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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 9 of 10

Mathematical and Physical Papers
  • Volume 3
  • George Gabriel Stokes
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1901
  • 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.

Mathematical and Physical Papers
  • Volume 1
  • George Gabriel Stokes
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1880
  • 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.

A History of the Study of Mathematics at Cambridge
  • Walter William Rouse Ball
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1889
  • For centuries, Cambridge University has attracted some of the world's greatest mathematicians. This 1889 book gives a compelling account of how mathematics developed at Cambridge from the middle ages to the late nineteenth century, from the viewpoint of a leading scholar based at Trinity College who was closely involved in teaching the subject. The achievements of notable individuals including Newton and his school are set in the context of the history of the university, its sometimes uneasy relationship with the town community, the college system, and the origin and growth of the mathematical tripos.

Dynamics
  • A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities
  • Arthur Stanley Ramsey
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1929
  • A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on dynamics, published in 1929, was based upon his lectures to students of the mathematical tripos, and reflects the way in which this branch of mathematics had expanded in the first three decades of the twentieth century. It assumes some knowledge of elementary dynamics, and contains an extensive collection of examples for solution, taken from scholarship and examination papers of the period. The subjects covered include vectors, rectilinear motion, harmonic motion, motion under constraint, impulsive motion, moments of inertia and motion of a rigid body. Ramsey published a companion volume, Statics, in 1934.

Statics
  • A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities
  • Arthur Stanley Ramsey
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1934
  • A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on statics, published in 1934, was intended as a companion volume to his Dynamics of 1929 and like the latter was based upon his lectures to students of the mathematical tripos, but it assumes no prior knowledge of the subject, provides an introduction and offers more that 100 example problems with their solutions. Topics include vectors, forces acting at a point, moments, friction, centres of gravity, work and energy, and elasticity.

Electricity and Magnetism
  • An Introduction to the Mathematical Theory
  • Arthur Stanley Ramsey
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1937
  • A. S. Ramsey (1867–1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first-year students at university'. This book on electricity and magnetism, first published in 1937, and based upon his lectures over many years, was 'adapted more particularly to the needs of candidates for Part I of the Mathematical Tripos'. It covers electrostatics, conductors and condensers, dielectrics, electrical images, currents, magnetism and electromagnetism, and magnetic induction. The book is interspersed with examples for solution, for some of which answers are provided.

An Elementary Course of Infinitesimal Calculus
  • Horace Lamb
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1897
  • 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'. The first edition of this work was published in 1897, the third revised edition in 1919, and a further corrected version just before his death. This edition, reissued here, remained in print until the 1950s. As with Lamb's other textbooks, each section is followed by examples.

Treatise on Natural Philosophy
  • Volume 1, 2nd edition
  • William Thomson, Peter Guthrie Tait
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1883
  • 'The term 'natural philosophy' was used by Newton, and is still used in British Universities, to denote the investigation of laws in the material world, and the deduction of results not directly observed.' This definition, from the Preface to the second edition of 1879, defines the proposed scope of the work: the two volumes reissued here are the only completed part of a survey of the entirety of the physical sciences by Lord Kelvin and his fellow Scot, Peter Guthrie Tait, first published in 1867. Although the partnership ceased after eighteen years of collaboration, the published books, containing chapters on kinematics, dynamics and statics, had a great influence on the development of physics in the second half of the nineteenth century.

Dynamics
  • 2nd edition
  • Horace Lamb
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1923
  • 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 Dynamics was first published in 1914 and the second edition, offered here, in 1923: it remained in print until the 1960s. It was intended as a sequel to his Statics (also reissued in this series), and like its predecessor is a textbook with examples.

Treatise on Natural Philosophy
  • Volume 2, 2nd edition
  • William Thomson, Peter Guthrie Tait
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1883
  • 'The term 'natural philosophy' was used by Newton, and is still used in British Universities, to denote the investigation of laws in the material world, and the deduction of results not directly observed.' This definition, from the Preface to the second edition of 1879, defines the proposed scope of the work: the two volumes reissued here are the only completed part of a survey of the entirety of the physical sciences by Lord Kelvin and his fellow Scot, Peter Guthrie Tait, first published in 1867. Although the partnership ceased after eighteen years of collaboration, the published books, containing chapters on kinematics, dynamics and statics, had a great influence on the development of physics in the second half of the nineteenth century.

The Theory of Sets of Points
  • William Henry Young, Grace Chisholm Young
  • Published online:
    07 September 2010
    Print publication:
    20 July 2009
    First published in:
    1906
  • The theory of sets, described in the preface to this book as 'Georg Cantor's magnificent theory' was first developed in the 1870s, and was recognised as one of the most important new branches of mathematical science. W. H. Young and his wife Grace Chisholm Young wrote this book, published in 1906, as a 'simple presentation'; but they warn that it is effectively a work in progress: the writing 'has necessarily involved attempts to extend the frontier of existing knowledge, and to fill in gaps which broke the connexion between isolated parts of the subject.' The Young's were a dynamic force in mathematical research: William had been Grace's tutor at Girton College; she was subsequently the first woman to be awarded a Ph. D by the University of Göttingen. Cantor himself said of the book: 'It is a pleasure for me to see with what diligence, skill and success you have worked.'

The Analytical Theory of Heat
  • Jean Baptiste Joseph Fourier
  • Translated by Alexander Freeman
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1878
  • First published in 1878, The Analytical Theory of Heat is Alexander Freeman's English translation of French mathematician Joseph Fourier's Théorie Analytique de la Chaleur, originally published in French in 1822. In this groundbreaking study, arguing that previous theories of mechanics advanced by such scientific greats as Archimedes, Galileo, Newton and their successors did not explain the laws of heat, Fourier set out to study the mathematical laws governing heat diffusion and proposed that an infinite mathematical series may be used to analyse the conduction of heat in solids. Known in scientific circles as the 'Fourier Series', this work paved the way for modern mathematical physics. This translation, now reissued, contains footnotes that cross-reference other writings by Fourier and his contemporaries, along with 20 figures and an extensive bibliography. This book will be especially useful for mathematicians who are interested in trigonometric series and their applications.

Oeuvres complètes
  • Series 2
  • Volume 3
  • Augustin-Louis Cauchy
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1897
  • 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.

The Mathematical Analysis of Logic
  • Being an Essay Towards a Calculus of Deductive Reasoning
  • George Boole
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1847
  • Self-taught mathematician George Boole (1815–1864) published a pamphlet in 1847 – The Mathematical Analysis of Logic – that launched him into history as one of the nineteenth century's most original thinkers. In the introduction, Boole closely adheres to two themes: the fundamental unity of all science and the close relationship between logic and mathematics. In the first chapter, he examines first principles of formal logic, and then moves on to Aristotelian syllogism, hypotheticals, and the properties of elective functions. Boole uses this pamphlet to answer a well-known logician of the day, Sir William Hamilton, who believed that only philosophers could study 'the science of real existence', while all mathematicians could do was measure things. In essence, The Mathematical Analysis of Logic humbly chides Hamilton and asks him to rethink his bias. Boole is compelling reading for anyone interested in intellectual history and the science of the mind.

Leçons sur les Séries Trigonométriques Proféssees au College de France
  • Henri Lebesgue
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1906
  • The two great works of the celebrated French mathematician Henri Lebesgue (1875–1941), Leçons sur l'intégration et la recherche des fonctions primitives professées au Collège de France (1904) and Leçons sur les séries trigonométriques professées au Collège de France (1906) arose from lecture courses he gave at the Collège de France while holding a teaching post at the University of Rennes. In 1901 Lebesgue formulated measure theory; and in 1902 his new definition of the definite integral, which generalised the Riemann integral, revolutionised integral calculus and greatly expanded the scope of Fourier analysis. The Lebesgue integral is regarded as one of the major achievements in modern real analysis, and remains central to the study of mathematics today. Both of Lebesgue's books are reissued in this series.

Euclid and His Modern Rivals
  • Charles L. Dodgson
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1879
  • Euclid and His Modern Rivals is a deeply convincing testament to the Greek mathematician's teachings of elementary geometry. Published in 1879, it is humorously constructed and written by Charles Dodgson (better known outside the mathematical world as Lewis Carroll, the author of Alice in Wonderland) in the form of an intentionally unscientific dramatic comedy. Dodgson, mathematical lecturer at Christ Church, Oxford, sets out to provide evidentiary support for the claim that The Manual of Euclid is essentially the defining and exclusive textbook to be used for teaching elementary geometry. Euclid's sequence and numbering of propositions and his treatment of parallels, states Dodgson, make convincing arguments that the Greek scholar's text stands alone in the field of mathematics. The author pointedly recognises the abundance of significant work in the field, but maintains that none of the subsequent manuals can effectively serve as substitutes to Euclid's early teachings of elementary geometry.

Leçons sur l'intégration et la recherche des fonctions primitives professées au Collège de France
  • Henri Leon Lebesgue
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1904
  • The two great works of the celebrated French mathematician Henri Lebesgue (1875–1941), Leçons sur l'intégration et la recherche des fonctions primitives professées au Collège de France (1904) and Leçons sur les séries trigonométriques professées au Collège de France (1906) arose from lecture courses he gave at the Collège de France while holding a teaching post at the University of Rennes. In 1901 Lebesgue formulated measure theory; and in 1902 his new definition of the definite integral, which generalised the Riemann integral, revolutionised integral calculus and greatly expanded the scope of Fourier analysis. The Lebesgue integral is regarded as one of the major achievements in modern real analysis, and remains central to the study of mathematics today. Both of Lebesgue's books are reissued in this series.

A Treatise on Universal Algebra
  • With Applications
  • Alfred North Whitehead
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1898
  • Alfred North Whitehead (1861–1947) was equally celebrated as a mathematician, a philosopher and a physicist. He collaborated with his former student Bertrand Russell on the first edition of Principia Mathematica (published in three volumes between 1910 and 1913), and after several years teaching and writing on physics and the philosophy of science at University College London and Imperial College, was invited to Harvard to teach philosophy and the theory of education. A Treatise on Universal Algebra was published in 1898, and was intended to be the first of two volumes, though the second (which was to cover quaternions, matrices and the general theory of linear algebras) was never published. This book discusses the general principles of the subject and covers the topics of the algebra of symbolic logic and of Grassmann's calculus of extension.

Oeuvres complètes
  • Series 2
  • Volume 13
  • Augustin-Louis Cauchy
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1932
  • 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.

A Treatise on the Calculus of Finite Differences
  • George Boole
  • Published online:
    29 August 2010
    Print publication:
    20 July 2009
    First published in:
    1860
  • Self-taught mathematician and father of Boolean algebra, George Boole (1815–1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations of partial and mixed differences. Boole also includes exercises for daring students to ponder, and also supplies answers. Long a proponent of positioning logic firmly in the camp of mathematics rather than philosophy, Boole was instrumental in developing a notational system that allowed logical statements to be symbolically represented by algebraic equations. One of history's most insightful mathematicians, Boole is compelling reading for today's student of logic and Boolean thinking.

Page 9 of 10