Discrete Mathematics

Author: Martin Aigner

Publisher: American Mathematical Soc.

ISBN: 9780821886151

Category: Mathematics

Page: 388

View: 3434

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The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Introductory Discrete Mathematics

Author: V. K . Balakrishnan

Publisher: Courier Corporation

ISBN: 0486140385

Category: Mathematics

Page: 256

View: 3941

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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.

A Beginner’s Guide to Discrete Mathematics

Author: W.D. Wallis

Publisher: Springer Science & Business Media

ISBN: 1475738269

Category: Mathematics

Page: 367

View: 6077

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This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.

Discrete Mathematics with Ducks

Author: sarah-marie belcastro

Publisher: CRC Press

ISBN: 1466504994

Category: Computers

Page: 580

View: 8369

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Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting. Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems. Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.

Discrete Mathematics

An Open Introduction

Author: Oscar Levin

Publisher: Createspace Independent Publishing Platform

ISBN: 9781534970748

Category:

Page: 342

View: 1631

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This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.

Discrete Mathematics

Author: Norman Biggs

Publisher: Oxford University Press

ISBN: 9780198507178

Category: Computers

Page: 425

View: 1960

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The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics includes new chapters on statements and proof, logical framework, natural numbers and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.Key Features:* Contains nine new introductory chapters, in addition to updated chapters from the previous edition* Contains over 1000 individual exercises and selected solutions* Companion website www.oup.com/mathematics/discretemath contains hints and solutions to all exercisesContents:The Language of Mathematics1. Statements and proofs2. Set notation3. The logical framework4. Natural numbers5. Functions6. How to count 7. Integers8. Divisibility and prime numbers9. Fractions and real numbersTechniques10. Principles of counting11. Subsets and designs12. Partition, classification and distribution13. Modular arithmeticAlgorithms and Graphs14. Algorithms and their efficiency15. Graphs16. Trees, sorting and searching17. Bipartite graphs and matching problems18. Digraphs, networks and flows19. Recursive techniquesAlgebraic Methods20. Groups21. Groups of permutations22. Rings, fields and polynomials23. Finite fields and some applications24. Error-correcting codes25. Generating functions26. Partitions of a positive integer27. Symmetry and counting

Discrete Mathematics

for New Technology

Author: Rowan Garnier

Publisher: CRC Press

ISBN: 9780750301350

Category: Technology & Engineering

Page: 696

View: 1495

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In a comprehensive yet easy-to-follow manner, Discrete Mathematics for New Technology follows the progression from the basic mathematical concepts covered by the GCSE in the UK and by high-school algebra in the USA to the more sophisticated mathematical concepts examined in the latter stages of the book. The book punctuates the rigorous treatment of theory with frequent uses of pertinent examples and exercises, enabling readers to achieve a feel for the subject at hand. The exercise hints and solutions are provided at the end of the book. Topics covered include logic and the nature of mathematical proof, set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras, and a thorough treatise on graph theory. Although aimed primarily at computer science students, the structured development of the mathematics enables this text to be used by undergraduate mathematicians, scientists, and others who require an understanding of discrete mathematics.

Discrete Mathematics with Applications

Author: Susanna S. Epp

Publisher: Cengage Learning

ISBN: 0495391328

Category: Mathematics

Page: 984

View: 9362

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Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH 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. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Discrete Mathematics

Elementary and Beyond

Author: László Lovász,József Pelikán,Katalin Vesztergombi

Publisher: Springer Science & Business Media

ISBN: 0387217770

Category: Mathematics

Page: 284

View: 4931

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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.

Discrete Mathematics Research Progress

Author: Kenneth Brian Moore

Publisher: Nova Publishers

ISBN: 9781604561234

Category: Mathematics

Page: 250

View: 9495

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Discrete mathematics, also called finite mathematics or Decision Maths, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasise concepts for computer science majors.

Discrete Mathematics with Applications

Author: Thomas Koshy

Publisher: Elsevier

ISBN: 9780080477343

Category: Mathematics

Page: 1042

View: 1512

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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)

Discrete Mathematics for New Technology, Second Edition

Author: Rowan Garnier,John Taylor

Publisher: CRC Press

ISBN: 9781420056983

Category: Mathematics

Page: 749

View: 5255

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Updated and expanded, Discrete Mathematics for New Technology, Second Edition provides a sympathetic and accessible introduction to discrete mathematics, including the core mathematics requirements for undergraduate computer science students. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined in the latter stages of the book. Although the theory is presented rigorously, it is illustrated by the frequent use of pertinent examples and is further reinforced with exercises-some with hints and solutions-to enable the reader to achieve a comprehensive understanding of the subject at hand. New to the Second Edition Numerous new examples and exercises designed to illustrate and reinforce mathematical concepts and facilitate students' progression through the topics New sections on typed set theory and an introduction to formal specification Presenting material that is at the foundations of mathematics itself, Discrete Mathematics for New Technology is a readable, friendly textbook designed for non-mathematicians as well as for computing and mathematics undergraduates alike.

Foundations of Discrete Mathematics

Author: K. D. Joshi

Publisher: New Age International

ISBN: 9788122401202

Category: Combinatorial analysis

Page: 748

View: 5025

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This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.

Discrete Mathematics

Author: Jean Gallier

Publisher: Springer Science & Business Media

ISBN: 9781441980472

Category: Mathematics

Page: 466

View: 6498

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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.

Discrete Mathematics

An Introduction for Software Engineers

Author: Mike Piff

Publisher: Cambridge University Press

ISBN: 9780521386227

Category: Computers

Page: 317

View: 2542

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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.

Pearls of Discrete Mathematics

Author: Martin Erickson

Publisher: CRC Press

ISBN: 1439816174

Category: Computers

Page: 280

View: 767

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Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

A Short Course in Discrete Mathematics

Author: Edward A. Bender,S. Gill Williamson

Publisher: Courier Corporation

ISBN: 0486439461

Category: Mathematics

Page: 240

View: 9702

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What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.