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Mathematics of the 19th Century
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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 various aspects of geometry are considered and three main lines are traced: the development of a theory of invariants and forms that determine certain geometric structures like curves of 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 a new understanding of the concept of functions. Main achievement of this time was the development of the theory of elliptic, algebraic, Abelian and automorphic functions.§ The book provides the reader with a good understanding of these two areas of mathematics in the nineteenth century and their significance today.
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