Algebraic Functions
Download Algebraic Functions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Functions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Algebraic Functions
Author: Gilbert Ames Bliss
language: en
Publisher: Courier Corporation
Release Date: 2004-01-01
This text surveys the approaches and basic results of all three classes of algebraic functions. Starting with a treatment of single-valued analytic functions, it introduces algebraic and rational functions and proceeds to the Riemann surface of an algebraic function, integrals of rational functions, and Abel's theorem. 1933 edition
Algebraic Functions
Author: Kenkichi Iwasawa
language: en
Publisher: American Mathematical Soc.
Release Date: 1993
This is a translation of Iwasawa's 1973 book, Theory of Algebraic Functions originally published in Japanese. Because the book treats mainly the classical part of the theory of algebraic functions, emphasizing analytic methods, it provides an excellent introduction to the subject from the classical viewpoint. Directed at graduate students, the book requires some basic knowledge of algebra, topology, and functions of a complex variable.
Theory of Algebraic Functions of One Variable
Author: Richard Dedekind
language: en
Publisher: American Mathematical Soc.
Release Date: 2012-07-23
This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veranderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself. The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians. Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation. The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.