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Ordered Sets Bernd Schroeder

Ordered Sets By Bernd Schroeder

Ordered Sets by Bernd Schroeder

Reviews:
$57.26
Condition - Good
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Summary

Offers an introduction to the basic tools of the theory of ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. This book covers topics such as chains and antichains, lowest upper and greatest lower bounds, retractions, and lattices.

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Ordered Sets Summary

Ordered Sets: An Introduction by Bernd Schroeder

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Ordered Sets Reviews

"The author has done the field a service by producing an excellent text strong in the presentation of certain topological aspects of the underlying diagrams, e.g., which should serve the developing community and field well and which can be recommended without reservations as one of the volumes which should grace a poseteer's library whether she is interested only or mainly in the theory of these objects or has directed her gaze towards applications. As a sourcebook of ideas and understanding it will make its mark. And deservedly so." -ZENTRALBLATT MATH "This book is a most successful introduction to the theory of ordered sets. The range of topics covered is wide yet the exposition is self-contained ... The focus on open problems makes for enthusiastic writing and provides continuity among the diverse topics that are discussed ... in each chapter the author proves a solid collection of basic results, presents one or more major theorems with detailed and nontrivial proofs, and states without proof one or two other important results. At the end of every chapter is an ample collection of exercises ... A novel aspect of [the twelfth] chapter is the presentation of much of the material in terms of constraint satisfaction problems." -MATHEMATICAL REVIEWS "...surprisingly, despite the extremely basic nature of the subject, this monograph has essentially no competition. But fortunately the first entry proves a gem. Undergraduate mathematics and computer science majors will find the first chapters offering background that will serve them well in many courses. The rest of the book, which features many open problems, constitutes an accessible and stimulating invitation to research ... Highly recommended." -CHOICE "There are two groups of people who will primarily profit from the book. First, researchers in the field of ordered sets and lattices and related fields like algebra, graphs, and combinatorics. The book provides an excellent look at the field with numerous remarks including historical remarks and open problems. Second, students who are looking for a PhD topic. The author presents the field of ordered sets in an attractive way and the many open problems presented in the book are invaluable. Mathematicians and computer scientists could use the book as a reference book, too...[T]he book is a success, it presents an in depth and up to date carefully written coverage of ordered sets." -SIGACT NEWS

Table of Contents

Preface * List of Figures * The Basics * Chains, Antichains and Fences * Upper and Lower Bounds * Retractions * Lattices * Truncated Lattices * The Dimension of Ordered Sets * Interval Orders * Lexicographic Sums * Sets P^Q = Hom (Q, P) and Products * Enumeration * Algorithmic Aspects * Appendix A: A Primer on Algebraic Topology * Appendix B: Order vs. Analysis * References * Index

Additional information

CIN0817641289G
9780817641283
0817641289
Ordered Sets: An Introduction by Bernd Schroeder
Bernd Schroeder
Used - Good
Hardback
Birkhauser Boston Inc
2002-12-06
391
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Ordered Sets