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On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises (Classic Reprint) - Tapa blanda
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Excerpt from On Riemann's Theory of Algebraic Functions and Their IntegralsAbout the PublisherForgotten Books publishes hundreds of thousands of rare and classic books.This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.The digital edition of all books may be viewed on our website before purchase.
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Excerpt from On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises
Theory of Functions treated geometrically. Part I, Winter-semester 1880 81, Part II, Summer-semester 1881.
I denote thus the contents of the investigations with which Riemann was concerned in the first part of his Theory of the Abelian Functions. The theory of the O-functions, as developed in the second part of the same treatise, is in the first place, as we know, of an essentially different character, and is excluded from the following presentation as it was from my course of lectures.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises
A presentation of the kind attempted is necessarily very subjective, and the more so in the case of Riemann's theory, since but scanty material for the purpose is to be found explicitly given in Riemann's papers. I am not sure that I should ever have reached a well-defined conception of the whole subject, had not Herr Prym, many years ago (1874), in the course of an opportune conversation, made me a communication which has increased in importance to me the longer I have thought over the matter. He told me that Riemann's surfaces originally are not necessarily many-sheeted surfaces over the plane, but that, on the contrary, complex functions of position can be studied on arbitrarily given curved surfaces in exactly the same way as on the surfaces over the plane. The following presentation will sufficiently show how valuable this remark has been to me. In natural combination with this there are certain physical considerations which have been lately developed, although restricted to simpler cases, from various points of view. I have not hesitated to take these physical conceptions as the starting-point of my presentation. Riemann, as we know, used Dirichlet's Principle in their place in his writings. But I have no doubt that he started from precisely those physical problems, and then, in order to give what was physically evident the support of mathematical reasoning, he afterwards substituted Dirichlet's Principle. Anyone who clearly understands the conditions under which Riemann worked in Gottingen, anyone who has followed Riemann's speculations as they have come down to us, partly in fragments, will, I think, share my opinion. - However that may be, the physical method seemed the true one for my purpose. For it is well known that Dirichlet's Principle is not sufficient for the actual foundation of the theorems to be established; moreover, the heuristic element, which to me was all-important, is brought out far more prominently by the physical method.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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On Riemann's Theory of Algebraic Functions and Their Integrals
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781331947264
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On Riemann's Theory of Algebraic Functions and Their Integrals
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781331947264
Cantidad disponible: 15 disponibles
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On Riemann's Theory of Algebraic Functions and Their Integrals
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
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Paperback. Condición: New. Print on Demand. This book takes a fascinating, intuitive approach to understanding a complex mathematical theory: the theory of algebraic functions and their integrals, a foundational area of mathematics developed by the renowned Bernhard Riemann in the 19th century. Rather than relying solely on abstract formulas, the author uses physical analogies to illuminate the subject. The book introduces the concept of "steady streamings" - imagined flows of fluid on surfaces - as a visual and relatable way to understand complex mathematical functions. The author then explores how these streamings can be visualized on surfaces of different shapes and topologies, particularly closed surfaces like spheres and tori, which are classified by their "genus" or the number of holes they have. By exploring these streamings and their properties, the book opens a window into the inner workings of algebraic functions and their integrals, offering a deeper understanding of their intricate relationships and behaviors. This book's unique approach, blending physical intuition with rigorous mathematical concepts, makes it a compelling and accessible resource for anyone seeking to delve into the world of Riemann's theory. The book's insights ultimately provide a new perspective on this vital area of mathematics, highlighting the power of visual and physical analogies in understanding complex mathematical ideas. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781331947264_0
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