Kategoria BISAC: Mathematics >> Discrete Mathematics

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of...

This book constitutes the refereed proceedings of the 5th International Workshop on Experimental and Efficient Algorithms, WEA 2006, held in Menorca, Spain, May 2006. The book presents 26 revised full papers together with 3 invited talks. The application areas addressed include most fields applying advanced algorithmic techniques, such as combinatorial optimization, approximation, graph theory, discrete mathematics, scheduling, searching, sorting, string matching, coding, networking, and more.

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs...

Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems.

Divided into three parts, it covers:

- Model Theory and Recursive Functions - introducing...

A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized...

The terminology covers all the major branches from elementary to advanced subjects: arithmetic, algebra, geometry, set theory, discrete mathematics, logic, Boolean algebra, linear algebra, matrix algebra,...

This book constitutes the refereed proceedings of the 9th European Conference on Artificial Life, ECAL 2007, held in Lisbon, Portugal. The 125 revised full papers cover morphogenesis and development, robotics and autonomous agents, evolutionary computation and theory, cellular automata, models of biological systems and their applications, ant colony and swarm systems, evolution of communication, simulation of social interactions, self-replication, artificial chemistry.

The primary objective of this essential text is to emphasize the deep relations existing between the semiring and dioid structures with graphs and their combinatorial properties. It does so at the same time as demonstrating the modeling and problem-solving flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures which either extend usual algebra or form a new branch of it.