Lehrbuch Der Topologie by H. Seifert, W. Threlfall

By H. Seifert, W. Threlfall

The Nineteen Thirties have been very important years within the improvement of contemporary topology, driven ahead via the looks of some pivotal books, of which this is often one. the point of interest is on combinatorial and algebraic topology, with as a lot point-set topology as wanted for the most issues. One sees from the trendy perspective that the authors are operating in a class of areas that comes with in the community finite simplicial complexes. (Their definition of manifold is extra effectively identified this present day as a "triangulizable homology manifold".) Amazingly, they be capable of accomplish much with out the handy instruments of homological algebra, similar to distinctive sequences and commutative diagrams, that have been constructed later. the most themes lined are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), neighborhood homology, floor topology, the basic crew and overlaying areas, three-manifolds, Poincar? duality, and the Lefschetz mounted aspect theorem. Few necessities are helpful. a last part stories the lemmas and theorems from team thought which are wanted within the textual content. As acknowledged within the creation to the $64000 ebook by means of Alexandroff and Hopf (which seemed a 12 months after Seifert and Threlfall): "Its full of life and instructive presentation makes this ebook rather appropriate as an advent or as a textbook."

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Contemporary aspects of complex analysis, diff. geometry and by Stancho Dimiev, Kouei Sekigawa

By Stancho Dimiev, Kouei Sekigawa

This quantity offers the state of the art contributions to the 7th foreign Workshop on complicated constructions and Vector Fields, which was once prepared as a continuation of the excessive profitable previous workshops on related examine. the quantity comprises works treating bold subject matters in differential geometry, mathematical physics and expertise equivalent to Bezier curves in area varieties, strength and catastrophy of a cleaning soap movie, computer-assisted stories of logistic maps, and robotics.

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Geometriekalküle by Jürgen Richter-Gebert, Thorsten Orendt (auth.)

By Jürgen Richter-Gebert, Thorsten Orendt (auth.)

Wie kann guy geometrische Objekte und Operationen so darstellen, dass sie durch möglichst einfache algebraische Manipulationen verarbeitet werden können? Dies ist die Leitfrage dieses Buches, welche im Verlauf von insgesamt 12 Kapiteln von verschiedenen Seiten beleuchtet wird. Unter diesem Blickwinkel werden Einführungen in projektive Geometrie, geometrische Invariantentheorie, Euklidische Geometrie (unter besonderer Berücksichtigung komplexer Zahlen) Möbiusgeometrie, und Lie‘sche Kreisgeometrie gegeben. Hierbei liegt der Schwerpunkt auf Eleganz der Methoden, welche nicht selten automatisch zu eleganten algorithmischen Ansätzen führen. Für den Leser stellt das Buch eine Brücke vom Grundwissen in der Linearen Algebra zu modernen (und klassischen) Ansätzen der Geometrie dar. Neben zahlreichen Übungsaufgaben, Abbildungen und im web verfügbaren interaktiven Visualisierungen wird jedes Kapitel durch einen „Exkurs" ergänzt, der Einblicke in Anwendungen oder weiterführende Themen gibt. Das Buch richtet sich an Studierende und Dozenten der Mathematik, Informatik und Physik ab dem dritten Semester.

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