Linear DEs and group theory from Riemann to Poincare

✍ Scribed by Jeremy Gray

• Book ID: 127428399
• Publisher: Birkhauser
• Year: 2000
• Tongue: English
• Weight: 4 MB
• Edition: 2nd
• Category: Library
• ISBN: 3764338377

✦ Synopsis

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 non-Euclidean 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, Picard-Vessiot 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 up-to-date 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.