Kategoria BISAC: Mathematics >> Discrete Mathematics

Formal verification increasingly has become recognized as an answer to the problem of how to create ever more complex control systems, which nonetheless are required to behave reliably. To be acceptable in an industrial setting, formal verification must be highly algorithmic; to cope with design complexity, it must support a top-down design methodology that leads from an abstract design to its detailed implementation. That combination of requirements points directly to the widely recognized solution of automata-theoretic verification, on account of its expressiveness, computational...

A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted,...

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years due mainly to the impetus of the authors and their collaborators a powerful connection has been established between stochastic geometry and the...

This book is based on the outcome of the "2012 Interdisciplinary Symposium on Complex Systems" held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to solving various problems including real-life applications. More exactly, readers will have an encounter with the structural complexity of vortex flows, the use of chaotic dynamics within evolutionary algorithms, complexity in synthetic biology,...

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models.

The text is primarily intended for use in a one-semester...

Wie ist ein Ring definiert, wann kann man Grenzprozesse vertauschen, was sind lineare Ordnungen und wozu benotigt man das Zornsche Lemma in der Linearen Algebra?

Das Buch will seinen Lesern helfen, sich in der Fulle der grundlegenden mathematischen Definitionen zurecht zu finden und exemplarische mathematische Ergebnisse einordnen und ihre Eigenheiten verstehen zu konnen. Es behandelt hierzu je zwolf Schlusselkonzepte der folgenden zwolf Themengebiete der Mathematik:

Wie funktioniert die Wahl des Deutschen Bundestags? Wie errechnen sich Sitze in Schweizer Kantonsparlamenten? Kann man Stimmzahlen uberhaupt fair auf Mandate umrechnen?

Sitzzuteilungsmethoden und ihre wichtigsten formalen Eigenschaften sind Thema dieses an der Universitat Augsburg erprobten Kompaktkurses. Verhaltniswahlsystemeund ihre Methoden, Stimmenzahlen am Ende einer demokratischen Wahl in Mandate zu verrechnen, werden hier ausfuhrlich und anschaulich behandelt. Zahlreiche Beispiele mit aktuellen Wahlergebnissen sichern dabei Realitatsnahe.

Verfassungsrechtliche und...

Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep relationships, such as the Lawson correspondence. The nearly 300 problems and exercises range from simple applications to open problems. Exercises are...

Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges.

This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains.