This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and nonEuclidean geometry. The text for this new edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann — Hilbert problem, the uniformization theorem, PicardVessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level. This work continues to be the only uptodate scholarly account of the history of a branch of mathematics that continues to generate important research, for which the mathematics has been the occasion for some of the most profound work by numerous 19th century figures: Riemann, Fuchs, Dedekind, Klein, and Poincar.

Authors: Gray J.J.  Pages: 179 Year: 2000 
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