This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?

This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.

This book describes the construction and the properties of CW-complexes. These spaces are important because firstly they are the correct framework for homotopy theory, and secondly most spaces that arise in pure mathematics are of this type. The authors discuss the foundations and also developments, for example, the theory of finite CW-complexes, CW-complexes in relation to the theory of fibrations, and Milnor's work on spaces of the type of CW-complexes. They establish very clearly the relationship between CW-complexes and the theory of simplicial complexes, which is developed in great detail. Exercises are provided throughout the book; some are straightforward, others extend the text in a non-trivial way. For the latter; further reference is given for their solution. Each chapter ends with a section sketching the historical development. An appendix gives basic results from topology, homology and homotopy theory. These features will aid graduate students, who can use the work as a course text. As a contemporary reference work it will be essential reading for the more specialized workers in algebraic topology and homotopy theory.

Parte general. Fundamentos fisicos y tecnicos de la ecografia. Fisica. Tecnica. Generalidades sobre la tencica de exploracion. Generalidades sobre la realizacion de uan ecografia. Artefactos. Parte especial. Tencica de exploracion especial y representacion de organos. Vejiga de la orina. Prostata. Utero. Ovario. Bazo, bazo accesorio. Rinon. Glandulas adrenales. Ureter. Higado. Vesicula biliar. Sistema gastrointestinal-Intestino. Sistema gastroinetistinal. Estomago. Pancreas. Mesenterio. omento. Ganglios linfaticos. Liquido libre abdominal. Hidroperitoneo. Ecografia del contenido escrotal. Testiculos y epididimo. Alteraciones del tejido peritesticular. Hidrotorax. Torax y diafragma. Diagnostico ecografico de cuerpos extranos. Fistulas, flemones. Puncion bajo control ecografico.

Das Groteske und das Absurde erscheinen in der Literatur des 20. Jahrhunderts als gängige Medien bei der Darstellung einer als zunehmend disharmonisch erfahrenen Realität. Es zeigt sich aber, daß vor allem in der Bestimmung des Grotesken große Differenzen auftreten, wobei auch das Verhältnis des Grotesken zum Absurden äußerst widersprüchlich gedeutet wird. Der vorliegende Text arbeitet die Gemeinsamkeiten und Unterschiede beider Kategorien heraus. Dabei wird eine Theorie der ästhetischen Gestaltung von Entfremdung entwickelt, die aus einem materialistisch orientieten sozialpsychologischen Ansatz hergeleitet wird und die im Besonderen auch die Schaffenshaltung der untersuchten Autoren berücksichtigt.