Bücher der Reihe Cambridge Library Collection - Mathematics

Nobel laureate Lord Rayleigh was justifiably renowned for the clarity and quality of his work, which has had a continuing impact on modern science. This first of six chronological volumes of his most important scientific papers covers the period 1869-1881, including the early work relating light scattering to wavelength.

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. This edition is the second, published in 1879.

The work of the Marquis de Laplace (1749-1827) was enormously influential on the development of mathematical physics, astronomy and statistics. His Exposition du systeme du monde (first published in 1796) is often regarded as the most important book on mechanics after Newton's Principia Mathematica, and the elegance and clarity of its style won Laplace a seat in the Academie Francaise. The book, which was translated into English in 1809, was intended to 'offer a complete solution of the great mechanical problem presented by the solar system'. It was in this work that Laplace offered his nebular hypothesis, which proposed that the solar system originated from the contraction and cooling of a cloud of incandescent gas. The book, here in its second edition of 1799, is an introduction to Laplace's multi-volume masterpiece, the Traite de Mecanique Celeste, of which Mary Somerville's English version is also reissued in this series.

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.

Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind.

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.

The work of the Marquis de Laplace (1749-1827) was enormously influential in the development of mathematical physics, astronomy and statistics. Educated in Normandy, he moved to Paris on obtaining a letter of introduction to d'Alembert, who acted as his mentor while he undertook teaching and independent research in probability, statistics and astronomy. Laplace survived the turmoil of the French Revolution, the rise of Napoleon and the restoration of the Bourbons by a series of manoeuvres which gave him a reputation for insincerity and hypocrisy even among his peers who could correctly assess his contributions to science. His Essai philosophique sur les probabilites, first published in 1814, and of which the fifth edition, revised by the author, is presented here, is a fundamental work which establishes six principles of probability in mathematical terms.

Adrien-Marie Legendre (1752-1833), one of the great French mathematicians active in the Revolutionary period, made important contributions to number theory, statistics, mathematical analysis and algebra. He taught at the Ecole Militaire, where he was a colleague of Laplace, and made his name with a paper on the trajectory of projectiles which won a prize of the Berlin Academy in 1782, and brought him to the attention of Lagrange. In 1794 he published Elements de geometrie, which remained a textbook for over 100 years. The first edition of his Essai sur la theorie des nombres was published in 1798, and the much improved second edition, which is offered here, in 1808. In it Legendre had taken account of criticism by Gauss of the mathematical proofs in the first edition, though he was bitter at the manner in which his younger rival had claimed credit for some of his solutions.

First published in 1878, The Analytical Theory of Heat is Alexander Freeman's English translation of French mathematician Joseph Fourier's Theorie 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.

French mathematician Joseph Fourier's Theorie Analytique de la Chaleur was originally published in 1822. In this groundbreaking study, arguing that previous theories of mechanics advanced by such outstanding scientists 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: this is now known as the 'Fourier Series'. His work paved the way for modern mathematical physics. This book will be especially useful for mathematicians who are interested in trigonometric series and their applications, and it is reissued simultaneously with Alexander Freeman's English translation, The Analytical Theory of Heat, of 1878.

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.

In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'Ecole Royale Polytechnique, a textbook designed to teach his students the basic theorems of calculus in as rigorous a way as possible. Cauchy was a pioneer of mathematical analysis, a branch of mathematics concerned with the idea of a limit, whether of a sequence or of a function. This book consists of 12 chapters that discuss real functions, infinitely small and large quantities, substitution groups, symmetrical functions, unknown variables, imaginary functions, and rational fractions in a recurrent series. It also provides formulas for solving various problems, such as converting the sine and cosine of a multiple polynomial arc and the Lagrange interpolation. Cauchy built on the work of Leibniz and Newton and is generally regarded as one of the greatest mathematicians in history. This is a reissue of one of his most important contributions.

Baron Cauchy (1789-1857) was the pre-eminent French mathematician of the nineteenth century. He was a pioneer in 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.

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.

Published in 1874, this two-volume work by Isaac Todhunter (1820-84), perhaps the greatest Victorian historian of mathematics, takes an important mathematical story from Newton, through the expeditions which settled certain questions in Newton's favour, to the investigations of Laplace which opened a new era in mathematical physics.

An indefatigable mathematician and university teacher at Cambridge, Isaac Todhunter (1820-84) is best remembered for his successful textbooks. This 1865 publication traces the progress of probability theory from its roots in the seventeenth century through to the early nineteenth century and Pierre-Simon Laplace's wide-ranging coverage of the subject.

A largely self-educated mathematician, George Boole (1815-64) was widely recognised for his ability and became the first professor of mathematics at Cork. The influence of this 1859 work can still be traced in many modern treatments of differential equations and numerical analysis.

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820-84) became known in his time for his successful textbooks. Edited and completed by Karl Pearson (1857-1936), and published between 1886 and 1893, this three-part work traces the mathematical understanding of elasticity from Galileo to Lord Kelvin.

First published in 1795 and reissued here in its 1815 sixth edition, The Elements of Algebra by James Wood (1760-1839) was one of the standard Cambridge texts for decades, also accompanying Charles Darwin aboard the Beagle. It gives an interesting glimpse of the mathematical standards expected of undergraduates.

The French mathematician Abraham de Moivre (1667-1754) is remembered for his formula which relates complex numbers and trigonometry. Reissued here is the revised and expanded 1738 second edition of the influential textbook on probability theory that he first published in English in 1718.

Edward John Routh (1831-1907) was a highly successful mathematics coach at Cambridge. He also contributed to the foundations of control theory and to the modern treatment of mechanics. Published between 1896 and 1902, this revised two-volume textbook offers extensive coverage of statics, with formulae and examples throughout.

Edward John Routh (1831-1907) was a highly successful mathematics coach at Cambridge. He also contributed to the foundations of control theory and to the modern treatment of mechanics. Published in 1898, this textbook offers extensive coverage of dynamics, with formulae and examples throughout.