Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, ...

Author: Willem Conradie

Publisher: John Wiley & Sons

ISBN: 9781118762677

Category: Mathematics

Page: 200

View: 700

Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.

This in turn means about the same as being formalizable and provable in Peano
arithmetic PA, introduced in 3.3. ... It is of special importance because most of
classical number theory and of discrete mathematics can be developed in it.

Author: Wolfgang Rautenberg

Publisher: Springer

ISBN: 1441912215

Category: Mathematics

Page: 320

View: 853

Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

Author: V. K . Balakrishnan

Publisher: Courier Corporation

ISBN: 9780486140384

Category: Mathematics

Page: 256

View: 885

This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

The text reflects the need to quickly introduce students from a variety of educational backgrounds to a number of essential mathematical concepts.

Author: Ovidiu Bagdasar

Publisher: Springer Science & Business Media

ISBN: 9783319017518

Category: Computers

Page: 109

View: 379

Adapted from a modular undergraduate course on computational mathematics, Concise Computer Mathematics delivers an easily accessible, self-contained introduction to the basic notions of mathematics necessary for a computer science degree. The text reflects the need to quickly introduce students from a variety of educational backgrounds to a number of essential mathematical concepts. The material is divided into four units: discrete mathematics (sets, relations, functions), logic (Boolean types, truth tables, proofs), linear algebra (vectors, matrices and graphics), and special topics (graph theory, number theory, basic elements of calculus). The chapters contain a brief theoretical presentation of the topic, followed by a selection of problems (which are direct applications of the theory) and additional supplementary problems (which may require a bit more work). Each chapter ends with answers or worked solutions for all of the problems.

The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts.

Author: T. Sengadir

Publisher: Pearson Education India

ISBN: 8131714055

Category: Applied mathematics

Page: 568

View: 210

Discrete Mathematics and Combinatorics provides a concise and practical introduction to the core components of discrete mathematics, featuring a balanced mix of basic theories and applications. The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts. Other pedagogical tools - illustrations, practice questions, and suggested reading - facilitate learning and mastering the subject."--Cover.

Intended for a one-term course in discrete mathematics, to prepare freshmen and sophomores for further work in computer science as well as mathematics.

Author: Steven Roman

Publisher: Harcourt College Pub

ISBN: 0155417304

Category: Mathematics

Page: 469

View: 989

Intended for a one-term course in discrete mathematics, to prepare freshmen and sophomores for further work in computer science as well as mathematics. Sets, proof techniques, logic, combinatorics, and graph theory are covered in concise form. All topics are motivated by concrete examples, often emphasizing the interplay between computer science and mathematics. Examples also illustrate all definitions. Applications and references cover a wide variety of realistic situations. Coverage of mathematical induction includes the stroung form of induction, and new sections have been added on nonhomogeneous recurrence relations and the essentials of probability.

This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions.

Author: Sergei Kurgalin

Publisher: Springer

ISBN: 3030422208

Category: Computers

Page: 500

View: 540

This practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity. This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions. Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including Turing machines, asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language.

This is the ideal text for a one-term discrete mathematics course to serve computer scientists as well as other students. It introduces students to the mathematical way of thinking, and also to many important modern applications.

Author: David J. Hunter

Publisher: Jones & Bartlett Publishers

ISBN: 9781449604424

Category: Computers

Page: 488

View: 523

Essentials of Discrete Mathematics, Second Edition is the ideal text for a one-term discrete mathematics course to serve computer science majors as well as students from a wide range of other disciplines. It introduces students to the mathematical way of thinking, and also to many important modern applications. The material is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical. This presentation results in a coherent outline that steadily builds upon mathematical sophistication. Graphs are introduced early and referred to throughout the text, providing a richer context for examples and applications. Students will encounter algorithms near the end of the text, after they have acquired the skills and experience needed to analyze them. The final chapter contains in-depth case studies from a variety of fields, including biology, sociology, linguistics, economics, and music. Clear and concise, Essentials of Discrete Mathematics presents a unified and complete picture of discrete mathematics that instructors can cover in a single semester.

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively.

Author: Hiroakira Ono

Publisher: Springer

ISBN: 9789811379970

Category: Philosophy

Page: 160

View: 398

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.

This text is deliberately non-mathematical and, wherever possible, links theory to practical considerations, in particular the implications for programming, computation and problem solving.

Author: Alan P. Parkes

Publisher: Springer Science & Business Media

ISBN: 9781848001213

Category: Computers

Page: 346

View: 680

A Concise Introduction to Languages, Machines and Logic provides an accessible introduction to three key topics within computer science: formal languages, abstract machines and formal logic. Written in an easy-to-read, informal style, this textbook assumes only a basic knowledge of programming on the part of the reader. The approach is deliberately non-mathematical, and features: - Clear explanations of formal notation and jargon, - Extensive use of examples to illustrate algorithms and proofs, - Pictorial representations of key concepts, - Chapter opening overviews providing an introduction and guidance to each topic, - End-of-chapter exercises and solutions, - Offers an intuitive approach to the topics. This reader-friendly textbook has been written with undergraduates in mind and will be suitable for use on course covering formal languages, formal logic, computability and automata theory. It will also make an excellent supplementary text for courses on algorithm complexity and compilers.

This stimulating guide provides a broad and accessible overview of formal methods for students of computer science and mathematics curious as to how formal methods are applied to the field of computing.

Author: Gerard O'Regan

Publisher: Springer

ISBN: 9783319640211

Category: Mathematics

Page: 322

View: 340

This invaluable textbook/reference provides an easy-to-read guide to the fundamentals of formal methods, highlighting the rich applications of formal methods across a diverse range of areas of computing. Topics and features: introduces the key concepts in software engineering, software reliability and dependability, formal methods, and discrete mathematics; presents a short history of logic, from Aristotle’s syllogistic logic and the logic of the Stoics, through Boole’s symbolic logic, to Frege’s work on predicate logic; covers propositional and predicate logic, as well as more advanced topics such as fuzzy logic, temporal logic, intuitionistic logic, undefined values, and the applications of logic to AI; examines the Z specification language, the Vienna Development Method (VDM) and Irish School of VDM, and the unified modelling language (UML); discusses Dijkstra’s calculus of weakest preconditions, Hoare’s axiomatic semantics of programming languages, and the classical approach of Parnas and his tabular expressions; provides coverage of automata theory, probability and statistics, model checking, and the nature of proof and theorem proving; reviews a selection of tools available to support the formal methodist, and considers the transfer of formal methods to industry; includes review questions and highlights key topics in every chapter, and supplies a helpful glossary at the end of the book. This stimulating guide provides a broad and accessible overview of formal methods for students of computer science and mathematics curious as to how formal methods are applied to the field of computing.

This book is written at an appropriate level for a wide variety of readers, and assumes a college algebra course as the only prerequisite.

Author: Bernard Kolman

Publisher: Prentice Hall

ISBN: 0132297515

Category: Mathematics

Page: 522

View: 793

Key Message: Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field, and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers, and assumes a college algebra course as the only prerequisite. Key Topics: Fundamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics.

This work is 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.

Author: Bernd Schröder

Publisher: Springer Science & Business Media

ISBN: 9781461200536

Category: Mathematics

Page: 391

View: 159

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.

physical phenomena has led to breakthroughs in physics, so the study of
mathematical models describing language approaches will likely ... Peppered
throughout the chapters on procedural, object-oriented, functional, and logic
programming languages are syntactic and semantic definitions. ... Readers of this
text are expected to know discrete mathematics and programming through data
structures.

Author: Daniel Cooke

Publisher: Brooks/Cole Publishing Company

ISBN: UCSC:32106011431852

Category: Computers

Page: 252

View: 965

Daniel Cooke's new text provides an innovative approach that makes the teaching of methods and mathematical tools employed in designing a language accessible to students. Although many professors find this material to be important, some limit the coverage of language design topics as a result of students' struggles with mathematics. The author covers material on language syntax, language semantics, and language translation in the first half of the book, while relying on the mathematics students have learned in their previous classes. He continues to draw on this material throughout the book as needed - after students have received the background they need in the formal underpinnings of all languages. The author presents paradigms and languages in the context of language design. For instance, in Chapter 5 he introduces imperative and procedural programming as the foundations of other languages, along with input/output, if and else statements, loop statements, and arithmetics. As new paradigms are introduced, he revisits these basic constructs and discusses the decisions to add, modify, and/or delete them based on the problem solving abstraction. As a result, students are better able to grasp new languages by understanding their unique features as well as features shared with other languages.

Presents a gentle introduction to all the basics of discrete mathematics.Introduces sets and logic, providing clear instructions on calculating values for mathematical expressions for small finite sets.

Author: Neville Dean

Publisher:

ISBN: 0133459438

Category: Mathematics

Page: 197

View: 876

Presents a gentle introduction to all the basics of discrete mathematics.Introduces sets and logic, providing clear instructions on calculating values for mathematical expressions for small finite sets. For simplicity, uses sets of numbers extensively -- but also covers non-numerical examples. Introduces relations and functions, and then discusses how they can be modeled using sets. Shows how modeling with sets and logic can be applied to practical problems. Includes a running case study, worked examples and self-test questions.Undergraduate courses in discrete mathematics.

This engaging work provides a concise introduction to the exciting world of computing, encompassing the theory, technology, history, and societal impact of computer software and computing devices.

Author: Gerard O'Regan

Publisher: Springer

ISBN: 9783319758442

Category: Computers

Page: 320

View: 168

This engaging work provides a concise introduction to the exciting world of computing, encompassing the theory, technology, history, and societal impact of computer software and computing devices. Spanning topics from global conflict to home gaming, international business, and human communication, this text reviews the key concepts unpinning the technology which has shaped the modern world. Topics and features: introduces the foundations of computing, the fundamentals of algorithms, and the essential concepts from mathematics and logic used in computer science; presents a concise history of computing, discussing the historical figures who made important contributions, and the machines which formed major milestones; examines the fields of human−computer interaction, and software engineering; provides accessible introductions to the core aspects of programming languages, operating systems, and databases; describes the Internet revolution, the invention of the smartphone, and the rise of social media, as well as the Internet of Things and cryptocurrencies; explores legal and ethical aspects of computing, including issues of hacking and cybercrime, and the nature of online privacy, free speech and censorship; discusses such innovations as distributed systems, service-oriented architecture, software as a service, cloud computing, and embedded systems; includes key learning topics and review questions in every chapter, and a helpful glossary. Offering an enjoyable overview of the fascinating and broad-ranging field of computing, this easy-to-understand primer introduces the general reader to the ideas on which the digital world was built, and the historical developments that helped to form the modern age.

Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof.

Author: Harry Lewis

Publisher: Princeton University Press

ISBN: 9780691179292

Category: Computers

Page: 408

View: 193

A more intuitive approach to the mathematical foundation of computer science Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, this flexible book can be tailored to fit the syllabi for a variety of courses. Proven in the classroom, Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. The text requires only precalculus, and where calculus is needed, a quick summary of the basic facts is provided. Essential Discrete Mathematics for Computer Science is the ideal introductory textbook for standard undergraduate courses, and is also suitable for high school courses, distance education for adult learners, and self-study. The essential introduction to discrete mathematics Features thirty-one short chapters, each suitable for a single class lesson Includes more than 300 exercises Almost every formula and theorem proved in full Breadth of content makes the book adaptable to a variety of courses Each chapter includes a concise summary Solutions manual available to instructors

The probability calculus is a set of mathematical formulas for computing
probabilities. It is usually represented ... The classical theory begins with the idea
of an experiment that can have n discrete possible outcomes. According the
principle of ...

Author: Burch Hurle

Publisher:

ISBN: 0534520081

Category: Logic

Page: 185

View: 211

Includes summary statements of main points, worked-out examples with answers, and answers to additional exercises from the text.

The probability calculus is a set of mathematical formulas for computing
probabilities . It is usually represented by a set ... The classical theory begins with
the idea of an experiment that can have n discrete possible outcomes . According
to the ...

Grimaldi , Ralph P . , Discrete and Combinatorial Mathematics : An Applied
Introduction , 3rd ed . , Addison - Wesley Publishing Company ... A very concise introduction to transfinite arithmetic , without many exercises . ... An intro duction
to real analysis , written in a simple style and including some basic logic and set
theory .