# The concept of a riemann surface

## The Concept of a Riemann Surface by Hermann Weyl

This classic on the general history of functions was written by one of the twentieth centurys best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemanns theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyls two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.

## The Concept of a Riemann Surface

In the Author's Own Words: "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context. The Concept of a Riemann Surface. Hermann Weyl. This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. In , he produced a revised edition, preserving some of his original approach but taking more careful account of the developments since then. This is the edition Dover has now brought back into print. When German mathematicians and the publishing house of Teubner approached me with the invitation to prepare a new edition, since requests for the book continued, it at first seemed appropriate to treat the book more or less as an historical document and send it into the world again unchanged except for a few minor improvements. But as I attempted to merge the appendix with the main text, I became ever more conscious of the deficiencies of both the appendix and the text. In other words, those looking for information on the history of topology, and especially on the development of the notion of a manifold, will need to look at both versions of the book.

In mathematics , particularly in complex analysis , a Riemann surface is a one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane : locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them.

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What is Riemann Surface? Understanding the Concept Without Math