On Riemann's Theory of Algebraic Functions and Their Integrals (Paperback)

Felix Klein

ISBN 10: 0486828336 / ISBN 13: 9780486828336

Published by Dover Publications Inc., New York, 2018

About this Item

Paperback. A great researcher, writer, and teacher in an era of tremendous mathematical ferment, Felix Klein (18491925) occupies a prominent place in the history of mathematics. His many talents included an ability to express complicated mathematical ideas directly and comprehensively, and this book, a consideration of the investigations in the first part of Riemann's Theory of Abelian Functions, is a prime example of his expository powers. The treatment introduces Riemann's approach to multiple-value functions and the geometrical representation of these functions by what later became known as Riemann surfaces. It further concentrates on the kinds of functions that can be defined on these surfaces, confining the treatment to rational functions and their integrals. The text then demonstrates how Riemann's mathematical ideas about Abelian integrals can be arrived at by thinking in terms of the flow of electric current on surfaces. Klein's primary concern is preserving the sequence of thought and offering intuitive explanations of Riemann's notions, rather than furnishing detailed proofs. Deeply significant in the area of complex functions, this work constitutes one of the best introductions to the origins of topological problems. AUTHOR: One of the greatest German mathematicians of his era, Felix Klein (18491925) taught at the University of Gottingen from 1887 until his retirement in 1913. He made major contributions to many areas of mathematics, including group theory, complex analysis, and non-Euclidean geometry. Dover also publishes Klein's classic two-volume work, Elementary Mathematics from an Advanced Standpoint, part one of which focuses on geometry and part two on arithmetic, algebra, and analysis. Focusing on functions defined on Riemann surfaces, this text demonstrates how Riemann's ideas about Abelian integrals can be arrived in terms of the flow of electric current on surfaces. 1893 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780486828336

Bibliographic Details

• Title: On Riemann's Theory of Algebraic Functions and Their Integrals (Paperback)
• Publisher: Dover Publications Inc., New York
• Publication Date: 2018
• Language: English
• ISBN 10: 0486828336
• ISBN 13: 9780486828336
• Binding: Paperback
• Condition: new

About this title

Synopsis

A great researcher, writer, and teacher in an era of tremendous mathematical ferment, Felix Klein (1849–1925) occupies a prominent place in the history of mathematics. His many talents included an ability to express complicated mathematical ideas directly and comprehensively, and this book, a consideration of the investigations in the first part of Riemann's Theory of Abelian Functions, is a prime example of his expository powers.
The treatment introduces Riemann's approach to multiple-value functions and the geometrical representation of these functions by what later became known as Riemann surfaces. It further concentrates on the kinds of functions that can be defined on these surfaces, confining the treatment to rational functions and their integrals. The text then demonstrates how Riemann's mathematical ideas about Abelian integrals can be arrived at by thinking in terms of the flow of electric current on surfaces. Klein's primary concern is preserving the sequence of thought and offering intuitive explanations of Riemann's notions, rather than furnishing detailed proofs. Deeply significant in the area of complex functions, this work constitutes one of the best introductions to the origins of topological problems.

About the Author

One of the greatest German mathematicians of his era, Felix Klein (1849–1925) taught at the University of Göttingen from 1887 until his retirement in 1913. He made major contributions to many areas of mathematics, including group theory, complex analysis, and non-Euclidean geometry. Dover also publishes Klein's classic two-volume work, Elementary Mathematics from an Advanced Standpoint, part one of which focuses on geometry and part two on arithmetic, algebra, and analysis.