Introduction to Lattices and Order

Author: B. A. Davey,H. A. Priestley

Publisher: Cambridge University Press

ISBN: 9780521784511

Category: Mathematics

Page: 298

View: 1584

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.

Lattices and Ordered Sets

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 9780387789019

Category: Mathematics

Page: 305

View: 3760

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

Author: Vijay K. Garg

Publisher: John Wiley & Sons

ISBN: 1119069734

Category: Computers

Page: 272

View: 375

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.

Semimodular Lattices

Author: N.A

Publisher: Springer-Verlag

ISBN: 3663124789

Category: Technology & Engineering

Page: 237

View: 8389

Lattices and Ordered Algebraic Structures

Author: T.S. Blyth

Publisher: Springer Science & Business Media

ISBN: 184628127X

Category: Mathematics

Page: 304

View: 5491

"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS

Ordered Sets

An Introduction with Connections from Combinatorics to Topology

Author: Bernd Schröder

Publisher: Birkhäuser

ISBN: 3319297880

Category: Mathematics

Page: 420

View: 4540

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.

Concept Lattices

Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings

Author: Peter Eklund

Publisher: Springer Science & Business Media

ISBN: 3540210431

Category: Computers

Page: 409

View: 7235

This book constitutes the refereed proceedings of the Second International Conference on Formal Concept Analysis, ICFCA 2004, held in Sydney, Australia in February 2004. The 27 revised full papers presented together with 7 invited papers were carefully reviewed and selected for inclusion in the book. Formal concept analysis emerged out of efforts to restructure lattice theory and has been extended into attribute exploration, Boolean judgment, and contextual logics in order to create a powerful general framework for knowledge representation and formal reasoning; among the application areas of formal concept analysis are data and knowledge processing, data visualization, information retrieval, machine learning, data analysis, and knowledge management. The papers in this book address all current issues in formal concept analysis, ranging from foundational and methodological issues to applications in various fields.

Kompendium der diskreten Mathematik

Author: Bernd Baumgarten

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486781324

Category: Mathematics

Page: 388

View: 9459

Das Kompendium präsentiert die für ein Mathematik- oder Informatikstudium benötigten Grundlagen der diskreten Mathematik in kompakter Form. Alle wichtigen Themen wie Mengen, Relationen und Funktionen, Logik, Graphen, abstrakte und lineare Algebra sowie diskrete Wahrscheinlichkeitstheorie werden abgedeckt. Damit erweist sich das Buch als nützlicher Begleiter für viele Vorlesungen im Studium.

Endliche Gruppen

Eine Einführung in die Theorie der endlichen Gruppen

Author: H. Kurzweil

Publisher: Springer-Verlag

ISBN: 3642953131

Category: Mathematics

Page: 190

View: 1786

Elementare Zahlentheorie

Author: Edmund Landau

Publisher: American Mathematical Soc.

ISBN: 0821836528

Category: Mathematics

Page: 180

View: 7518

Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German.

Mathematical Foundations of Image Processing and Analysis

Author: Jean-Charles Pinoli

Publisher: John Wiley & Sons

ISBN: 1118649125

Category: Technology & Engineering

Page: 464

View: 4193

Image processing and image analysis are typically important fieldsin information science and technology. By “imageprocessing”, we generally understand all kinds of operationperformed on images (or sequences of images) in order to increasetheir quality, restore their original content, emphasize someparticular aspect of the information or optimize theirtransmission, or to perform radiometric and/or spatial analysis. By“image analysis” we understand, however, all kinds ofoperation performed on images (or sequences of images) in order toextract qualitative or quantitative data, perform measurements andapply statistical analysis. Whereas there are nowadays many booksdealing with image processing, only a small number deal with imageanalysis. The methods and techniques involved in these fields ofcourse have a wide range of applications in our daily world:industrial vision, material imaging, medical imaging, biologicalimaging, multimedia applications, satellite imaging, qualitycontrol, traffic control, and so on

Lectures on Soft Computing and Fuzzy Logic

Author: Antonio Di Nola,Giangiacomo Gerla

Publisher: Springer Science & Business Media

ISBN: 9783790813968

Category: Computers

Page: 337

View: 1451

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

Moderne Algebra

Author: Bartel Eckmann L. Van der van der Waerden,Emil Artin,Emmy Noether

Publisher: Springer-Verlag

ISBN: 3662364344

Category: Mathematics

Page: 274

View: 4442

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Models, Algebras, and Proofs

Author: Xavier Caicedo,Carlos Montenegro

Publisher: CRC Press

ISBN: 9780824719708

Category: Mathematics

Page: 472

View: 9999

"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide."

Introduction to Nanotechnology

Author: Charles P. Poole, Jr.,Frank J. Owens

Publisher: John Wiley & Sons

ISBN: 9780471079354

Category: Technology & Engineering

Page: 400

View: 3568

This self-confessed introduction provides technical administrators and managers with a broad, practical overview of the subject and gives researchers working in different areas an appreciation of developments in nanotechnology outside their own fields of expertise.

Theory of Lattice-Ordered Groups

Author: Michael Darnel

Publisher: CRC Press

ISBN: 9780824793265

Category: Mathematics

Page: 560

View: 9252

Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.

Introduction to Operator Theory in Riesz Spaces

Author: Adriaan C. Zaanen

Publisher: Springer Science & Business Media

ISBN: 3642606377

Category: Mathematics

Page: 312

View: 4877

Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).