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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 2 of 10

Cours d'analyse de l'ecole polytechnique
  • Volume 1, Calcul différentiel
  • Camille Jordan
  • Published online:
    05 October 2014
    Print publication:
    21 November 2013
  • One of the great algebraists of the nineteenth century, Marie Ennemond Camille Jordan (1838–1922) became known for his work on matrices, Galois theory and group theory. However, his most profound effect on how we see mathematics came through his Cours d'analyse, which appeared in three editions. Reissued here is the first edition, which was published in three volumes between 1882 and 1887. While highly influential in its time, it now appears to us a transitional work between the partially rigorous 'epsilon delta' calculus of Cauchy and his successors, and the new 'real number' analysis of Weierstrass and Cantor. The first two volumes follow the old tradition while the third volume incorporates a substantial amount of the new analysis. Ten years later, the even more influential second edition followed the new point of view from its start. Volume 1 (1882) covers differential calculus.

The Mathematical Works of Isaac Barrow
  • Edited for Trinity College
  • Isaac Barrow
  • Edited by William Whewell
  • Published online:
    05 October 2014
    Print publication:
    05 September 2013
    First published in:
    1860
  • The Cambridge polymath Isaac Barrow (1630–77) gained recognition as a theologian, classicist and mathematician. This one-volume collection of his mathematical writings, dutifully edited by one of his successors as Master of Trinity College, William Whewell (1794–1866), was first published in 1860. Containing significant contributions to the field, the work consists chiefly of the lectures on mathematics, optics and geometry that Barrow gave in his position as Lucasian Professor of Mathematics between 1663 and 1669. It includes the first general statement of the fundamental theorem of calculus as well as Barrow's 'differential triangle'. Not only did he precede Isaac Newton in the Lucasian chair, but his works were also to be found in the library of Gottfried Leibniz. However, rather than considering arid questions of priority, scholars can see in these Latin texts the status of advanced mathematics just before the great revolution of Newton and Leibniz.

Mathematische Werke
  • Herausgegeben unter Mitwirkung einer von der königlich preussischen Akademie der Wissenschaften eingesetzten Commission
  • Volume 5
  • Karl Weierstrass
  • Edited by Johannes Knoblauch
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1915
  • 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 (1855–1915), Volume 5 was published in 1915.

Cours d'analyse de l'ecole polytechnique
  • Volume 2, Calcul intégral; Intégrales définies et indéfinies
  • Camille Jordan
  • Published online:
    05 October 2014
    Print publication:
    21 November 2013
  • One of the great algebraists of the nineteenth century, Marie Ennemond Camille Jordan (1838–1922) became known for his work on matrices, Galois theory and group theory. However, his most profound effect on how we see mathematics came through his Cours d'analyse, which appeared in three editions. Reissued here is the first edition, which was published in three volumes between 1882 and 1887. While highly influential in its time, it now appears to us a transitional work between the partially rigorous 'epsilon delta' calculus of Cauchy and his successors, and the new 'real number' analysis of Weierstrass and Cantor. The first two volumes follow the old tradition while the third volume incorporates a substantial amount of the new analysis. Ten years later, the even more influential second edition followed the new point of view from its start. Volume 2 (1883) covers the theory of integrals.

Cours d'analyse de l'ecole polytechnique
  • Volume 3, Calcul intégral; équations différentielles
  • Camille Jordan
  • Published online:
    05 October 2014
    Print publication:
    21 November 2013
  • One of the great algebraists of the nineteenth century, Marie Ennemond Camille Jordan (1838–1922) became known for his work on matrices, Galois theory and group theory. However, his most profound effect on how we see mathematics came through his Cours d'analyse, which appeared in three editions. Reissued here is the first edition, which was published in three volumes between 1882 and 1887. While highly influential in its time, it now appears to us a transitional work between the partially rigorous 'epsilon delta' calculus of Cauchy and his successors, and the new 'real number' analysis of Weierstrass and Cantor. The first two volumes follow the old tradition while the third volume incorporates a substantial amount of the new analysis. Ten years later, the even more influential second edition followed the new point of view from its start. Volume 3 (1887) covers the integration of differential equations and the calculus of variations.

Jacob Steiner's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 1
  • Jakob Steiner
  • Edited by Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    03 October 2013
    First published in:
    1881
  • The Swiss mathematician Jakob Steiner (1796–1863) came from a poor background with an incomplete education, yet such was his mathematical talent that eventually the Prussian university system adapted itself to him rather than he to it. A geometer in an age dominated by analysts, he pursued his own interests in his own way. The elegant results which bear his name - including Steiner circles, systems and symmetrisation - are known to most mathematicians today. Considered by many to be the greatest geometer since Apollonius of Perga, Steiner did important work on systemising geometry, laying the foundation for much later work on projective geometry. Edited by the eminent mathematician Karl Weierstrass (1815–97), this two-volume edition of Steiner's collected works offers scholars access to his influential writings in the original German. Volume 1 was published in 1881.

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 4
  • Carl Gustav Jacob Jacobi
  • Edited by Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1886
  • 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 4 appeared in 1886.

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 3
  • Carl Gustav Jacob Jacobi
  • Edited 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 by fellow German mathematician Karl Weierstrass (1815–97), Volume 3 appeared in 1884.

Oeuvres de Fourier
  • Publiées par les soins de Gaston Darboux
  • Volume 2
  • Jean Baptiste Joseph Fourier
  • Edited by Jean Gaston Darboux
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1890
  • Following the French Revolution, the physicist and mathematician Jean Baptiste Joseph Fourier (1768–1830) taught at the École Normale Supérieure and later succeeded Lagrange at the École Polytechnique. He was promoted to administrative positions under Napoleon, but continued to pursue his scientific interests. From 1822 until his death he served as the permanent secretary for mathematical sciences at the Académie des Sciences. These selected works were edited by the mathematician Jean Gaston Darboux (1842–1917) and published in two volumes between 1888 and 1890. Volume 2 contains several extraordinary contributions: the first paper to address the question of why the earth's surface is warm (which we now call the greenhouse effect), the first paper to address the cooling of the earth's interior (still a major research topic) and the first paper on optimisation under linear constraints, along with the results on roots of polynomials which first made Fourier's reputation.

Die Ausdehnungslehre
  • Vollständig und in strenger Form bearbeitet
  • Hermann Grassmann
  • Published online:
    05 October 2014
    Print publication:
    16 October 2013
  • In 1844, the Prussian schoolmaster Hermann Grassmann (1809–77) published Die Lineale Ausdehnungslehre (also reissued in the Cambridge Library Collection). This revolutionary work anticipated the modern theory of vector spaces and exterior algebras. It was little understood at the time and the few sympathetic mathematicians, rather than trying harder to comprehend it, urged Grassmann to write an extended version of his theories. The present work is that version, first published in 1862. However, this also proved too far ahead of its time and Grassmann turned to historical linguistics, in which field his contributions are still remembered. His mathematical work eventually found champions such as Hankel, Peano, Whitehead and Élie Cartan, and it is now recognised for the brilliant achievement that it was in the history of mathematics.

Mathematische Werke
  • Herausgegeben unter Mitwirkung einer von der königlich preussischen Akademie der Wissenschaften eingesetzten Commission
  • Volume 6
  • Karl Weierstrass
  • Edited by Rudolf Rothe
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1915
  • 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 6 was published in 1915.

C. G. J. Jacobi's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 1
  • Carl Gustav Jacob Jacobi
  • Edited by C. W. Borchardt
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1881
  • 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 Carl Wilhelm Borchardt (1817–80), Volume 1 appeared in 1881.

The Doctrine of Chances
  • Or, a Method of Calculating the Probability of Events in Play
  • Abraham de Moivre
  • Published online:
    05 October 2014
    Print publication:
    27 June 2013
    First published in:
    1738
  • A Huguenot exile in England, the French mathematician Abraham de Moivre (1667–1754) formed friendships with such luminaries as Edmond Halley and Isaac Newton. Making his living from private tuition, he became a fellow of the Royal Society in 1697 and published papers on a range of topics. Probability theory had been pioneered by Pascal, Fermat and Huygens, with further development by the Bernoullis. Originally published in 1718, The Doctrine of Chances was the first English textbook on the new science and so influential that for a time the whole subject was known by the title of the work. Reissued here is the revised and expanded 1738 second edition which contains the remarkable discovery that when a coin is tossed many times, the binomial distribution may be approximated by the normal distribution. This version of the central limit theorem stands as one of de Moivre's most significant contributions to mathematics.

Oeuvres de Fourier
  • Publiées par les soins de Gaston Darboux
  • Volume 1
  • Jean Baptiste Joseph Fourier
  • Edited by Jean Gaston Darboux
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1888
  • Following the French Revolution, the physicist and mathematician Jean Baptiste Joseph Fourier (1768–1830) taught at the École Normale Supérieure and later succeeded Lagrange at the École Polytechnique. He was promoted to administrative positions under Napoleon, but continued to pursue his scientific interests. From 1822 until his death he served as the permanent secretary for mathematical sciences at the Académie des Sciences. Thanks to his substantial contributions to the field, Fourier's name has passed as an adjective into the mathematical vocabulary of every major language. These selected works were edited by the mathematician Jean Gaston Darboux (1842–1917) and published in two volumes between 1888 and 1890. Volume 1 is given over entirely to the immortal Théorie analytique de la chaleur (1822), from which the world learnt about the heat equation and the series which bears Fourier's name.

Mathematical Papers of the Late George Green
  • George Green
  • Edited by N. M. Ferrers
  • Published online:
    05 October 2014
    Print publication:
    13 February 2014
  • A miller's son, George Green (1793–1841) received little formal schooling yet managed to acquire significant knowledge of modern mathematics, especially French work. In 1828 he published his Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, the work for which he is now celebrated. Admitted to Cambridge in 1833 as a mature student, Green went on to become a fellow of Gonville and Caius College. His early death, however, cut short a promising career as a mathematical physicist. While English contemporaries saw what he might have achieved, they did not understand what he had actually achieved. Only when William Thomson (later Lord Kelvin) rediscovered Green's first publication and shared it with the French mathematical elite was his greatness truly appreciated. Edited by the Cambridge mathematician Norman Macleod Ferrers (1829–1903) and published in 1871, this collection comprises Green's influential essay and nine further papers.

Mathematische Werke
  • Herausgegeben unter Mitwirkung einer von der königlich preussischen Akademie der Wissenschaften eingesetzten Commission
  • Volume 2
  • Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    18 April 2013
    First published in:
    1895
  • 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. Volume 2 was published in 1895.

Jacob Steiner's Gesammelte Werke
  • Herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften
  • Volume 2
  • Jakob Steiner
  • Edited by Karl Weierstrass
  • Published online:
    05 October 2014
    Print publication:
    03 October 2013
    First published in:
    1882
  • The Swiss mathematician Jakob Steiner (1796–1863) came from a poor background with an incomplete education, yet such was his mathematical talent that eventually the Prussian university system adapted itself to him rather than he to it. A geometer in an age dominated by analysts, he pursued his own interests in his own way. The elegant results which bear his name - including Steiner circles, systems and symmetrisation - are known to most mathematicians today. Considered by many to be the greatest geometer since Apollonius of Perga, Steiner did important work on systemising geometry, laying the foundation for much later work on projective geometry. Edited by the eminent mathematician Karl Weierstrass (1815–97), this two-volume edition of Steiner's collected works offers scholars access to his influential writings in the original German. Volume 2 was published in 1882.

Popular Instructions on the Calculation of Probabilities
  • To Which Are Appended Notes by Richard Beamish
  • Lambert Adolphe Jacques Quetelet
  • Edited and translated by Richard Beamish
  • Published online:
    05 October 2014
    Print publication:
    19 September 2013
    First published in:
    1839
  • The Belgian polymath Lambert Adolphe Jacques Quetelet (1796–1874) was regarded by John Maynard Keynes as a 'parent of modern statistical method'. Applying his training in mathematics to the physical and psychological dimensions of individuals, his Treatise on Man (also reissued in this series) identified the 'average man' in statistical terms. Reissued here is the 1839 English translation of his 1828 work, which appeared at a time when the application of probability was moving away from gaming tables towards more useful areas of life. Quetelet believed that probability had more influence on human affairs than had been accepted, and this work marked his move from a focus on mathematics and the natural sciences to the study of statistics and, eventually, the investigation of social phenomena. Written as a summary of lectures given in Brussels, the work was translated from French by the engineer Richard Beamish (1798–1873).

Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass
  • Bernhard Riemann
  • Edited by Richard Dedekind, Heinrich Martin Weber
  • Published online:
    05 October 2014
    Print publication:
    03 October 2013
    First published in:
    1876
  • Great mathematicians write for the future and Georg Friedrich Bernhard Riemann (1826–66) was one of the greatest mathematicians of all time. Edited by Heinrich Martin Weber, with assistance from Richard Dedekind, this edition of his collected works in German first appeared in 1876. Riemann's interests ranged from pure mathematics to mathematical physics. He wrote a short paper on number theory which provided the key to the prime number theorem, and his zeta hypothesis has given mathematicians the most famous of today's unsolved problems. Moreover, his famous 1854 lecture 'On the hypotheses which underlie geometry' set in motion studies which culminated in Einstein's general theory of relativity. Even Riemann's over-optimistic use of the Dirichlet principle to prove the conformal mapping theorem turned out to be immensely fruitful. The alert reader will further profit from finding here the seeds of modern distribution theory, algebraic topology and measure theory.

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.

Page 2 of 10