and Gauss (whose work also appears in this series). Germain is best known for her work on number theory, notably Fermat's Last Theorem, but she played an important part in establishing the foundations of elasticity. This book, described by her slightly younger contemporary Navier as 'a work which few men are able to read and which only one woman was able to write', contains her research on the topic, which was awarded a prize by the Paris Academy of Sciences. This work was published in Paris in 1821.

Vorlesungen uber Zahlentheorie
  • Peter Gustav Lejeune Dirichlet
  • Edited by R. Dedekind
  • Published online:
    05 April 2014
    Print publication:
    22 August 2013
    First published in:
    1879
  • Peter Gustav Lejeune Dirichlet (1805–59) may be considered the father of modern number theory. He studied in Paris, coming under the influence of mathematicians like Fourier and Legendre, and then taught at Berlin and Göttingen universities, where he was the successor to Gauss. This book contains lectures on number theory given by Dirichlet in 1856–7. They include his famous proofs of the class number theorem for binary quadratic forms and the existence of an infinity of primes in every appropriate arithmetical progression. The material was first published in 1863 by Richard Dedekind (1831–1916), professor at Braunschweig, who had been a junior colleague of Dirichlet at Göttingen. The second edition appeared in 1871; this reissue is of the third, revised and expanded, edition of 1879; a fourth edition appeared as late as 1894. The appendices contain further work by both Dirichlet and Dedekind.

A Synopsis of Elementary Results in Pure and Applied Mathematics
  • Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations
  • Volume 1
  • George Shoobridge Carr
  • Published online:
    05 March 2014
    Print publication:
    05 September 2013
    First published in:
    1886
  • When George Shoobridge Carr (1837–1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887–1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 1, presented here in its 1886 printing, contains sections on mathematical tables, algebra, the theory of equations, plane trigonometry, spherical trigonometry, elementary geometry and geometrical conics.

A Treatise on Analytical Statics
  • With Numerous Examples
  • Volume 1
  • Edward John Routh
  • Published online:
    05 March 2014
    Print publication:
    05 September 2013
    First published in:
    1891
  • As senior wrangler in 1854, Edward John Routh (1831–1907) was the man who beat James Clerk Maxwell in the Cambridge mathematics tripos. He went on to become a highly successful coach in mathematics at Cambridge, producing a total of twenty-seven senior wranglers during his career - an unrivalled achievement. In addition to his considerable teaching commitments, Routh was also a very able and productive researcher who contributed to the foundations of control theory and to the modern treatment of mechanics. This two-volume textbook, which first appeared in 1891–2 and is reissued here in the revised edition that was published between 1896 and 1902, offers extensive coverage of statics, providing formulae and examples throughout for the benefit of students. While the growth of modern physics and mathematics may have forced out the problem-based mechanics of Routh's textbooks from the undergraduate syllabus, the utility and importance of his work is undiminished.

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 5
  • Carl Gustav Jacob Jacobi
  • Edited by Karl Weierstrass
  • Published online:
    05 March 2014
    Print publication:
    18 April 2013
    First published in:
    1890
  • One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804–51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802–29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815–97), Volume 5 appeared in 1890.

Lilawati; or a Treatise on Arithmetic and Geometry
  • Bhascara Acharya
  • Translated by John Taylor
  • Published online:
    05 March 2014
    Print publication:
    28 March 2013
    First published in:
    1816
  • An important mathematician and astronomer in medieval India, Bhascara Acharya (1114–85) wrote treatises on arithmetic, algebra, geometry and astronomy. He is also believed to have been head of the astronomical observatory at Ujjain, which was the leading centre of mathematical sciences in India. Forming part of his Sanskrit magnum opus Siddhānta Shiromani, the present work is his treatise on arithmetic, including coverage of geometry. It was first published in English in 1816 after being translated by the East India Company surgeon John Taylor (d.1821). Used as a textbook in India for centuries, it provides the basic mathematics needed for astronomy. Topics covered include arithmetical terms, plane geometry, solid geometry and indeterminate equations. Of enduring interest in the history of mathematics, this work also contains Bhascara's pictorial proof of Pythagoras' theorem.

Aristarchus of Samos, the Ancient Copernicus
  • A History of Greek Astronomy to Aristarchus, Together with Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon
  • Thomas Heath
  • Published online:
    05 March 2014
    Print publication:
    26 September 2013
  • The Greek astronomer Aristarchus of Samos was active in the third century BCE, more than a thousand years before Copernicus presented his model of a heliocentric solar system. It was Aristarchus, however, who first suggested - in a work that is now lost - that the planets revolve around the sun. Edited by Sir Thomas Little Heath (1861–1940), this 1913 publication contains the ancient astronomer's only surviving treatise, which does not propound the heliocentric hypothesis. The Greek text is based principally on the tenth-century manuscript Vaticanus Graecus 204. Heath also provides a facing-page English translation and explanatory notes. The treatise is prefaced by a substantial history of ancient Greek astronomy, ranging from Homer's first mention of constellations to work by Heraclides of Pontus in the fourth century BCE relating to the Earth's rotation. Heath's collection of translated ancient texts, Greek Astronomy (1932), is also reissued in this series.

Memoirs of the Analytical Society
  • Charles Babbage, John Herschel
  • Published online:
    05 March 2014
    Print publication:
    26 September 2013
  • By the end of the eighteenth century, British mathematics had been stuck in a rut for a hundred years. Calculus was still taught in the style of Newton, with no recognition of the great advances made in continental Europe. The examination system at Cambridge even mandated the use of Newtonian notation. As discontented undergraduates, Charles Babbage (1791–1871) and John Herschel (1792–1871) formed the Analytical Society in 1811. The group, including William Whewell and George Peacock, sought to promote the new continental mathematics. Babbage's preface to the present work, first published in 1813, may be considered the movement's manifesto. He provided the first paper here, and Herschel the two others. Although the group was relatively short-lived, its ideas took root as its erstwhile members rose to prominence. As the society's sole publication, this remains a significant text in the history of British mathematics.

A Treatise on Dynamics of a Particle
  • With Numerous Examples
  • Edward John Routh
  • Published online:
    05 March 2014
    Print publication:
    06 June 2013
    First published in:
    1898
  • As senior wrangler in 1854, Edward John Routh (1831–1907) was the man who beat James Clerk Maxwell in the Cambridge mathematics tripos. He went on to become a highly successful coach in mathematics at Cambridge, producing a total of twenty-seven senior wranglers during his career - an unrivalled achievement. In addition to his considerable teaching commitments, Routh was also a very able and productive researcher who contributed to the foundations of control theory and to the modern treatment of mechanics. This textbook, first published in 1898, offers extensive coverage of dynamics, providing formulae and examples throughout. While the growth of modern physics and mathematics may have forced out the problem-based mechanics of Routh's textbooks from the undergraduate syllabus, the utility and importance of his work is undiminished.

A Treatise on Analytical Statics
  • With Numerous Examples
  • Volume 2
  • Edward John Routh
  • Published online:
    05 March 2014
    Print publication:
    05 September 2013
    First published in:
    1892
  • As senior wrangler in 1854, Edward John Routh (1831–1907) was the man who beat James Clerk Maxwell in the Cambridge mathematics tripos. He went on to become a highly successful coach in mathematics at Cambridge, producing a total of twenty-seven senior wranglers during his career - an unrivalled achievement. In addition to his considerable teaching commitments, Routh was also a very able and productive researcher who contributed to the foundations of control theory and to the modern treatment of mechanics. This two-volume textbook, which first appeared in 1891–2 and is reissued here in the revised edition that was published between 1896 and 1902, offers extensive coverage of statics, providing formulae and examples throughout for the benefit of students. While the growth of modern physics and mathematics may have forced out the problem-based mechanics of Routh's textbooks from the undergraduate syllabus, the utility and importance of his work is undiminished.

A Synopsis of Elementary Results in Pure and Applied Mathematics
  • Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations
  • Volume 2
  • George Shoobridge Carr
  • Published online:
    05 March 2014
    Print publication:
    05 September 2013
    First published in:
    1886
  • When George Shoobridge Carr (1837–1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887–1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 2 contains sections on differential calculus, integral calculus, calculus of variations, differential equations, calculus of finite differences, plane coordinate geometry and solid coordinate geometry. Also included is a historically valuable index insofar as it provides references to 890 volumes of 32 periodicals dating back to 1800.

Fundamenta nova theoriae functionum ellipticarum
  • Carl Gustav Jacob Jacobi
  • Published online:
    05 October 2013
    Print publication:
    15 November 2012
    First published in:
    1829
  • Carl Gustav Jacob Jacobi (1804–51) was one of the nineteenth century's greatest mathematicians, as attested by the diversity of mathematical objects named after him. His early work on number theory had already attracted the attention of Carl Friedrich Gauss, but his reputation was made by his work on elliptic functions. Elliptic integrals had been studied for a long time, but in 1827 Jacobi and Niels Henrik Abel realised independently that the correct way to view them was by means of their inverse functions - what we now call the elliptic functions. The next few years witnessed a flowering of the subject as the two mathematicians pushed ahead. Adrien-Marie Legendre, an expert on the old theory, wrote: 'I congratulate myself that I have lived long enough to witness these magnanimous conflicts between two equally strong young athletes'. This Latin work, first published in 1829, is Jacobi's pioneering account of the new theory.

Die Lineale Ausdehnungslehre ein neuer Zweig der Mathematik
  • Dargestellt und durch Anwendungen auf die übrigen Zweige der Mathematik, wie auch auf die Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erläutert
  • Hermann Grassmann
  • Published online:
    05 October 2013
    Print publication:
    13 December 2012
    First published in:
    1844
  • The Prussian schoolmaster Hermann Grassmann (1809–77) taught a range of subjects including mathematics, science and Latin and wrote several secondary-school textbooks. Although he was never appointed to a university post, he devoted much energy to mathematical research and developed revolutionary new insights. Die lineale Ausdehnungslehre, published in 1844, is an astonishing work which was not understood by the mathematicians of its time but which anticipated developments that took a century to come to fruition - vector spaces, dimension, exterior products and many other ideas. Admired rather than read by the next generation, it was only fully appreciated by mathematicians such as Peano and Whitehead.

The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies
  • Being Part II of a Treatise on the Whole Subject
  • Edward John Routh
  • Published online:
    05 October 2013
    Print publication:
    21 March 2013
    First published in:
    1892
  • As senior wrangler in 1854, Edward John Routh (1831–1907) was the man who beat James Clerk Maxwell in the Cambridge mathematics tripos. He went on to become a highly successful coach in mathematics at Cambridge, producing a total of twenty-seven senior wranglers during his career - an unrivalled achievement. In addition to his considerable teaching commitments, Routh was also a very able and productive researcher who contributed to the foundations of control theory and to the modern treatment of mechanics. First published in one volume in 1860, this textbook helped disseminate Routh's investigations into stability. This revised fifth edition was published in two volumes between 1891 and 1892. The second part develops the extensive coverage of dynamics, providing formulae and examples throughout. While the growth of modern physics and mathematics may have forced out the problem-based mechanics of Routh's textbooks from the undergraduate syllabus, the utility and importance of his work is undiminished.

Werke
  • Volume 4
  • Carl Friedrich Gauss
  • Published online:
    05 September 2013
    Print publication:
    03 November 2011
    First published in:
    1873
  • 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 4, published in 1873, contains Gauss' theoretical work on differential geometry and probability, reviews of work by contemporaries including Herschel, and notes relating to geodesic surveys of the Kingdom of Hanover from the 1820s to the 1840s, together with a description of the heliotrope Gauss invented for the surveys.

Oeuvres complètes de Niels Henrik Abel
  • Nouvelle édition
  • Volume 2
  • Niels Henrik Abel
  • Edited by L. Sylow, S. Lie
  • Published online:
    05 August 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 2 contains additional articles on elliptic functions and infinite series. It also includes extracts from Abel's letters, as well as detailed notes and commentary by Sylow and Lie on Abel's pioneering work.

Page 3 of 10