Introduction to Lattices and Order
BeschreibungOrdered 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.
InhaltsverzeichnisPreface; 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.
Pressestimmen'Recommended for every academic mathematics collection.' Choice '... an excellent introductory textbook on ordered sets and lattices and it is intended for undergraduate and beginning graduate students in mathematics.' Vaclav Slavic, Zentralblatt fur Mathematik 'I used Introduction to Lattices and Order as the sole textbook in a one semester course. The students enrolled were a heterogeneous group including modestly prepared undergraduates, well trained graduate students, and a few applications-oriented computer science students ... In short, the textbook was a success.' Joel Berman, Australian Mathematical Society Gazette '... a well-written, satisfying, informative, and stimulating account of applications that are of great interest, particularly in computer science and social science ... it will surely become a classic.' Mathematical Reviews 'Altogether, this is a great book. It would be interesting (and educational) to give a course based on it - almost makes me wish I hadn't retired!' Australian Mathematical Society Gazette '... a valuable source to anyone who needs to use ordered structures in any context.' EMS Newsletter 'It can be recommended as a valuable source to anyone who needs to use ordered structures in any context.' European Mathematical Society 'The book is written in a very engaging and fluid style. The understanding of the content is aided tremendously by the very large number of beautiful lattice diagrams ... The book provides a wonderful and accessible introduction to lattice theory, of equal interest to both computer scientists and mathematicians.' Jonathan Cohen, SIGACT News
Untertitel: 36 diagrams, 75exercises. Sprache: Englisch.
Verlag: Cambridge University Pr.
Erscheinungsdatum: April 2002