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Theory of Algebraic Functions of One Variable by Richard Dedekind, Heinrich Weber Translated and introduced by John Stillwell

Theory of Algebraic Functions of One Variable

by Richard Dedekind, Heinrich Weber Translated and introduced by John Stillwell
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Book cover type: Paperback
  • ISBN13: 9781470425906
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Orient Blackswan Pvt Ltd
  • Publisher Imprint: Orient Blackswan Pvt Ltd
  • Publication Date:
  • Pages: 160
  • Original Price: INR 1320.0
  • Language: English
  • Edition: N/A
  • Item Weight: 290 grams
  • BISAC Subject(s): N/A

This book is the first English translation of the classic long paper Theorie der Algebraischen Functionen Einer Veränderlichen (Theory of Algebraic Functions of One Variable), published by Dedekind and Weber in 1882. 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

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