Cambridge Library Collection - Mathematics – serie
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183 produkter
183 produkter
The Mathematical Analysis of Logic
Being an Essay Towards a Calculus of Deductive Reasoning
Häftad, Engelska, 2009
277 kr
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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.
398 kr
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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.
Babbage's Calculating Engines
Being a Collection of Papers Relating to them; their History and Construction
Häftad, Engelska, 2010
452 kr
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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.
573 kr
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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.
An Investigation of the Laws of Thought
On Which Are Founded the Mathematical Theories of Logic and Probabilities
Häftad, Engelska, 2009
587 kr
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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.
654 kr
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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.
398 kr
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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 probabilités, 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.
829 kr
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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 École 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 Eléments de géométrie, which remained a textbook for over 100 years. The first edition of his Essai sur la théorie 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.
587 kr
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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 Mécanique 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.
573 kr
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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 Mécanique 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.
654 kr
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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.
735 kr
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French mathematician Joseph Fourier's Théorie 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.
Leçons sur l'intégration et la recherche des fonctions primitives professées au Collège de France
Häftad, Franska, 2009
371 kr
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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.
371 kr
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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.
492 kr
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In 1770, one of the founders of pure mathematics, Leonard Euler (1707-1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Grüson, Professor of Mathematics to the royal cadets. Volume 1 begins with elementary mathematics of determinate quantities and includes four sections on simple calculations (addition, subtraction, division, multiplication), and progresses to compound calculations (fractions), ratios and proportions. This landmark book showed students the beauty of mathematics, and more significantly, how to do it. It provides tangible evidence of the lively and international mathematical community that flourished despite the political uncertainties of the late eighteenth century.
533 kr
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In 1770, one of the founders of pure mathematics, Leonard Euler (1707-1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of the English edition of 1822 (which also appears in this series), and of this 1790s German edition by Johann Philipp Grüson, Professor of Mathematics to the royal cadets. Volume 2 consists of two parts: 16 chapters on algebraic equations, followed by 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. It provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.
398 kr
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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.
829 kr
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In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'École 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.
519 kr
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The work of the Marquis de Laplace (1749-1827) was enormously influential on the development of mathematical physics, astronomy and statistics. His Exposition du système 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 Académie Française. 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 Traité de Mécanique Céleste, of which Mary Somerville's English version is also reissued in this series.
492 kr
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In 1770, one of the founders of pure mathematics, the Swiss-born mathematician Leonard Euler (1707-1783), published an algebra textbook for students. It was soon translated into French, with notes and additions by Joseph-Louis Lagrange, another giant of eighteenth-century mathematics, and the French edition was used as the basis of this three-volume 1790s German edition. Volume 3 consists of the German translation of Lagrange's additional material, which the German publisher printed in a separate volume to enable those who already owned Euler's Algebra to obtain the supplementary material 'without incurring unnecessary expenditure'. The translator (the tutor to the sons of the Duke of Württemberg) added notes and further appendices of his own. This book provides tangible evidence of the lively international mathematical community that flourished despite the political uncertainties of the late eighteenth century.
735 kr
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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 ... 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.
398 kr
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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.
492 kr
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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.
533 kr
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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.
573 kr
Skickas inom 7-10 vardagar
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.
533 kr
Skickas inom 7-10 vardagar
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.
654 kr
Skickas inom 7-10 vardagar
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 ... 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.
533 kr
Skickas inom 7-10 vardagar
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.
735 kr
Skickas inom 7-10 vardagar
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 ... 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.
829 kr
Skickas inom 7-10 vardagar
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 ... 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.