Continuous Lattices and Related Topics
Author: Rudolf-Eberhard Hoffmann
Publisher:
Published: 1982
Total Pages: 330
ISBN-13:
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Continuous Lattices and Their Applications
Author: Rudolf E. Hoffmann
Publisher: CRC Press
Published: 2020-12-17
Total Pages: 392
ISBN-13: 1000111083
DOWNLOAD EBOOKThis book contains articles on the notion of a continuous lattice, which has its roots in Dana Scott's work on a mathematical theory of computation, presented at a conference on categorical and topological aspects of continuous lattices held in 1982.
A Compendium of Continuous Lattices
Author: G. Gierz
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 390
ISBN-13: 3642676782
DOWNLOAD EBOOKA mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.
Continuous Lattices and Domains
Author: G. Gierz
Publisher: Cambridge University Press
Published: 2003-03-06
Total Pages: 640
ISBN-13: 9780521803380
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Continuous Lattices
Author: B. Banaschewski
Publisher: Springer
Published: 2006-11-14
Total Pages: 428
ISBN-13: 3540387552
DOWNLOAD EBOOKStatistical Mechanics of Lattice Systems
Author: Sacha Friedli
Publisher: Cambridge University Press
Published: 2017-11-23
Total Pages: 643
ISBN-13: 1107184827
DOWNLOAD EBOOKA self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Lattice Theory: Special Topics and Applications
Author: George Grätzer
Publisher: Springer
Published: 2014-08-27
Total Pages: 472
ISBN-13: 3319064134
DOWNLOAD EBOOKGeorge 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.
Computing the Continuous Discretely
Author: Matthias Beck
Publisher: Springer
Published: 2015-11-14
Total Pages: 295
ISBN-13: 1493929690
DOWNLOAD EBOOKThis richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Semigroups in Complete Lattices
Author: Patrik Eklund
Publisher: Springer
Published: 2018-06-09
Total Pages: 343
ISBN-13: 3319789481
DOWNLOAD EBOOKThis monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.
General Lattice Theory
Author: George Grätzer
Publisher: Springer Science & Business Media
Published: 2002-11-21
Total Pages: 688
ISBN-13: 9783764369965
DOWNLOAD EBOOK"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
