On Riemann's Theory of Algebraic Functions and their Integrals A Supplement to the Usual Treatises

by Felix Klein, Frances Hardcastle (Translator)

The pamphlet which I here lay before the public, has grown from lectures delivered during the past year, in which, among other objects, I had in view a presentation of Riemann's theory of algebraic functions and their integrals. Lectures on higher mathematics offer peculiar diffculties; with the best will of the lecturer they ultimately fulfil a very modest pur-pose. Being usually intended to give a systematic development of the subject, they are either confined to the elements or are lost amid details. I thought it well in this case, as previously in others, to adopt the opposite course. I assumed that the ordinary presentation, as given in text-books on the elements of Riemann's theory, was known; moreover, when particular points required to be more fully dealt with, I referred to the fundamental monographs. But to compensate for this, I de-voted great care to the presentation of the true train of thought, and endeavoured to obtain a general view of the scope and ef-ficiency of the methods. I believe I have frequently obtained good results by these means, though, of course, only with a gifted audience; experience will show whether this pamphlet, based on the same principles, will prove equally useful.

Genres: Mathematics

116 pages, Kindle Edition

First published December 15, 2003