Author : George Gratzer
Publisher : Courier Corporation
Page : 242 pages
File Size : 37,37 MB
Release : 2009-01-01
Category : Mathematics
ISBN : 048647173X
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 : Viktor Viktorovich Zharinov
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 17,4 MB
Release : 1985
Category : Mathematics
ISBN : 9780821830888
Algebraic methods have penetrated deeply into contemporary complex analysis, having an essential influence on both the choice of problems and on the methods for solving them. This monograph deals with the applications of distributive lattices of subspaces to problems in multidimensional complex analysis.
Author : Mai Gehrke
Publisher : Cambridge University Press
Page : 369 pages
File Size : 30,9 MB
Release : 2024-02-29
Category : Computers
ISBN : 1009349694
Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Author : Raymond Balbes
Publisher :
Page : 316 pages
File Size : 44,40 MB
Release : 2011-11-23
Category : Lattices, Distributive
ISBN : 9780983801108
Discussing the foundations of the theory of distributive lattices and the techniques used in this field, this resource also presents a number of special topics to which the theory is applied. In developing the theory, the authors have made use of the methods and tools of universal algebra and elementary category theory.
Author : Aleksandr Vasilʹevich Mikhalev
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 26,16 MB
Release : 2002
Category : Mathematics
ISBN : 9780792370727
Provides a succinct, but thorough treatment of algebra. In a collection that spans about 150 sections, organized in 9 chapters, algebraists are provided with a standard knowledge set for their areas of expertise.
Author : Ralph N. McKenzie
Publisher : American Mathematical Society
Page : 386 pages
File Size : 31,92 MB
Release : 2018-07-09
Category : Mathematics
ISBN : 1470442957
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Author : B. A. Davey
Publisher : Cambridge University Press
Page : 316 pages
File Size : 35,22 MB
Release : 2002-04-18
Category : Mathematics
ISBN : 1107717523
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 : K. D. Joshi
Publisher : New Age International
Page : 768 pages
File Size : 26,67 MB
Release : 1989
Category : Mathematics
ISBN : 9788122401202
This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.
Author : George Grätzer
Publisher : Springer Science & Business Media
Page : 688 pages
File Size : 29,2 MB
Release : 2002-11-21
Category : Mathematics
ISBN : 9783764369965
"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
Author : G. Grätzer
Publisher : Birkhäuser
Page : 392 pages
File Size : 29,35 MB
Release : 2012-12-06
Category : Science
ISBN : 3034876335
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]).
