Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since...
Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators a...
Ever since F. Klein designed his "Erlanger programm", geometries have been studied in close connection with their groups of automorphisms. It must be admitted that the presence of a large automorphismgroup does not always have strong implications for the incidence-th- retical behaviour of a geometry. For exampl~ O. H. Kegel and A. Schleiermacher [Geometriae Dedicata 2, 379 - 395 (1974)J constructed a projective plane with a transitive action of its collineation group on quadrangles, in which, nevertheless every four points generate a free subplane. However, there are several important special...
Ever since F. Klein designed his "Erlanger programm", geometries have been studied in close connection with their groups of automorphisms. It must be ...
When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de veloped branch of mathematics has been dealt with in a variety of mono graphs, so that - in spite of its technical complexity - it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes- which right now has reached a peak once more -, the numerous other applications of ring theory in geometry have not...
When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concr...
Staszewski, Reiner Strambach, Karl Völklein, Helmut
Im Mittelpunkt des Buchs steht der Begriff des Gleichungssystems, wobei neben linearen Gleichungssystemen auch solche von linearen Differentialgleichungen (und sogar nicht-lineare algebraische Gleichungssysteme) betrachtet werden. Alle Grundbegriffe der Linearen Algebra werden sofort durch die Anwendung auf solche Gleichungssysteme motiviert. Dadurch wird der Aufbau der Linearen Algebra und der Sinn der eingefuhrten Begriffe fur den Anfanger wesentlich verstandlicher, ohne die geringsten Abstriche bei der mathematischen Exaktheit vornehmen zu mussen.
Im Mittelpunkt des Buchs steht der Begriff des Gleichungssystems, wobei neben linearen Gleichungssystemen auch solche von linearen Differentialgleichu...
