This book is the second volume of a study of the history of mathematics in the nineteenth century. The first part of the book describes the development of geometry. The many varieties of geometry are considered and three main themes are traced: the development of a theory of invariants and forms that determine certain geometric structures such as curves or surfaces; the enlargement of conceptions of space which led to non-Euclidean geometry; and the penetration of algebraic methods into geometry in connection with algebraic geometry and the geometry of transformation groups. The second part, on analytic function theory, shows how the work of mathematicians like Cauchy, Riemann and Weierstrass led to new ways of understanding functions. Drawing much of their inspiration from the study of algebraic functions and their integral, these mathematicians and others created a unified, yet comprehensive theory in which the original algebraic problems were subsumed in special areas devoted to elliptic, algebraic, Abelian and automorphic functions. The use of power series expansions made it possible to include completely general transcendental functions in the same theory and opened up the study of the very fertile subject of entire functions. This book will be a valuable source of information for the general reader, as well as historians of science. It provides the reader with a good understanding of the overall picture of these two areas in the nineteenth century and their significance today.
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Text: English (translation)
Original Language: Russian --This text refers to an alternate Hardcover edition.
Original Language: Russian --This text refers to an alternate Hardcover edition.
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Although the main achievements of eighteenth-century mathematics were connected with the development of mathematical analysis, important discoveries were made in the course of the century in geometry also. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oval quadric, hyperelliptic integrals, analytic function theory, imaginary geometry, des fonctions elliptiques, absolute geometry, elliptic functions, projective properties, intrinsic geometry, extended manifold, automorphic functions, hyperbolic plane, theta functions, fifth postulate, metric concepts, hypergeometric equation, infinitesimal level, osculating plane, linear congruences, cubic surface, elliptic geometry, projective geometry, hypergeometric series, algebraic functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
University of Berlin, Paris Academy, Mathematische Werke, Comptes Rendus, Crelle's Journal, Abel'schen Functionen, Ecole Polytechnique, Acta Math, Karl Weierstrass, Ecole Normale, Erlanger Programm, Berlin Academy of Sciences, Technische Hochschule, Geometrische Untersuchungen, University of Erlangen, University of Halle, Abelschen Funktionen, Erster Teil, Petersburg Academy of Sciences, Petersburg University, University of Dorpat, Zur Funktionenlehre, Briefe von Weierstrass, Gesammelte Werke, The Casorati-Weierstrass New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Although the main achievements of eighteenth-century mathematics were connected with the development of mathematical analysis, important discoveries were made in the course of the century in geometry also. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oval quadric, hyperelliptic integrals, analytic function theory, imaginary geometry, des fonctions elliptiques, absolute geometry, elliptic functions, projective properties, intrinsic geometry, extended manifold, automorphic functions, hyperbolic plane, theta functions, fifth postulate, metric concepts, hypergeometric equation, infinitesimal level, osculating plane, linear congruences, cubic surface, elliptic geometry, projective geometry, hypergeometric series, algebraic functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
University of Berlin, Paris Academy, Mathematische Werke, Comptes Rendus, Crelle's Journal, Abel'schen Functionen, Ecole Polytechnique, Acta Math, Karl Weierstrass, Ecole Normale, Erlanger Programm, Berlin Academy of Sciences, Technische Hochschule, Geometrische Untersuchungen, University of Erlangen, University of Halle, Abelschen Funktionen, Erster Teil, Petersburg Academy of Sciences, Petersburg University, University of Dorpat, Zur Funktionenlehre, Briefe von Weierstrass, Gesammelte Werke, The Casorati-Weierstrass New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 32
books:
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- Elliptic Functions according to Eisenstein and Kronecker by Andre Weil on page 168, and Back Matter
- Mathematical Thought from Ancient to Modern Times, Vol. 1 by Morris Kline on page 131, and Back Matter
- Mathematical Papers by W. Clifford on page 74, and Back Matter
- Bibliography and Research Manual of the History of Mathematics by K.O. May in Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter
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