Synopsis
This is the first introductory textbook on ordered sets and lattices, and covers both the basic theory and its applications. The importance of ordered structures has been increasingly recognised in recent years due to an explosion of interest in computer science and all areas of discrete mathematics. The authors provide a thorough introduction to ordered sets, lattices, distributive lattices and Boolean algebras. Ordered sets, and in particular lattices, can be represented pictorially, and this key feature is emphasised throughout. Lattices are also considered as algebraic structures and their study from this viewpoint reinforces ideas encountered in the theory of groups and rings. The representation of distributive lattices by ordered topological spaces is presented; a self-contained treatment of the requisite topology is included. Two chapters are devoted to topics with application to computer science. These cover complete partial orders, domains (including their relation to information systems), and fixpoint theory. Another chapter deals with formal concept analysis - a new and important application of lattice theory of interest to mathematicians and social scientists. Prerequisites are minimal; all that is assumed is exposure to the notation of set theory and elementary abstract algebra. The numerous classroom-tested exercises will make the book especially useful for course accompaniment, but it will also be valuable as a background reference for mathematicians, logicians and computer scientists.
Revue de presse
'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 für 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
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