The Concept of a Riemann Surface (Dover Books on Mathematics) by Hermann Weyl (PDF)

Description

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 author intended this book not only to develop the basic ideas of Riemann’s theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl’s 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.

User’s Reviews

Editorial Reviews: About the Author Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zürich, Göttingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies. Hermann Weyl: The Search for Beautiful Truths One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885–1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl’s life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years. 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 are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.” “A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.” — Hermann Weyl Critical Acclaim for Space, Time, Matter: “A classic of physics . . . the first systematic presentation of Einstein’s theory of relativity.” — British Journal for Philosophy and Science

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Arrived on time and in good condition. Very good purchase.

⭐I was looking for a readable book by non-mathematician about the subject. Unfortunately this one is not a good introduction. Moreover, notation is somewhat old. Do not recommend for beginner.

⭐quite interesting

⭐Maybe it’s excellent.But I read its first paragraph and immediately saw that it’s way beyond my understanding.Can someone recommend a book which would prepare me for reading this one. My math knowledge includes all high school stuff, 2 years of calculus and some linear algebra.

⭐This is a profound book on complex analysis and Riemannian geometry, all scientists who need mathematics should study such a masterpiece of Hermann Weyl.

⭐Excellent

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