discrete mathematics pdf book
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This book contains a judicious mix of concepts and solved examples that make it ideal for the beginners taking the Discrete Mathematics course. Features Exhaustive coverage of Set Theory. Comprehensive coverage of Graph Theory and Combinatorics. Excellent discussion of Group theory applications-Coding. Detailed explanation of the solution procedure of the worked examples. Pedagogy includes 341 solved examples 566 short answer questions 556 descriptive questions Over 500 figures and tables
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.
Hein (Portland State U.) offers an introductory textbook that aims to give the reader a holistic understanding of discrete mathematics and computer science, through careful illustration of relationships between key concepts. Focusing on computation and the construction of objects, the text is organi
Written for the one-term course, the Third Edition of Essentials of Discrete Mathematics is designed to serve computer science majors as well as students from a wide range of disciplines. 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. tudents 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.
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
Written in an accessible style, this text provides a complete coverage of discrete mathematics and its applications at an appropriate level of rigour. The book discusses algebraic structures, mathematical logic, lattices, Boolean algebra, graph theory, automata theory, grammars and recurrence relations. It covers the important topics such as coding theory, Dijkstra’s shortest path algorithm, reverse polish notation, Warshall’s algorithm, Menger’s theorem, Turing machine, and LR(k) parsers, which form a part of the fundamental applications of discrete mathematics in computer science. In addition, Pigeonhole principle, ring homomorphism, field and integral domain, trees, network flows, languages, and recurrence relations. The text is supported with a large number of examples, worked-out problems and diagrams that help students understand the theoretical explanations. The book is intended as a text for postgraduate students of mathematics, computer science, and computer applications. In addition, it will be extremely useful for the undergraduate students of computer science and engineering.
Description:This book is intended to be a textbook for the student pursuing B.E.B.Tech in Computer Science or MCAM Tech and NIELIT - B & C Level or equivalent courses. Topics included are self contained. Sequence is maintained in such a way that no prerequisite is necessary. This book contains topics ranging from set, relation, recurrence relation, generating function, posets, lattice, methods of proofs, Quine McKluskey Method, Floyd Warshall's algorithm, finite automata, bipartite graph etc. Only necessary theorems have been included, and wherever required, theirs applicability has been demonstrated using appropriate examples. Whenever required, a diagram is used to make the concept easily understood to the reader. It contains good number of solved examples and exercises for hands on practice.Table of Contents:Chapter 1 : Seti Chapter 2 : Relationi Chapter 3 : Number Theoryi Chapter 4 : Functioni Chapter 5 : Predicate Calculusi Chapter 6 : Poseti Chapter 7 : Latticei Chapter 8 : Finite Boolean Algebrai Chapter 9 : Recursive Equationsi Chapter 10 : Generating Functioni Chapter 11 : Method Of Proofsi Chapter 12 : Permutationsi Chapter 13 : Combinationsi Chapter 14 : Groupi Chapter 15 : Cyclic Groupi Chapter 16 : Permutationi Chapter 17 : Matrixi Chapter 18 : Graphi Chapter 19 : Path and Circuiti Chapter 20 : Graph Algorithmsi Chapter 21 : Formal Languagei Chapter 22 : Finite Automatai Chapter 23 : Galois Field