Böcker i Cambridge Library Collection - Mathematics-serien

Originally published between 1880 and 1886, this two-volume work by George Shoobridge Carr (1837-1914) was intended as an aid to students preparing for the Cambridge Mathematical Tripos. Most notably, it played an important part in the mathematical education of the Indian prodigy Srinivasa Ramanujan (1887-1920).

The mathematician Charles Babbage (1791-1871) was one of the most original thinkers of the nineteenth century. In this influential 1830 publication, he criticises the continued failure of government to support science and scientists. In addition, he identifies the weaknesses of the then existing scientific societies, saving his most caustic remarks for the Royal Society. Asserting that the societies were operated largely by small groups of amateurs possessing only superficial interest and knowledge of science, Babbage explores the importance of the relationships between science, technology and society. Exposing the absence of a true scientific culture, he states, 'The pursuit of science does not, in England, constitute a distinct profession, as it does in other countries.' These concerns found favour with many, influencing reforms of the Royal Society and leading to the founding of the British Association.

Successful long-distance navigation depends on knowing latitude and longitude, and the determination of longitude depends on knowing the exact time at some fixed point on the earth's surface. Since Newton it had been hoped that a method based on accurate prediction of the moon's orbit would give such a time. Building on the work of Euler, Thomas Mayer and others, the astronomer and mathematician Nevil Maskelyne (1732-1811) was able to devise such a method and yearly publication of the Nautical Almanac and Astronomical Ephemeris placed it in the hands of every ship's captain. First published in 1767 and reissued here in the revised third edition of 1802, the present work provided the necessary tables and instructions. The development of rugged and accurate chronometers eventually displaced Maskelyne's method, but navigators continued to make use of it for many decades. This edition of the tables notably formed part of the library of the Beagle on Darwin's famous voyage.

Described by one reviewer as 'one of the most perfect books ever written on theoretical astronomy', this work in Latin by the German mathematician Carl Friedrich Gauss (1777-1855), the 'Prince of Mathematicians', derived from his attempt to solve an astronomical puzzle: where in the heavens would the dwarf planet Ceres, first sighted in 1801, reappear? Gauss' predicted position was correct to within half a degree, and this led him to develop a streamlined and sophisticated method of calculating the effect of the larger planets and the sun on the orbits of planetoids, which he published in 1809. As well as providing a tool for astronomers, Gauss' method also offered a way of reducing inaccuracy of calculations arising from measurement error; the primacy of this discovery was however disputed between him and the French mathematician Legendre, whose Essai sur la theorie des nombres 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.

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.

The Cambridge polymath Isaac Barrow (1630-77) was Lucasian Professor of Mathematics between 1663 and 1669. This one-volume collection of his mathematical writings in Latin was first published in 1860. It includes the first general statement of the fundamental theorem of calculus as well as Barrow's 'differential triangle'.

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.

Originally published between 1880 and 1886, this two-volume work by George Shoobridge Carr (1837-1914) was intended as an aid to students preparing for the Cambridge Mathematical Tripos. Most notably, it played an important part in the mathematical education of the Indian prodigy Srinivasa Ramanujan (1887-1920).

This three-volume German edition of the groundbreaking 1770 algebra textbook by the Swiss-born mathematician Leonard Euler (1707-1783) draws heavily upon additional material by Joseph-Louis Lagrange that appeared in an early French translation. Volume 2 contains material on algebraic equations and on analyses of indeterminate quantities.

An important figure in mathematical logic and abstract algebra, Augustus De Morgan (1806-71) also wrote wittily on paradoxical and illogical thinking through time. Edited by his widow and published in 1872, this entertaining work parades all varieties of crackpot, from circle-squarers to inventors of perpetual motion machines.

Published in 1810, this report on the current state of mathematics was commissioned by Napoleon I and written by French mathematician and astronomer Jean-Baptiste Delambre (1749-1822). It presents an overview of progress during Napoleon's reign in the fields of geometry, algebra, astronomy and geography.

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.

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.

From short notes to major treatises, this twelve-volume collection contains the complete scientific works of the German mathematician, physicist and astronomer Carl Friedrich Gauss (1777-1855). Volume 3, which appeared in 1866, focuses on analysis and includes Gauss' first (1799) proof of the fundamental theorem of algebra.

From short notes to major treatises, this twelve-volume collection contains the complete scientific works of the German mathematician, physicist and astronomer Carl Friedrich Gauss (1777-1855). Volume 4, published in 1873, focuses on probability, differential geometry and topography, and includes data from Gauss' geodesic surveys of the Kingdom of Hanover.

Sir George Stokes 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, and these collected papers (issued between 1880 and 1905) constitute the main surviving record of the work of this outstanding mathematician.

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.

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.

One of the nineteenth century's greatest mathematicians, Carl Jacobi (1804-51) did important work on elliptic functions, rational mechanics, number theory and partial differential equations. His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891.

Considered by many to be the greatest geometer since Apollonius of Perga, the Swiss mathematician Jakob Steiner (1796-1863) did important work on systemising geometry. This two-volume edition of his collected works in German was edited by Karl Weierstrass (1815-97) and published between 1881 and 1882.

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.

Henry Frederick Baker (1866-1956) was a renowned British mathematician specialising in algebraic geometry. First published between 1922 and 1925, this six-volume work provides a detailed insight into the geometry which was developing at the time of publication. Volume 1 describes the foundations of projective geometry.