Plane Algebraic Curves (eBook)

Translated by John Stillwell
Artikelnummer: 978-3-0348-0493-6
Einband: PDF
Verfügbarkeit: Download, sofort verfügbar (Link per E-Mail)
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In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, "Plane Algebraic Curves" reflects the authors? concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities.

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In the first chapter one finds many special curves with very attractive geometric presentations - the wealth of illustrations is a distinctive characteristic of this book - and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout's theorem and a detailed discussion of cubics. The heart of this book - and how else could it be with the first author - is the chapter on the resolution of singularities (always over the complex numbers).  (?) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject.

(Mathematical Reviews)


In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, "Plane Algebraic Curves" reflects the authors? concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities.

---

In the first chapter one finds many special curves with very attractive geometric presentations - the wealth of illustrations is a distinctive characteristic of this book - and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout's theorem and a detailed discussion of cubics. The heart of this book - and how else could it be with the first author - is the chapter on the resolution of singularities (always over the complex numbers).  (?) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject.

(Mathematical Reviews)


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VerlagSpringer Basel
EinbandPDF
Erscheinungsjahr2012
Seitenangabe721 S.
AusgabekennzeichenEnglisch
AbbildungenX, 721 p. 301 illus.
Masse60'726 KB
PlattformPDF
ReiheModern Birkhäuser Classics; Mathematics and Statistics; Mathematics and Statistics
AutorBrieskorn, Egbert / Knörrer, Horst / Stillwell, John (Übers.)

Alle Bände der Reihe "Modern Birkhäuser Classics; Mathematics and Statistics; Mathematics and Statistics (R0)"

Über den Autor Egbert Brieskorn

Egbert Brieskorn was professor of mathematics in Göttingen and Bonn and visiting professor at a number of foreign universities. Among mathematicians he was known for his fundamental contributions to the singularity theory of complex hypersurfaces. In Bonn he initiated the project "Felix Hausdorff - Gesammelte Werke"(10 volumes, 2001-2020) and served as head of the group of five editors responsible for the complete edition. For many years he worked on a biography of Hausdorff, which was to appear in the Hausdorff edition, though only about half of it was completed at the time of his death. Brieskorn was also the author of original and successful textbooks. He devoted decades of work to ecology and species conservation, for which he received the Cross of Merit on Ribbon of the Federal Republic of Germany. Walter Purkert was professor of the history of mathematics in Leipzig and visiting professor in Wuppertal. He later taught historyof mathematics in Bonn, where as a starting point for the Hausdorff editorial project, he published a finding aid with descriptions of the contents of Hausdorff's extensive estate. Thereafter, he served full-time as coordinator of the edition, overseeing the work of its editors, while contributing to a number of the volumes. After Egbert Brieskorn's death, he spent several years completing their Hausdorff biography, published in 2018 as Volume IB of the edition. Purkert also wrote a well-received biography of Georg Cantor. He is a corresponding member of the Académie Internationale d'Histoire des Sciences in Paris.

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