On Riemann's Theory of Algebraic Functions and Their Integrals

Book Details

• Author: Felix Klein

• Publisher: Dover

• Language: English

• Binding: Paperback

• ISBN: 9780486828336

• Pages: 96

• Cover: Paperback

• Dimensions: 8.9 x 6.0 x 0.3 inches

About The Book
Felix Klein (1849–1925), one of the greatest German mathematicians of his era, was renowned for his ability to clearly express complex mathematical ideas. In Riemann's Theory of Abelian Functions, Klein offers a comprehensive examination of the first part of Riemann's groundbreaking work. This book serves as a prime example of Klein's expository prowess, presenting Riemann's investigation into multiple-value functions and their geometric representation through what became known as Riemann surfaces.

Focusing on rational functions and their integrals, Klein simplifies Riemann's complex mathematical ideas by illustrating them through the flow of electric current on surfaces, thus making abstract concepts more intuitive. While avoiding detailed proofs, Klein preserves the sequence of thought and provides insightful explanations, making this work an invaluable resource for understanding the early origins of topological problems in complex functions.

Klein's exploration of Riemann's Abelian integrals is a deeply significant contribution to the field of complex analysis, and this book serves as one of the best introductions to the fascinating world of topological mathematics. It's an essential read for those seeking to understand the historical foundations of modern mathematics.