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Lattice Theory

2009-01-01 Mathematics
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Release : 2009-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 73X/5 ( reviews)

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Book Synopsis Lattice Theory by : George Gratzer

Download or read book Lattice Theory written by George Gratzer. This book was released on 2009-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.

Lattice Theory: Foundation

2011-02-14 Mathematics
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Release : 2011-02-14
Genre : Mathematics
Kind : eBook
Book Rating : 185/5 ( reviews)

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Book Synopsis Lattice Theory: Foundation by : George Grätzer

Download or read book Lattice Theory: Foundation written by George Grätzer. This book was released on 2011-02-14. Available in PDF, EPUB and Kindle. Book excerpt: This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews

General Lattice Theory

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 335/5 ( reviews)

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Book Synopsis General Lattice Theory by : G. Grätzer

Download or read book General Lattice Theory written by G. Grätzer. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce the lattice concept. Independently, Richard Dedekind's research on ideals of algebraic numbers led to the same discov ery. In fact, Dedekind also introduced modularity, a weakened form of distri butivity. Although some of the early results of these mathematicians and of Edward V. Huntington are very elegant and far from trivial, they did not attract the attention of the mathematical community. It was Garrett Birkhoff's work in the mid-thirties that started the general develop ment of lattice theory. In a brilliant series of papers he demonstrated the importance of lattice theory and showed that it provides a unifying framework for hitherto unrelated developments in many mathematical disciplines. Birkhoff himself, Valere Glivenko, Karl Menger, John von Neumann, Oystein Ore, and others had developed enough of this new field for Birkhoff to attempt to "seIl" it to the general mathematical community, which he did with astonishing success in the first edition of his Lattice Theory. The further development of the subject matter can best be followed by com paring the first, second, and third editions of his book (G. Birkhoff [1940], [1948], and [1967]).

Lattice Theory

1948 Algebra, Abstract
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Release : 1948
Genre : Algebra, Abstract
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Book Rating : /5 ( reviews)

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Book Synopsis Lattice Theory by : Garrett Birkhoff

Download or read book Lattice Theory written by Garrett Birkhoff. This book was released on 1948. Available in PDF, EPUB and Kindle. Book excerpt:

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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