Joseph-Louis Lagrange (1736 1813), one of the notable French mathematicians of the Revolutionary period, is remembered for his work in the fields of analysis, number theory and mechanics. Like Laplace and Legendre, Lagrange was assisted by d'Alembert, and it was on the recommendation of the latter and the urging of Frederick the Great himself that Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin. The two-volume M canique analytique was first published in 1788; the edition presented here is that of 1811 15, revised by the author before his death. In this work, claimed to be the most important on classical mechanics since Newton, Lagrange developed the law of virtual work, from which single principle the whole of solid and fluid mechanics can be derived.

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

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.

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.

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.

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.

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.

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.

Mathematics has a reputation of being dull and difficult. Here is an antidote. This lively exploration of arithmetic considers its basic processes and manipulations, demonstrating their value and power and justifying an enduring interest in the subject. With humour and insight, the author shows how basic mathematics relates to everyday life - as true now as when this book was originally published in 1940. The introductory treatment of millions, billions and even trillions could be profitably read by aspiring bankers, economists or politicians. H. G. Wells is gently teased for his mistake in applying the law of proportionality in a novel. McKay politely adjusts the astronomical scales selected by the eminent cosmologist Sir James Jeans. He confidently navigates the hazards of averages, approximations and units. For anyone interested in what numbers mean and how they can be used most effectively, this book will still educate and delight.

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 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.

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.

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 Ecole Polytechnique, the Faculte des Sciences de Paris and the Ecole Normale Superieure 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.

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 Ecole Polytechnique, the Faculte des Sciences de Paris and the Ecole Normale Superieure 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.

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 Ecole Polytechnique, the Faculte des Sciences de Paris and the Ecole Normale Superieure 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.

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 Ecole Polytechnique, the Faculte des Sciences de Paris and the Ecole Normale Superieure 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.

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 first volume contains 100 papers published between 1841 and 1851.

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. Volume 3 contains 64 papers first published between 1857 and 1862.

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 by his successor in the Sadleirian Chair. This volume contains 76 papers published between 1856 and 1862, plus one from 1891.

Arthur Cayley (1821 1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge, qualified as a lawyer, and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he became 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 (while this volume was in the press) under the editorship of his successor in the Sadleirian Chair. This volume contains 70 papers published mostly between 1871 and 1873, as well as a 36-page obituary of the author.

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 74 papers, mostly published between 1874 and 1877.

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 93 papers mostly published between 1878 and 1883.

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 89 papers mostly published between 1883 and 1889.

Arthur Cayley (1821-1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge, 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 a complete listing of all the papers, and a thorough index of persons and topics from Abel to Zornow.

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.

Unparalleled in its depth of coverage, "The Princeton Companion to Mathematics" surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.Features nearly 200 entries, organized thematically and written by an international team of distinguished contributorsPresents major ideas and branches of pure mathematics in a clear, accessible styleDefines and explains important mathematical concepts, methods, theorems, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, algebra, analysis, geometry, logic, probability, and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, cross-references, and a comprehensive index

Contributors incude:

Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Bela Bollobas, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, Jose Ferreiros, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvea, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolo Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, Janos Kollar, T. W. Korner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-Francois Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lutzen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rudiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger"