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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 7 of 10

The Collected Mathematical Papers
  • Volume 6
  • Arthur Cayley
  • Published online:
    07 September 2011
    Print publication:
    20 July 2009
    First published in:
    1893
  • 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 33 papers published between 1865 and 1872.

Œuvres de Charles Hermite
  • Volume 2
  • Charles Hermite
  • Published online:
    07 September 2011
    Print publication:
    20 July 2009
    First published in:
    1908
  • 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.

Vollständige Anleitung zur Niedern und Höhern Algebra
  • Volume 2
  • Leonhard Euler
  • Published online:
    05 August 2011
    Print publication:
    20 July 2009
    First published in:
    1797
  • In 1770, one of the founders of pure mathematics, 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 the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Grüson, Professor of Mathematics to the royal cadets. Volume 2 consists of two parts: 16 chapters on algebraic equations, followed by 15 chapters on analyses of indeterminate quantities. Here, Euler shows the reader several ways to solve polynomial equations up to the fourth degree. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.

Vollständige Anleitung zur Niedern und Höhern Algebra
  • Volume 1
  • Leonhard Euler
  • Published online:
    05 August 2011
    Print publication:
    20 July 2009
    First published in:
    1796
  • In 1770, one of the founders of pure mathematics, 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 the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Grüson, Professor of Mathematics to the royal cadets. Volume 1 begins with elementary mathematics of determinate quantities and includes four sections on simple calculations (addition, subtraction, division, multiplication), and progresses to compound calculations (fractions), ratios and proportions. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively and international mathematical community that flourished despite the political uncertainties of the late eighteenth century.

Oeuvres complètes
  • Series 1
  • Volume 3
  • Augustin-Louis Cauchy
  • Published online:
    05 August 2011
    Print publication:
    20 July 2009
    First published in:
    1911
  • 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.

Elementary Principles in Statistical Mechanics
  • Developed with Especial Reference to the Rational Foundation of Thermodynamics
  • Josiah Willard Gibbs
  • Published online:
    05 August 2011
    Print publication:
    16 September 2010
    First published in:
    1902
  • Josiah Willard Gibbs (1839–1903) was the greatest American mathematician and physicist of the nineteenth century. He played a key role in the development of vector analysis (his book on this topic is also reissued in this series), but his deepest work was in the development of thermodynamics and statistical physics. This book, Elementary Principles in Statistical Mechanics, first published in 1902, gives his mature vision of these subjects. Mathematicians, physicists and engineers familiar with such things as Gibbs entropy, Gibbs inequality and the Gibbs distribution will find them here discussed in Gibbs' own words.

The Collected Mathematical Papers
  • Volume 5
  • Arthur Cayley
  • Published online:
    05 August 2011
    Print publication:
    20 July 2009
    First published in:
    1892
  • 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 84 papers, mostly published between 1861 and 1866.

Oeuvres complètes
  • Series 2
  • Volume 4
  • Augustin-Louis Cauchy
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1899
  • Augustin-Louis, Baron Cauchy (1789–1857) was the pre-eminent French mathematician of the nineteenth century. He began his career as a military engineer during the Napoleonic Wars, but even then was publishing significant mathematical papers, and was persuaded by Lagrange and Laplace to devote himself entirely to mathematics. His greatest contributions are considered to be the Cours d'analyse de l'École Royale Polytechnique (1821), Résumé des leçons sur le calcul infinitésimal (1823) and Leçons sur les applications du calcul infinitésimal à la géométrie (1826–8), and his pioneering work encompassed a huge range of topics, most significantly real analysis, the theory of functions of a complex variable, and theoretical mechanics. Twenty-six volumes of his collected papers were published between 1882 and 1958. The first series (volumes 1-12) consists of papers published by the Académie des Sciences de l'Institut de France; the second series (volumes 13-26) of papers published elsewhere.

Elements of Algebra
  • 3rd edition
  • Leonard Euler
  • Translated by John Hewlett
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1822
  • In 1770, one of the founders of pure mathematics, Swiss mathematician Leonard Euler (1707–1783), published Elements of Algebra, a mathematics textbook for students. This edition of Euler's classic, published in 1822, is an English translation which includes notes added by Euler's tutor, Johann Bernoulli, and additions by Joseph-Louis Lagrange, both giants in eighteenth-century mathematics, as well as a short biography of Euler. Part 1 begins with elementary mathematics of determinate quantities and includes four sections on simple calculations (adding, subtracting, division, multiplication), and then progresses to compound calculations (fractions), ratios and proportions and algebraic equations. Part 2 consists of 15 chapters on analyses of indeterminate quantities. Here, Euler shows the reader several ways to solve polynomial equations up to the fourth degree. This landmark book showed students the beauty of mathematics, and more significantly, how to do it.

Principles of Geometry
  • Volume 3, Solid Geometry
  • H. F. Baker
  • Published online:
    05 July 2011
    Print publication:
    31 October 2010
    First published in:
    1923
  • Henry Frederick Baker (1866–1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the third volume, describes the principal configurations of space of three dimensions.

Principles of Geometry
  • Volume 5, Analytical Principles of the Theory of Curves
  • H. F. Baker
  • Published online:
    05 July 2011
    Print publication:
    31 October 2010
    First published in:
    1933
  • Henry Frederick Baker (1866–1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the fifth volume, describes the birational geometry of curves.

Principles of Geometry
  • Volume 1, Foundations
  • H. F. Baker
  • Published online:
    05 July 2011
    Print publication:
    31 October 2010
    First published in:
    1922
  • Henry Frederick Baker (1866–1956) was a renowned British mathematician specialising in algebraic geometry. He was elected a Fellow of the Royal Society in 1898 and appointed the Lowndean Professor of Astronomy and Geometry in the University of Cambridge in 1914. First published between 1922 and 1925, the six-volume Principles of Geometry was a synthesis of Baker's lecture series on geometry and was the first British work on geometry to use axiomatic methods without the use of co-ordinates. The first four volumes describe the projective geometry of space of between two and five dimensions, with the last two volumes reflecting Baker's later research interests in the birational theory of surfaces. The work as a whole provides a detailed insight into the geometry which was developing at the time of publication. This, the first volume, describes the foundations of projective geometry.

The New Quantum Mechanics
  • George Birtwistle
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1928
  • George Birtwistle (1877–1929) published The New Quantum Mechanics in 1928. His stated aim was to give a detailed account of work which had brought the relatively new subject of quantum mechanics to the fore in the previous few years. The earlier chapters give a restatement of Alfred Landé's theory of multiplets which reconciles it with the new mechanics which follow. Later chapters present the matrix theory of Heisenberg, the q-number theory of Dirac and the wave mechanics of Schroedinger, and synthesise new theories, statistics and controversies in the work of de Broglie, Bose, Einstein, Fermi and Dirac. The book gives a complete overview of the state of quantum mechanics at the end of the second decade of the twentieth century, making it a valuable benchmark for historians of science and mathematicians alike.

The Collected Mathematical Papers
  • Volume 13
  • Arthur Cayley
  • Published online:
    05 July 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 final volume contains 80 papers published between 1889 and 1895.

Scientific Papers
  • Volume 1, 1869–1881
  • John William Strutt
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1899
  • Lord Rayleigh (1842–1919) won the Nobel Prize for physics in 1904. His early research was in optics and acoustics but his first published paper, from 1869, was an explanation of Maxwell's electromagnetic theory. In 1871, he related the degree of light scattering to wavelength (part of the explanation for why the sky is blue), and in 1872 he wrote his classic Theory of Sound (not included here). He became a Fellow of the Royal Society and inherited his father's peerage in 1873. Rayleigh nevertheless continued groundbreaking research, including the first description of Moiré interference (1874). In 1881, while president of the London Mathematical Society (1878–1880) and successor to Maxwell as Cavendish Professor of Experimental Physics at Cambridge (1879–1884), Rayleigh published a paper on diffraction gratings which led to improvements in the spectroscope and future developments in high-resolution spectroscopy. This volume contains papers from 1869 to 1881.

Scientific Papers
  • Volume 3, 1887–1892
  • John William Strutt
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1902
  • This volume includes papers from 1887, when Lord Rayleigh became Professor of Natural Philosophy at the Royal Institution in London, to 1892. An 1888 contribution on the densities of hydrogen and oxygen led to a series of experiments on the densities of the atmospheric gases. This resulted in the unsettling discovery that the density of atmospheric nitrogen seemed very slightly to exceed the density of nitrogen derived from its chemical compounds. A substantial 1888 paper, on the wave theory of light, was written for the Encyclopaedia Britannica in the immediate aftermath of the crucial Michelson–Morley experiment in which the speed of light had been measured. In addition, this wide-ranging volume shows Rayleigh's developing interest in the properties of liquid surfaces, with a discourse on foams (1890), and a paper on surface films (1892). It also includes a charming brief appreciation (1890) of James Clerk Maxwell's legacy to science.

Scientific Papers
  • Volume 6, 1911–1919
  • John William Strutt
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1920
  • This final volume of papers by Lord Rayleigh covers the period from 1911 to his death in 1919. The first of the Solvay Conferences in 1911 played a key role in the foundation of quantum theory. Although invited, Rayleigh did not attend. His principal achievements lay in development and consolidation across classical physics, in which he continued to work. In a 1917 paper, he used electromagnetic theory to derive a formula for expressing the reflection properties from a regularly stratified medium. In 1919, he investigated the iridescent colours of birds and insects. Rayleigh continued his long-standing participation in the Society for Psychical Research, founded in 1882 for the study of 'debatable phenomena'. One of his last publications was his presidential address to that society, which considers several highly unorthodox views and practices. He concludes by asserting the importance to scientists of maintaining open minds in the pursuit of truth.

Scientific Papers
  • Volume 4, 1892–1901
  • John William Strutt
  • Published online:
    05 July 2011
    Print publication:
    20 July 2009
    First published in:
    1903
  • This volume of Lord Rayleigh's collected papers begins with a brief 1892 piece in which the author addresses the troubling discrepancies between the apparent density of nitrogen derived from different sources. Intrigued by this anomaly and by earlier observations by Cavendish, Rayleigh investigated whether it might be due to a previously undiscovered atmospheric constituent. This led to Rayleigh's discovery of the chemically inert element, argon, to his 1904 Nobel Prize in physics, and to the discovery of all the 'rare' gases. Debate over the nature of Roentgen rays, is reflected in a short 1898 paper, written in the wake of their discovery. 1900 saw a key contribution, the elegant description of the distribution of longer wavelengths in blackbody radiation. Now known as the Rayleigh–Jeans' Law, this complemented Wien's equation describing the shorter wavelengths. Planck's law combined these, in a crucial step toward the eventual development of quantum mechanics.

Mathematical and Physical Papers
  • Volume 5
  • George Gabriel Stokes
  • Published online:
    01 June 2011
    Print publication:
    20 July 2009
    First published in:
    1905
  • Sir George Stokes (1819–1903) established the science of hydrodynamics with his law of viscosity describing the velocity of a small sphere through a viscous fluid. He published no books, but was a prolific lecturer and writer of papers for the Royal Society, the British Association for the Advancement of Science, the Victoria Institute and other mathematical and scientific institutions. These collected papers (issued between 1880 and 1905) are therefore the only readily available record of the work of an outstanding and influential mathematician, who was Lucasian Professor of Mathematics in Cambridge for over fifty years, Master of Pembroke College, President of the Royal Society (1885–1890), Associate Secretary of the Royal Commission on the University of Cambridge and a Member of Parliament for the University.

Statics
  • Including Hydrostatics and the Elements of the Theory of Elasticity
  • 3rd edition
  • Horace Lamb
  • Published online:
    01 June 2011
    Print publication:
    20 July 2009
    First published in:
    1912
  • Sir Horace Lamb (1849–1934) the British mathematician, wrote a number of influential works in classical physics. A pupil of Stokes and Clerk Maxwell, he taught for ten years as the first professor of mathematics at the University of Adelaide before returning to Britain to take up the post of professor of physics at the Victoria University of Manchester (where he had first studied mathematics at Owens College). As a teacher and writer his stated aim was clarity: 'somehow to make these dry bones live'. His Statics was first published in 1912, and the third edition, offered here, in 1928. It was intended as a textbook for students with some knowledge of mechanics, and deals mainly with two-dimensional problems: examples are provided at the end of each section.

Page 7 of 10