Kategoria BISAC: Mathematics >> Topology - General

Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages:

1. It leads more quickly to the essentials of the subject,
2. An absence of signs and orientation considerations simplifies the theory,
3. Computations and advanced applications can be presented at an earlier stage,
4. Simple geometrical interpretations of (co)chains.

Mod 2 (co)homology was developed in the first quarter of the twentieth...

This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs.

While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for...

Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the...

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data.

The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application...

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis.

Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent...

The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to...

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level.

The first volume, Topological and Function Spaces (c) 2011, provided an introduction from scratch to...