Introduction to Lattices and Order

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Klappentext
Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.

Zusammenfassung
The explosive development of theoretical computer science in recent years has influenced this new edition: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added.

Inhalt
Preface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index.

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