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Introduction to Lattices and Order

2002-04-18 Mathematics
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Release : 2002-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 511/5 ( reviews)

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Book Synopsis Introduction to Lattices and Order by : B. A. Davey

Download or read book Introduction to Lattices and Order written by B. A. Davey. This book was released on 2002-04-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Lattices and Order

2002-04-18 Mathematics
Download Introduction to Lattices and Order PDF Online Free

Author :
Release : 2002-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 523/5 ( reviews)

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Book Synopsis Introduction to Lattices and Order by : B. A. Davey

Download or read book Introduction to Lattices and Order written by B. A. Davey. This book was released on 2002-04-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Lattices and Order

1990 Lattice theory
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Author :
Release : 1990
Genre : Lattice theory
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to Lattices and Order by : B. A. Davey

Download or read book Introduction to Lattices and Order written by B. A. Davey. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt:

Lattices and Ordered Sets

2008-12-15 Mathematics
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Release : 2008-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Lattices and Ordered Sets by : Steven Roman

Download or read book Lattices and Ordered Sets written by Steven Roman. This book was released on 2008-12-15. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.

Introduction to Lattice Theory with Computer Science Applications

2016-03-02 Computers
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Release : 2016-03-02
Genre : Computers
Kind : eBook
Book Rating : 734/5 ( reviews)

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Book Synopsis Introduction to Lattice Theory with Computer Science Applications by : Vijay K. Garg

Download or read book Introduction to Lattice Theory with Computer Science Applications written by Vijay K. Garg. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.

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