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General Lattice Theory
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Book Synopsis General Lattice Theory by : G. Grätzer
Download or read book General Lattice Theory written by G. Grätzer and published by Birkhäuser. This book was released on 2012-12-06 with total page 392 pages. 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]).
Book Synopsis General Lattice Theory by : George Grätzer
Download or read book General Lattice Theory written by George Grätzer and published by Springer Science & Business Media. This book was released on 2002-11-21 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
Download or read book Lattice Theory written by George Gratzer and published by Courier Corporation. This book was released on 2009-01-01 with total page 242 pages. 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.
Book Synopsis General Lattice Theory by : George Gratzer
Download or read book General Lattice Theory written by George Gratzer and published by . This book was released on 1998 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lattice Theory: Foundation by : George Grätzer
Download or read book Lattice Theory: Foundation written by George Grätzer and published by Springer Science & Business Media. This book was released on 2011-02-14 with total page 614 pages. 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
Book Synopsis Pure and Applied Mathematics by : George A. Gratzer
Download or read book Pure and Applied Mathematics written by George A. Gratzer and published by . This book was released on 1978 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Lattice Theory by : George Grätzer
Download or read book General Lattice Theory written by George Grätzer and published by Birkhäuser. This book was released on 2002-12-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
Book Synopsis Lattice Theory by : Garrett Birkhoff
Download or read book Lattice Theory written by Garrett Birkhoff and published by American Mathematical Soc.. This book was released on 1948 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Lattice Theory by : G. Gratzer
Download or read book General Lattice Theory written by G. Gratzer and published by . This book was released on 1978-01-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 and published by Cambridge University Press. This book was released on 2002-04-18 with total page 316 pages. 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.
Book Synopsis Varieties of Lattices by : Peter Jipsen
Download or read book Varieties of Lattices written by Peter Jipsen and published by Springer. This book was released on 2006-11-15 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.
Book Synopsis Lattice Theory: Special Topics and Applications by : George Grätzer
Download or read book Lattice Theory: Special Topics and Applications written by George Grätzer and published by Birkhäuser. This book was released on 2016-10-08 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Book Synopsis Lattice Functions and Equations by : Sergiu Rudeanu
Download or read book Lattice Functions and Equations written by Sergiu Rudeanu and published by Springer Science & Business Media. This book was released on 2001-07-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.
Book Synopsis Lattice Theory: Special Topics and Applications by : George Grätzer
Download or read book Lattice Theory: Special Topics and Applications written by George Grätzer and published by Springer. This book was released on 2014-08-27 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.
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 and published by John Wiley & Sons. This book was released on 2016-03-02 with total page 272 pages. 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.
Book Synopsis The Ergodic Theory of Lattice Subgroups (AM-172) by : Alexander Gorodnik
Download or read book The Ergodic Theory of Lattice Subgroups (AM-172) written by Alexander Gorodnik and published by Princeton University Press. This book was released on 2010 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established.
Download or read book Lattice written by Deepayan Sarkar and published by Springer Science & Business Media. This book was released on 2008-02-15 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the author of the lattice system, this book describes lattice in considerable depth, beginning with the essentials and systematically delving into specific low levels details as necessary. No prior experience with lattice is required to read the book, although basic familiarity with R is assumed. The book contains close to 150 figures produced with lattice. Many of the examples emphasize principles of good graphical design; almost all use real data sets that are publicly available in various R packages. All code and figures in the book are also available online, along with supplementary material covering more advanced topics.
