Bücher der Reihe Cambridge Library Collection - Mathematics

Sir James Jeans has used his remarkable gifts of exposition to set out all that is relevant in the science of acoustics to the art of music. He offers a simple but precise account (illustrated with well-chosen photographs and diagrams) of the anatomical origin and workings of the human ear; the nature of sound vibrations; simple tones and complex sounds; the principles and operation of musical instruments; harmony and the musical scale; the effects of music on men and animals; and the practical problems of acoustical design. Scientists who appreciate music, musicians with an interest in science and laymen who care for both, will thoroughly enjoy this book.

The famous and prolific nineteenth-century mathematician, engineer and inventor Charles Babbage (1791-1871) was an early pioneer of computing. He planned several calculating machines, but none was built in his lifetime. On his death his youngest son, Henry P. Babbage, was charged with the task of completing an unfinished volume of papers on the machines, which was finally published in 1889 and is reissued here. The papers, by a variety of authors, were collected from journals including The Philosophical Magazine, The Edinburgh Review and Scientific Memoirs. They relate to the construction and potential application of Charles Babbage's calculating engines, notably the Difference Engine and the more complex Analytical Engine, which was to be programmed using punched cards. The book also includes correspondence with members of scientific societies, as well as proceedings, catalogues and drawings. Included is a complete catalogue of the drawings of the Analytical Engine.

The British physicist Sir Joseph John Thomson, the discoverer of the electron, published the first edition of his Elements of the Mathematical Theory of Electricity and Magnetism in 1895; this fourth edition was issued in 1909, three years after he was awarded the Nobel Prize in Physics for his theoretical and experimental investigations on the conduction of electricity by gases. In this book for students his intention is to give 'an account of the fundamental principles of the mathematical theory of electricity and magnetism and their more important applications, using only simple mathematics.' Starting at the basic level of describing electrical phenomena such as rubbing a stick of sealing wax with cloth to produce a charge, he guides the reader through electrostatics, induction, magnetism, thermoelectric currents and the theory of light. This textbook, by one of the greatest scientists of his day, is still a fascinating introduction to the topic.

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.

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.

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.

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.

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 Lande'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.

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.

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 Gottingen. Cantor himself said of the book: 'It is a pleasure for me to see with what diligence, skill and success you have worked.'

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.

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.

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.

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.

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.

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.

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.

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.

These selected works by French physicist and mathematician Joseph Fourier (1768-1830) were published in two volumes in 1888-90. Volume 1 is given over entirely to the immortal Theorie analytique de la chaleur (1822), from which the world learnt about the heat equation and the series which bears Fourier's name.

Originally published in 1881, this is the first volume of the collected works of the Norwegian mathematician Niels Henrik Abel (1802-29). It contains many of Abel's fundamental discoveries, including his proofs of the 'impossibility theorem' and the binomial theorem, and his famous 'Paris memoir' on elliptic functions.

Peter Dirichlet (1805-59) belonged to a network of influential French and German mathematicians, and his many achievements included foundational work in analytic number theory. These two volumes, which appeared in 1889-97, are a collection of all his published work, together with several unpublished papers and selected correspondence.

The German mathematician Karl Weierstrass (1815-97) is generally considered to be the father of modern analysis. This seven-volume edition of his collected mathematical works in German, published between 1894 and 1927, demonstrates his rigorous approach, which still dominates the first analysis course at any university.

The French mathematician Gerard Desargues (1591-1661) was one of the founders of projective geometry. His writings, published in two volumes in 1864 by Noel-Germinal Poudra (1794-1894), reveal Desargues' important role in the scientific debates of the seventeenth century. Volume 1 contains the majority of Desargues' treatises.