Felix Hausdorff significantly influenced modern mathematics, becoming a pivotal figure in its evolution during the 20th century. His contributions extended beyond traditional boundaries, impacting various mathematical disciplines. The book delves into his groundbreaking ideas and the profound legacy he left on the field, highlighting his unique approach to mathematical concepts and his role in advancing theoretical frameworks. Through an exploration of his life and work, readers gain insight into the complexities of his thought and the broader implications for the scientific community.
Egbert Brieskorn Books
Ebene algebraische Kurven
- 964 pages
- 34 hours of reading
In a comprehensive introduction to the theory of plane algebraic curves, the authors explore this classical area of mathematics, which has roots in ancient Greek studies and continues to inspire research today. Originating from course notes at the University of Bonn, the text emphasizes motivation, imagination, and understanding for students. Curves, as classical objects, are examined from various perspectives, providing a foundation for modern explorations of singularities. The first chapter features many special curves with appealing geometric presentations, complemented by a wealth of illustrations. It also introduces projective geometry over the complex numbers. The second chapter presents a straightforward proof of Bezout’s theorem alongside an in-depth discussion of cubics. Central to the text is the chapter on the resolution of singularities, focusing on complex numbers. Notably, the book offers insights into further research on the topics covered, with numerous references to the literature. A variety of examples enriches this successful representation of a classical yet vibrant subject.
Lineare Algebra und analytische Geometrie
Noten zu einer Vorlesung mit historischen Anmerkungen von Erhard Scholz
- 548 pages
- 20 hours of reading
InhaltsverzeichnisV. Die Klassifikation der Endomorphismen endlichdimensionaler Vektorräume.- Einleitende Bemerkungen zum Klassifikationsproblem.- § 11 Normalformen.- Literatur zu § 11.- VI. Vektorräume mit einer Sesquilinearform.- Einleitende Bemerkungen.- § 12 Vektorräume mit Hermiteschen Formen und ihre Endanorphismen.- Bemerkungen zur Geschichte der Geometrie der klassischen Gruppen Euklidische Geometrie und orthogonale Gruppe · symmetrische Bilinearformen, verallgemeinerte orthogonale Gruppen · Hermitesche Formen, unitäre Geometrie · schiefsymmetrische Formen, symplektische Geometrie · die klassischen Gruppen als Liegruppen.- Literatur zu § 12.- Quellenverzeichnis der Abbildungen.- Stichwortverzeichnis.