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Saturday, November 21, 2020 | History

5 edition of Universal Algebra and Applications in Theoretical Computer Science found in the catalog.

Universal Algebra and Applications in Theoretical Computer Science

  • 147 Want to read
  • 29 Currently reading

Published by Chapman & Hall/CRC .
Written in English

    Subjects:
  • Algebra,
  • Mathematics for scientists & engineers,
  • Number theory,
  • Mathematics,
  • Theory Of Computing,
  • Science/Mathematics,
  • Algebra - General,
  • Applied,
  • Mathematics / Algebra / General,
  • Algebra, Universal,
  • Computer Science

  • The Physical Object
    FormatHardcover
    Number of Pages383
    ID Numbers
    Open LibraryOL8795280M
    ISBN 101584882549
    ISBN 109781584882541


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Universal Algebra and Applications in Theoretical Computer Science by Klaus Denecke Download PDF EPUB FB2

Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core by: Universal Algebra and Applications in Theoretical Computer Science is written in a style accessible to beginners, with every new concept clearly explained and numerous examples provided.

The main ideas of concept lattices as an important tool for conceptual analysis of data are developed, and several examples are given.

Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core cturer: Chapman and Hall/CRC.

Universal Algebra and Applications in Theoretical Computer Science book Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field.

The first half of the book provides a solid grounding in the core material. Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.

Each chapter is followed Universal Algebra and Applications in Theoretical Computer Science book an extensive list of exercises and by: Introduces the basic concepts of universal algebra and surveys some of the developments in the field.

This book focuses on applications in theoretical computer science and various topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The present book was conceived as an introduction for the user of universal algebra, rather than a handbook for the specialist, but when the first edition appeared inthere were practically no other books entir~ly devoted to the subject, whether introductory or by: A new model-theoretic approach to universal algebra is offered in this book.

Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. UNIVERSAL ALGEBRA and APPLICATIONS in THEORETICAL COMPUTER SCIENCE Klaus Denecke Shelly L.

Wismath CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C. Abstract. In the last two decades universal algebra has become useful and important in theoretical computer science.

In particular, structural aspects such as syntax and semantics, data abstraction, etc., are mainly investigated by methods of universal algebra. The material in this book divides naturally into two parts. One part can be described as “what every mathematician (or at least every algebraist) should know about universal algebra.” It would form a short introductory course to universal algebra, and would consist.

Description: This is an online text on universal algebra with a strong emphasis on applications and examples from computer science. The text introduces some basic algebraic concepts, such as signatures, algebras, homomorphisms, initial algebras, free algebras, and illustrates them with numerous interactive applications to computer science topics.

Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely group theory, universal algebra and related areas, to applications in several different areas of computer science.

Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications."--Provided by publisher.

Universal Algebra, heralded as " the standard reference in a field notorious for the lack of standardization," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.

Each chapter is followed by an extensive list of exercises and problems. Researchers in coputer algebra will benefit from the extensive bibliography, and lecturers will find it a mine of ideas for interesting topics that might be discussed in a course on computer algebra and its applications.

Finally, to all computer algebra aficionados this book will also provide wonderful entertainment for many a rainy day.". The material in this book divides naturally into two parts.

One part can be described as “what every mathematician (or at least every algebraist) should know about universal algebra.” It would form a short introductory course to universal algebra, and would consist of Chapter I. Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science.

Yet most of. The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.4/5(1).

The necessary underpinnings are offered by universal algebra, necessarily in a many-sorted variant, building on the classical single-sorted version. This chapter summarizes the basic concepts and results concerning many-sorted algebras that will be required for the rest of this book.

Nation Notes on Lattice Theory, online at JB's Books page. Burris and Sankappanavar, A Course in Universal Algebra, out of print but available online in pdf form. Denecke and Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, FL, ISBN: This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g.

semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. But you could probably google "Category theory for computer science" as well, and end up finding really good notes for free:) And just like Chas Brown states, cryptography is another part of CS where algebra has found applications.

You will probably find a lot of group and field theory applied there. Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing with things like generation of permutations, projective planes, orthogonal latin squares, graphs, difference sets, block designs, and Hadamard matrices.

Computer Science from theory to practice; Computer Science, being a science of the arti cial, has had many of its constructs and ideas inspired by Set Theory. The strong tradition, universality and neutrality of Set Theory make it rm common ground on which to provide uni cation between seemingly disparate areas and notations of Computer Science.

Universal Algebra heralded as " the standard reference in a field notorious for the lack of standardization", has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science.

Each chapter is followed by an extensive list of exercises and problems. of the term algebra of the least -theory is the starting point for studying lambda calculus by universal algebraic methods, through the variety generated by the term algebra of.

In [63] Salibra has shown that the variety generated by the term algebra of is axiomatized by the finite schema of identities characterizing -abstraction algebras.

$1$-Universal Algebra by George Graetzer. And any book on lattices by George Graetzer. $2$- Lectures on boolean algebra by Halmos or his new text which is co-authored with Givant. $3$- Algebraic methods in philosophical logic by Dunn and Hardegree which will gather all the stuff of lattices, universal algebra and boolean algebrs together.

The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature.

Finite Semigroups and Universal Algebra (Series in Algebra, Vol 3) Jorge Almeida Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics.

Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in.

Universal Algebra for Computer Scientists and a great selection of related books, art and collectibles available now at - Universal Algebra for Computer Scientists E a T C S Monographs on Theoretical Computer Science by Wechler, Wolfgang - AbeBooks.

Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely group theory, universal algebra and related areas, to applications in several different From the computational side, the book aims to reflect the rapidly emerging area of algorithmic problems in algebra, their computational complexity and.

$\begingroup$ i am not disputing the relevance of ramsey theory, let alone graph theory, to tcs. i am saying that the OP asked about applications of algebra and ramsey theory is not something usually associated with algebra, afaik.

but since you seem to have some connection ramsey theory -> algebra -> tcs in mind, maybe you can add that to your. A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science.

This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June; Groups, Algorithms, and Cryptography, held during the Joint Mathematics Meeting in San Antonio, TX, January; and Applications of Algebra to Cryptography, held during the Joint AMS-Israel Mathematical Union.

Linear Algebra, Theory and Applications was written by Dr. Kenneth Kuttler of Brigham Young University for teaching Linear Algebra II. After The Saylor Foundation accepted his submission to Wave I of the Open Textbook Challenge, this textbook was relicens\ ed as CC-BY A universal algebra A is denoted by the same symbol as its base set.

A class of algebras always means a class of universal algebras of the same similarity type. A variety—equational class—is a class of algebras closed under subalgebras, homomorphic images, and direct products. An algebra A is called congruence modular if Con A is modular.

Abstract. In Chapter 8, we present several additional practical applications of linear algebra in mathematics and the sciences. These include an introduction to graph theory, applying Ohm’s and Kirchhoff’s laws in circuit theory, approximating data using the least-squares method, Markov chains, an introduction to coding theory via Hill substitutions, how the formulas for conic sections.

Applications of categories. Categories now appear in many branches of mathematics, some areas of theoretical computer science where they can correspond to types or to database schemas, and mathematical physics where they can be used to describe vector spaces.

Probably the first application of category theory outside pure mathematics was the "metabolism-repair" model of autonomous living. Universal algebra has also been studied using the techniques of category this approach, instead of writing a list of operations and equations obeyed by those operations, one can describe an algebraic structure using categories of a special sort, known as Lawvere theories or more generally algebraic atively, one can describe algebraic structures using monads.Benjamin Fine is a contributing author, "On secret sharing protocols" with Chi Sing Chum, Anja IS Moldenhauer, Gerhard Rosenberger, and Xiaowen Zhang.

Book description: This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June; Groups, Algorithms, and Cryptography, held.

Every time I’ve taught the course (undergraduate), I’ve been saddled with someone else’s choice of text. And they’ve generally been isomorphic (the same) and not particularly inspiring. So I’m going with speculation here - in terms of what I think.