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| boolean algebra and its applications download: Boolean Algebra and Its Applications J. Eldon Whitesitt, 2012-05-24 Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition. |
| boolean algebra and its applications download: Boolean Algebra and Its Applications J. Eldon Whitesitt, 2010-03-18 This introduction to Boolean algebra begins with an intuitive approach to set theory and an axiomatic account of the fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. Answers to selected problems appear at the end. 1961 edition. |
| boolean algebra and its applications download: Boolean Valued Analysis A.G. Kusraev, Semën Samsonovich Kutateladze, 2012-10-26 Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models. |
| boolean algebra and its applications download: Abstract Algebra Thomas Judson, 2023-08-11 Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory. |
| boolean algebra and its applications download: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| boolean algebra and its applications download: Boolean Functions and Their Applications in Cryptography Chuan-Kun Wu, Dengguo Feng, 2016-02-23 This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions. |
| boolean algebra and its applications download: Analysis of Boolean Functions Ryan O'Donnell, 2014-06-05 This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics. |
| boolean algebra and its applications download: Orthomodular Lattices L. Beran, 2012-12-06 Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Bowever, the tree of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programmi ng profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as completely integrable systems, chaos, synergetics and large-s.cale order, which are almost impossible to fit into the existing classifica tion schemes. They draw upon widely different sections of mathe matics. |
| boolean algebra and its applications download: Cryptographic Boolean Functions and Applications Thomas W. Cusick, Pantelimon Stănică, 2009 Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce). Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. -Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions -Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography -Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource. -Organized logically to help the reader easily understand the topic |
| boolean algebra and its applications download: Boolean Algebra and Its Applications J Eldon (John Eldon) 1922- Whitesitt, 2021-09-09 This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| boolean algebra and its applications download: Algebraic Logic Paul R. Halmos, 2016-03-17 Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic and polyadic algebras, these articles are essentially self-contained and accessible to a general mathematical audience, requiring no specialized knowledge of algebra or logic. Part One addresses monadic algebras, with articles on general theory, representation, and freedom. Part Two explores polyadic algebras, progressing from general theory and terms to equality. Part Three offers three items on polyadic Boolean algebras, including a survey of predicates, terms, operations, and equality. The book concludes with an additional bibliography and index. |
| boolean algebra and its applications download: Boolean Functions Yves Crama, Peter L. Hammer, 2011-05-16 Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics. |
| boolean algebra and its applications download: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| boolean algebra and its applications download: Bebop to the Boolean Boogie Clive Maxfield, 2008-12-05 This entertaining and readable book provides a solid, comprehensive introduction to contemporary electronics. It's not a how-to-do electronics book, but rather an in-depth explanation of how today's integrated circuits work, how they are designed and manufactured, and how they are put together into powerful and sophisticated electronic systems. In addition to the technical details, it's packed with practical information of interest and use to engineers and support personnel in the electronics industry. It even tells how to pronounce the alphabet soup of acronyms that runs rampant in the industry. - Written in conversational, fun style that has generated a strong following for the author and sales of over 14,000 copies for the first two editions - The Third Edition is even bigger and better, with lots of new material, illustrations, and an expanded glossary - Ideal for training incoming engineers and technicians, and for people in marketing or other related fields or anyone else who needs to familiarize themselves with electronics terms and technology |
| boolean algebra and its applications download: Lectures on Boolean Algebras Paul R. Halmos, 2018-09-12 This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included. |
| boolean algebra and its applications download: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| boolean algebra and its applications download: Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference Robert Rolland, James Hirschfeld, Jean Chaumine, 2008-04-17 This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry. |
| boolean algebra and its applications download: Discrete Mathematics with Applications Thomas Koshy, 2004-01-19 This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor's Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828) |
| boolean algebra and its applications download: Logic and Its Applications Md. Aquil Khan, Amaldev Manuel, 2019-02-05 This book collects the refereed proceedings of the 8th Indian Conference on Logic and Its Applications, ICLA 2019, held in Delhi, India, in March 2019. The volume contains 13 full revised papers along with 6 invited talks presented at the conference. The aim of this conference series is to bring together researchers from a wide variety of fields in which formal logic plays a significant role. Areas of interest include mathematical and philosophical logic, computer science logic, foundations and philosophy of mathematics and the sciences, use of formal logic in areas of theoretical computer science and artificial intelligence, logic and linguistics, and the relationship between logic and other branches of knowledge. Of special interest are studies in systems of logic in the Indian tradition, and historical research on logic. |
| boolean algebra and its applications download: Boolean Reasoning Frank Markham Brown, 2012-02-10 Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition. |
| boolean algebra and its applications download: An Introduction to Semi-tensor Product of Matrices and Its Applications Dai-Zhan Cheng, Yin Zhao, 2012 A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others. |
| boolean algebra and its applications download: Algebraic Methods of Mathematical Logic Ladislav Rieger, 2014-05-12 Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic. |
| boolean algebra and its applications download: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
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| boolean algebra and its applications download: Foundations of Computation Carol Critchlow, David Eck, 2011 Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science. |
| boolean algebra and its applications download: Boolean Differential Equations Bernd Steinbach, Christian Posthoff, 2013-06-01 The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly. |
| boolean algebra and its applications download: Applied Abstract Algebra Rudolf Lidl, Günter Pilz, 2013-03-14 Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields. |
| boolean algebra and its applications download: Embedded Systems Dictionary Jack Ganssle, 2003-01-04 This technical dictionary defines the 2,500 most-used words in the embedded systems field, with over 4,500 entries and cross-references. Designed to serve both the technical and non-technical audience, this book defines advanced terms in two steps. The fi |
| boolean algebra and its applications download: Digital Logic Design Brian Holdsworth, Clive Woods, 2002-11-01 New, updated and expanded topics in the fourth edition include: EBCDIC, Grey code, practical applications of flip-flops, linear and shaft encoders, memory elements and FPGAs. The section on fault-finding has been expanded. A new chapter is dedicated to the interface between digital components and analog voltages. - A highly accessible, comprehensive and fully up to date digital systems text - A well known and respected text now revamped for current courses - Part of the Newnes suite of texts for HND/1st year modules |
| boolean algebra and its applications download: Linear Algebra and Its Applications with R Ruriko Yoshida, 2021-06-23 The book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. These students tend not to realize the importance of linear algebra in applied sciences since traditional linear algebra courses tend to cover mathematical contexts but not the computational aspect of linear algebra or its applications to data science and bioinformatics. The author presents the topics in a traditional course yet offers lectures as well as lab exercises on simulated and empirical data sets. This textbook provides students a theoretical basis which can then be applied to the practical R and Python problems, providing the tools needed for real-world applications. Each section starts with working examples to demonstrate how tools from linear algebra can help solve problems in applied science. These exercises start from easy computations, such as computing determinants of matrices, to practical applications on simulated and empirical data sets with R so that students learn how to get started with R along with computational examples in each section and then they learn how to apply what they learn to problems in applied sciences. This book is designed from first principles to demonstrate the importance of linear algebra through working computational examples with R and python including tutorials on how to install R in the Appendix. If a student has never seen R, they can get started without any additional help. Since Python is one of the most popular languages in data science, optimization, and computer science, code supplements are available for students who feel more comfortable with Python. R is used primarily for computational examples to develop student’s practical computational skills. Table of Contents Preface List of Figures List of Tables 1. Systems of Linear Equations and Matrices 2. Matrix Arithmetic 3. Deteminants 4. Vector Spaces 5. Inner Product Space 6. Eigen values and Eigen vectors 7. Linear Regression 8. Linear Programming Network Analysis Appendices A) Introduction to RStudio via Amazon Web Service (AWS) B) Introduction to R Bibliography Index Biography Dr. Ruriko Yoshida is an Associate Professor of Operations Research at the Naval Postgraduate School. She received her Ph.D. in Mathematics from the University of California, Davis. Her research topics cover a wide variety of areas: applications of algebraic combinatorics to statistical problems such as statistical learning on non-Euclidean spaces, sensor networks, phylogenetics, and phylogenomics. She teaches courses in statistics, stochastic models, probability, and data science. |
| boolean algebra and its applications download: Sequences and Their Applications -- SETA 2012 Tor Helleseth, Jonathan Jedwab, 2012-06-26 This book constitutes the refereed proceedings of the 7th International Conference on Sequences and Their Applications, SETA 2012, held in Waterloo, Canada, in June 2012. The 28 full papers presented together with 2 invited papers in this volume were carefully reviewed and selected from 48 submissions. The papers are grouped in topical sections on perfect sequences; finite fields; boolean functions; Golomb 80th birthday session; linear complexity; frequency hopping; correlation of sequences; bounds on sequences, cryptography; aperiodic correlation; and Walsh transform. |
| boolean algebra and its applications download: Proof Theory and Algebra in Logic Hiroakira Ono, 2019-08-02 This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic. |
| boolean algebra and its applications download: Digital Design Mohammad Karim, Xinghao Chen, 2017-12-19 In today’s digital design environment, engineers must achieve quick turn-around time with ready accesses to circuit synthesis and simulation applications. This type of productivity relies on the principles and practices of computer aided design (CAD). Digital Design: Basic Concepts and Principles addresses the many challenging issues critical to today’s digital design practices such as hazards and logic minimization, finite-state-machine synthesis, cycles and races, and testability theories while providing hands-on experience using one of the industry’s most popular design application, Xilinx Web PACKTM. The authors begin by discussing conventional and unconventional number systems, binary coding theories, and arithmetic as well as logic functions and Boolean algebra. Building upon classic theories of digital systems, the book illustrates the importance of logic minimization using the Karnaugh map technique. It continues by discussing implementation options and examining the pros and cons of each method in addition to an assessment of tradeoffs that often accompany design practices. The book also covers testability, emphasizing that a good digital design must be easy to verify and test with the lowest cost possible. Throughout the text, the authors analyze combinational and sequential logic elements and illustrate the designs of these components in structural, hierarchical, and behavior VHDL descriptions. Coveringfundamentals and best practices, Digital Design: Basic Concepts and Principles provides you with critical knowledge of how each digital component ties together to form a system and develops the skills you need to design and simulate these digital components using modern CAD software. |
| boolean algebra and its applications download: Universal Algebra, Algebraic Logic, and Databases B. Plotkin, 2012-10-12 Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills. |
| boolean algebra and its applications download: Complexity Classifications of Boolean Constraint Satisfaction Problems Nadia Creignou, Sanjeev Khanna, Madhu Sudan, 2001-01-01 Many fundamental combinatorial problems, arising in such diverse fields as artificial intelligence, logic, graph theory, and linear algebra, can be formulated as Boolean constraint satisfaction problems (CSP). This book is devoted to the study of the complexity of such problems. The authors' goal is to develop a framework for classifying the complexity of Boolean CSP in a uniform way. In doing so, they bring out common themes underlying many concepts and results in both algorithms and complexity theory. The results and techniques presented here show that Boolean CSP provide an excellent framework for discovering and formally validating global inferences about the nature of computation. |
| boolean algebra and its applications download: Lattice Functions and Equations Sergiu Rudeanu, 2001-07-30 One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations. |
| boolean algebra and its applications download: MODERN ALGEBRA WITH APPLICATIONS William J Gilbert, 2008-09 Market_Desc: Upper undergraduate and graduate level modern algebra courses Special Features: · Includes applications so students can see right away how to use the theory· This classic text has sold almost 12,000 units· Contains numerous examples· Includes chapters on Boolean Algebras, groups, quotient groups, symmetry groups in three dimensions, Polya-Burnside method of enumeration, monoids and machines, rings and fields, polynomial and Euclidean rings, quotient rings, field extensions, Latin squares, geometrical constructions, and error-correcting codes· Andwers to odd-numbered exercises so students can check their work About The Book: The book covers all the group, ring, and field theory that is usually contained in a standard modern algebra course; the exact sections containing this material are indicated in the Table of Contents. It stops short of the Sylow theorems and Galois theory. These topics could only be touched on in a first course, and the author feels that more time should be spent on them if they are to be appreciated. |
| boolean algebra and its applications download: The Bulletin of Symbolic Logic , 2004 |
| boolean algebra and its applications download: Boolean Methods in Operations Research and Related Areas P. L. Hammer, S. Rudeanu, 2012-12-06 In classical analysis, there is a vast difference between the class of problems that may be handled by means of the methods of calculus and the class of problems requiring combinatorial techniques. With the advent of the digital computer, the distinction begins to blur, and with the increasing emphasis on problems involving optimization over structures, tIlE' distinction vanishes. What is necessary for the analytic and computational treatment of significant questions arising in modern control theory, mathematical economics, scheduling theory, operations research, bioengineering, and so forth is a new and more flexible mathematical theory which subsumes both the cla8sical continuous and discrete t 19orithms. The work by HAMMER (IVANESCU) and RUDEANU on Boolean methods represents an important step in this dnectlOn, and it is thus a great pleasure to welcome it into print. It will certainly stimulate a great deal of additional research in both theory and application. RICHARD BELLMAN University of Southern California FOf(,WOl' |
Boolean algebra - Wikipedia
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and …
What is a Boolean? - Computer Hope
Jun 1, 2025 · In computer science, a boolean or bool is a data type with two possible values: true or false. It is named after the English mathematician and logician George Boole, whose …
Boolean Algebra - GeeksforGeeks
Apr 15, 2025 · Boolean Algebra is a branch of algebra that deals with boolean values—true and false. It is fundamental to digital logic design and computer science, providing a mathematical …
How Boolean Logic Works - HowStuffWorks
May 22, 2024 · A subsection of mathematical logic, Boolean logic deals with operations involving the two Boolean values: true and false. Although Boolean logic dates back to the mid-19th …
What Boolean Logic Is & How It’s Used In Programming
Mar 21, 2022 · Boolean logic is a type of algebra in which results are calculated as either TRUE or FALSE (known as truth values or truth variables). Instead of using arithmetic operators like …
What is Boolean in computing? – TechTarget Definition
Nov 7, 2022 · In computing, the term Boolean means a result that can only have one of two possible values: true or false. Boolean logic takes two statements or expressions and applies …
BOOLEAN Definition & Meaning - Merriam-Webster
The meaning of BOOLEAN is of, relating to, or being a logical combinatorial system (such as Boolean algebra) that represents symbolically relationships (such as those implied by the …
Boolean Algebra - Math is Fun
Boolean Algebra is about true and false and logic. The simplest thing we can do is to "not" or "invert": We can write this down in a "truth table" (we use T for true and F for false): We can …
Boolean Algebra Solver - Boolean Expression Calculator
Boolean Algebra expression simplifier & solver. Detailed steps, Logic circuits, KMap, Truth table, & Quizes. All in one boolean expression calculator. Online tool. Learn boolean algebra.
Boolean - Wikipedia
Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: Boolean circuit, a mathematical model for …
Boolean algebra - Wikipedia
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and …
What is a Boolean? - Computer Hope
Jun 1, 2025 · In computer science, a boolean or bool is a data type with two possible values: true or false. It is named after the English mathematician and logician George Boole, whose …
Boolean Algebra - GeeksforGeeks
Apr 15, 2025 · Boolean Algebra is a branch of algebra that deals with boolean values—true and false. It is fundamental to digital logic design and computer science, providing a mathematical …
How Boolean Logic Works - HowStuffWorks
May 22, 2024 · A subsection of mathematical logic, Boolean logic deals with operations involving the two Boolean values: true and false. Although Boolean logic dates back to the mid-19th …
What Boolean Logic Is & How It’s Used In Programming
Mar 21, 2022 · Boolean logic is a type of algebra in which results are calculated as either TRUE or FALSE (known as truth values or truth variables). Instead of using arithmetic operators like …
What is Boolean in computing? – TechTarget Definition
Nov 7, 2022 · In computing, the term Boolean means a result that can only have one of two possible values: true or false. Boolean logic takes two statements or expressions and applies …
BOOLEAN Definition & Meaning - Merriam-Webster
The meaning of BOOLEAN is of, relating to, or being a logical combinatorial system (such as Boolean algebra) that represents symbolically relationships (such as those implied by the …
Boolean Algebra - Math is Fun
Boolean Algebra is about true and false and logic. The simplest thing we can do is to "not" or "invert": We can write this down in a "truth table" (we use T for true and F for false): We can …
Boolean Algebra Solver - Boolean Expression Calculator
Boolean Algebra expression simplifier & solver. Detailed steps, Logic circuits, KMap, Truth table, & Quizes. All in one boolean expression calculator. Online tool. Learn boolean algebra.
Boolean - Wikipedia
Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: Boolean circuit, a mathematical model for …
