Lattice Theory Foundation

Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 46,6 Mb
Release : 2011-02-14
Category : Mathematics
ISBN : 9783034800181

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Lattice Theory: Foundation by George Grätzer Pdf

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

Author : George Grätzer,Friedrich Wehrung
Publisher : Springer
Page : 472 pages
File Size : 53,9 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9783319064130

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Lattice Theory: Special Topics and Applications by George Grätzer,Friedrich Wehrung Pdf

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.

Author : George Grätzer,Friedrich Wehrung
Publisher : Birkhäuser
Page : 616 pages
File Size : 44,6 Mb
Release : 2016-10-08
Category : Mathematics
ISBN : 9783319442365

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Lattice Theory: Special Topics and Applications by George Grätzer,Friedrich Wehrung Pdf

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.

Author : G. Grätzer
Publisher : Birkhäuser
Page : 392 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034876339

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General Lattice Theory by G. Grätzer Pdf

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]).

Author : Attila Askar
Publisher : World Scientific
Page : 208 pages
File Size : 52,6 Mb
Release : 1986-07-01
Category : Electronic
ISBN : 9789814518956

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Lattice Dynamical Foundations Of Continuum Theories: Elasticity, Piezoelectricity, Viscoelasticity, Plasticity by Attila Askar Pdf

This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.

Author : George Gratzer
Publisher : Courier Corporation
Page : 242 pages
File Size : 54,5 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780486471730

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Lattice Theory by George Gratzer Pdf

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.

Author : B. A. Davey,H. A. Priestley
Publisher : Cambridge University Press
Page : 316 pages
File Size : 40,8 Mb
Release : 2002-04-18
Category : Mathematics
ISBN : 9781107717527

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Introduction to Lattices and Order by B. A. Davey,H. A. Priestley Pdf

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.

Author : Bernhard Ganter,Rudolf Wille
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642598302

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Formal Concept Analysis by Bernhard Ganter,Rudolf Wille Pdf

This first textbook on formal concept analysis gives a systematic presentation of the mathematical foundations and their relations to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. The mathematical foundations are treated thoroughly and are illuminated by means of numerous examples, making the basic theory readily accessible in compact form.

Author : George Grätzer,Friedrich Wehrung
Publisher : Birkhäuser
Page : 0 pages
File Size : 53,7 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 3319482629

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Lattice Theory by George Grätzer,Friedrich Wehrung Pdf

This three-volume-set comprises the complete lattice theory project. Volume 1 of the set, Lattice Theory: Foundation, is the revised and enlarged third edition of General Lattice Theory. It focuses on introducing the field and covers the fundamental concepts and results. The two Special Topics and Applications volumes (volumes 2 and 3 of the set), jointly edited by George Grätzer and Friedrich Wehrung, update the reader on some of the vast areas not in Foundation. Volume 1 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. Volume 2 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.

Author : Heinz J Rothe
Publisher : World Scientific
Page : 397 pages
File Size : 45,6 Mb
Release : 1992-01-29
Category : Electronic
ISBN : 9789814602303

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Lattice Gauge Theories: An Introduction by Heinz J Rothe Pdf

This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.

Author : H.H. Schaefer
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642659706

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Banach Lattices and Positive Operators by H.H. Schaefer Pdf

Author : Y. N. Singh
Publisher : New Age International
Page : 24 pages
File Size : 42,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9788122416671

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Mathematical Foundation of Computer Science by Y. N. Singh Pdf

The Interesting Feature Of This Book Is Its Organization And Structure. That Consists Of Systematizing Of The Definitions, Methods, And Results That Something Resembling A Theory. Simplicity, Clarity, And Precision Of Mathematical Language Makes Theoretical Topics More Appealing To The Readers Who Are Of Mathematical Or Non-Mathematical Background. For Quick References And Immediate Attentions3⁄4Concepts And Definitions, Methods And Theorems, And Key Notes Are Presented Through Highlighted Points From Beginning To End. Whenever, Necessary And Probable A Visual Approach Of Presentation Is Used. The Amalgamation Of Text And Figures Make Mathematical Rigors Easier To Understand. Each Chapter Begins With The Detailed Contents, Which Are Discussed Inside The Chapter And Conclude With A Summary Of The Material Covered In The Chapter. Summary Provides A Brief Overview Of All The Topics Covered In The Chapter. To Demonstrate The Principles Better, The Applicability Of The Concepts Discussed In Each Topic Are Illustrated By Several Examples Followed By The Practice Sets Or Exercises.

Author : Yang Xu,Da Ruan,Keyun Qin,Jun Liu
Publisher : Springer
Page : 397 pages
File Size : 40,8 Mb
Release : 2012-11-02
Category : Technology & Engineering
ISBN : 9783540448471

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Lattice-Valued Logic by Yang Xu,Da Ruan,Keyun Qin,Jun Liu Pdf

Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.

Author : Gerhard X. Ritter,Gonzalo Urcid
Publisher : CRC Press
Page : 292 pages
File Size : 45,7 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9781000412604

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Introduction to Lattice Algebra by Gerhard X. Ritter,Gonzalo Urcid Pdf

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises.

Author : Avrim Blum,John Hopcroft,Ravindran Kannan
Publisher : Cambridge University Press
Page : 433 pages
File Size : 41,8 Mb
Release : 2020-01-23
Category : Computers
ISBN : 9781108485067

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Foundations of Data Science by Avrim Blum,John Hopcroft,Ravindran Kannan Pdf

Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.