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: 299

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.

This new edition includes new chapters on statements and proof, logical framework, natural numbers and the integers and updated exercises from the previous edition.

Author: Norman L. Biggs

Publisher: Oxford University Press

ISBN: 0198507178

Category: Computers

Page: 425

View: 209

Discrete mathematics is a compulsory subject for undergraduate computer scientists. This new edition includes new chapters on statements and proof, logical framework, natural numbers and the integers and updated exercises from the previous edition.

This edition focuses on adding a theme of how to do proofs and picking topics that tie better into the computer science world. Also included is a new section called "Office Hours" which stresses how to do proofs.

Author: Kenneth A. Ross

Publisher:

ISBN: STANFORD:36105022126861

Category: Computers

Page: 684

View: 738

This edition focuses on adding a theme of how to do proofs and picking topics that tie better into the computer science world. Also included is a new section called "Office Hours" which stresses how to do proofs.

As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students.

Author: Amanda Chetwynd

Publisher: Elsevier

ISBN: 9780080928609

Category: Mathematics

Page: 224

View: 240

As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks). Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.

Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought.

Author: Susanna S. Epp

Publisher: Brooks/Cole Publishing Company

ISBN: 0534359450

Category: Mathematics

Page: 902

View: 976

Susanna Epp's DISCRETE MATHEMATICS, THIRD EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics.

Author: Jean Gallier

Publisher: Springer

ISBN: 1441980466

Category: Mathematics

Page: 466

View: 478

This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.

This new edition includes: • An expanded section on encryption • Additional examples of the ways in which theory can be applied to problems in computing • Many more exercises covering a range of levels, from the basic to the more ...

Author: Peter Grossman

Publisher: Macmillan International Higher Education

ISBN: 9780230374058

Category: Computers

Page: 328

View: 817

Discrete Mathematics for Computing presents the essential mathematics needed for the study of computing and information systems. The subject is covered in a gentle and informal style, but without compromising the need for correct methodology. It is perfect for students with a limited background in mathematics. This new edition includes: • An expanded section on encryption • Additional examples of the ways in which theory can be applied to problems in computing • Many more exercises covering a range of levels, from the basic to the more advanced This book is ideal for students taking a one-semester introductory course in discrete mathematics - particularly for first year undergraduates studying Computing and Information Systems. PETER GROSSMAN has worked in both MA26 and industrial roles as a mathematician and computing professional. As a lecturer in mathematics, he was responsible for coordinating and developing mathematics courses for Computing students. He has also applied his skills in areas as diverse as calculator design, irrigation systems and underground mine layouts. He lives and works in Melbourne, Australia.

The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners.

Author: Kevin Ferland

Publisher: Cengage Learning

ISBN: 0618415386

Category: Mathematics

Page: 720

View: 151

Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for students who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Key features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the ...

Author: W.D. Wallis

Publisher: Springer Science & Business Media

ISBN: 0817682864

Category: Mathematics

Page: 427

View: 857

Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students. —Choice reviews (Review of the First Edition) Very appropriately entitled as a 'beginner's guide', this textbook presents itself as the first exposure to discrete mathematics and rigorous proof for the mathematics or computer science student. —Zentralblatt Math (Review of the First Edition) This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory of voting as well as numerous new examples and exercises throughout the book * Introduces functions, vectors, matrices, number systems, scientific notations, and the representation of numbers in computers * Provides examples which then lead into easy practice problems throughout the text and full exercise at the end of each chapter * Full solutions for practice problems are provided at the end of the book This text is intended for undergraduates in mathematics and computer science, however, featured special topics and applications may also interest graduate students.

The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics.

Author: Eric Gossett

Publisher: John Wiley & Sons

ISBN: 9780470457931

Category: Mathematics

Page: 928

View: 326

A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.

The excitement of discrete mathematics comes from discovery, the act of
uncovering beautiful and important properties of graphs, partitions, permutations,
and other combinatorial objects. The appeal of discrete mathematics is its
concreteness ...

Author: Sriram Pemmaraju

Publisher: Cambridge University Press

ISBN: 0521806860

Category: Computers

Page: 480

View: 343

This definitive reference on Combinatorica contains examples of all 450 functions plus tutorial text.

Discrete mathematics is the basic language which every student of computing should take pride in mastering and this book should prove an essential tool in this aim.

Author: Mike Piff

Publisher: Cambridge University Press

ISBN: 0521386225

Category: Computers

Page: 317

View: 179

Discrete mathematics is the basic language which every student of computing should take pride in mastering and this book should prove an essential tool in this aim.

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics.

Author: L. Lovász

Publisher: Springer Science & Business Media

ISBN: 0387955852

Category: Mathematics

Page: 284

View: 474

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Activity 2 : Help with Proofs Discrete mathematics is often the first course in which
students are introduced to the concept of proofs . The calculator will not prove or
disprove a statement but can be used as an aid to determine the suspected ...

Author: Brian Hopkins

Publisher: MAA

ISBN: 0883851849

Category: Mathematics

Page: 323

View: 323

Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome. The book contains eleven history modules that allow students to explore topics in their original context. Sources range from eleventh century Chinese figures that prompted Leibniz to write on binary arithmetic, to a 1959 article on automata theory. Excerpts include: Pascal's "Treatise on the Arithmetical Triangle," Hamilton's "Account of the Icosian Game," and Cantor's (translated) "Contributions to the Founding of the Theory of Transfinite Numbers." Five articles complete the book. Three address extensions of standard discrete mathematics content: an exploration of historical counting problems with attention to discovering formulas, a discussion of how computers store graphs, and a survey connecting the principle of inclusion-exclusion to Möbius inversion. Finally, there are two articles on pedagogy specifically related to discrete mathematics courses: a summary of adapting a group discovery method to larger classes, and a discussion of using logic in encouraging students to construct proofs.

Appendix B Resources on the Web Home page for Discrete Mathematics Using a
Computer. The book's web page contains a variety of useful information, and is
an integral part of the book: • You can download the Software Tools for Discrete ...

Author: Cordelia Hall

Publisher: Springer Science & Business Media

ISBN: 9781852330897

Category: Computers

Page: 339

View: 957

This volume offers a new, hands-on approach to teaching Discrete Mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up. This practical approach provides students with instant feedback and also allows lecturers to monitor progress easily. All the material needed to use the book will be available via ftp (the software is freely available and runs on Mac, PC and Unix platforms), including a special module which implements the concepts to be learned.No prior knowledge of Functional Programming is required: apart from List Comprehension (which is comprehensively covered in the text) everything the students need is either provided for them or can be picked up easily as they go along. An Instructors Guide will also be available on the WWW to help lecturers adapt existing courses.

Author: Richard D. RingeisenPublish On: 1988-01-01

He or she will also find applications of discrete mathematics in fields from
chemistry to airline scheduling . Articles that nicely survey a given field , as well
as those that represent the very forefront of a given research topic , are also
included .

and Theoretical Computer Science and Discrete Mathematics Volume 4. 1991
THE VICTOR KLEE FESTSCHRIFT On Sign-Nonsingular Matrices and the
Conversion of the Permanent into the Determinant RICHARD A. BRUALDI AND
BRYAN ...

Author: Peter Gritzmann

Publisher: American Mathematical Soc.

ISBN: 0821870831

Category: Mathematics

Page: 608

View: 864

This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.

This approachable text studies discrete objects and the relationsips that bind them.

Author: Thomas Koshy

Publisher: Elsevier

ISBN: 0080477348

Category: Mathematics

Page: 1042

View: 384

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)

The book will enable the students to develop the requisite computational skills needed in software engineering.

Author: Babu Ram

Publisher: Pearson Education India

ISBN: 8131733106

Category: Computer science

Page: 584

View: 532

Discrete Mathematics will be of use to any undergraduate as well as post graduate courses in Computer Science and Mathematics. The syllabi of all these courses have been studied in depth and utmost care has been taken to ensure that all the essential topics in discrete structures are adequately emphasized. The book will enable the students to develop the requisite computational skills needed in software engineering.