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MODES
by Anna B Romanowska (Warsaw University of Technology, Poland) & Jonathan D H Smith (Iowa State University, USA)
This book is an introduction to the theory and application of modes — structures that capture the common underlying algebra of convex sets, affine spaces and certain ordered sets. Modes appear in many branches of mathematics, particularly geometry and combinatorics, and have been used in computer science, economics, physics, and biology. The initial stage of the theory was set out in the authors' research monograph Modal Theory (published in 1985). The present book provides a more complete theory, the result of research conducted during the subsequent 15 years. It contains a clear introduction to selected topics from universal algebra, category theory and model theory, and the foundations of the theory of modes, as well as more advanced topics leading to the forefront of current research in the field.
The authors have included a wide range of exercises, usually placed at the end of the section, and indexed alphabetically. Some exercises are simply designed to familiarize readers with the notation and concepts. Others are more difficult, extending the content of the sections in which they appear, and providing a foretaste of further research.
Contents:
- Algebras
- Categories of Algebras
- Varieties, Prevarieties and
Quasivarieties
- Constructing Algebras and Quasivarieties
- Introduction to Modes
- Mal'cev Modes and Affine Spaces
- Subreducts of Affine Spaces
- Binary Modes
- Hierarchical Statistical Mechanics
- Recent Developments and Open Problems
Readership: Researchers and graduate students in algebra, discrete mathematics
and information theory.
"The final chapter gives an interesting survey of recent developments and open problems ... There are excellent exercises in every chapter."
“This book explains a very broad spectrum of notions and results in modern algebra. Each chapter, except the last, contains exercises as well as comments on the literature. It certainly fills a gap in the spectrum of mathematical literature.”
| 636pp |
Pub. date: Oct 2002 |
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