Discrete Structures, Logic, and Computability
Résumé
The book contains a wide range of material that focuses on those parts of discrete mathematics, logic, and computability needed for computer science students. The topics can be taught in a variety of ways depending on the length of the course, the emphasis, and the background of students . For example, the preface includes syllabai for fourteen different courses in discrete mathematics ranging in length from ten weeks to a full year. It also includes syllabai for two courses in logic, and two courses in computability.
The book is organized more along the lines of technique than on a subject-by-subject basis so that it doesn't fragment into a vast collection of seemingly unrelated ideas. The focus throughout the book is on the computation and construction of objects. So many traditional topics are dispersed throughout the text to places where they fit naturally with the techniques under discussion. Therefore there is a spiral approach to learning these topics. For example, to read about properties of-and techniques for processing-natural numbers, lists, strings, graphs, or trees, it's necessary to look in the index or scan the table of contents to find the several places where they are found.
Every example has a title and, for ease of scanning, there are special marks to indicate the beginning and ending of each example. Titles and subtitles are used extensively to make it easy to find things. Important facts and results are boxed for easy reference. The second color also makes it easy to find things. There is a minimum of horizontal lines in the book so that scanning is easy.
Exercises at the end of each section are categorized by topic and ordered within each topic by difficulty. There is also a collection of exercises at the end of each section labeled proofs and/or challenges. There are over 1700 exercises with answers provided for about half of them. The exercises with answers in the book are marked in color.
The symbol glossary makes it easy to check definitions. The index is extensive so that topics can be easily found.
The chapter guidelines and chapter summaries let students see what is to be covered and then to check whether they know the details about what was covered.
Contents
Elementary Notions and Notations- A Proof Primer
- Sets
- Ordered Structures
- Graphs and Trees
- Definitions and Examples
- Constructing Functions
- Properties of Functions
- Countability
- Inductively Defined Sets
- Recursive Functions and Procedures
- Grammars
- Properties of Binary Relations
- Equivalence Relations
- Order Relations
- Inductive Proof
- Analyzing Algorithms
- Finding Closed Forms
- Counting and Discrete Probability
- Solving Recurrences
- Comparing Rates of Growth
- How Do We Reason?
- Propositional Calculus
- Formal Reasoning
- Formal Axiom Systems
- First-Order Predicate Calculus
- Equivalent Formulas
- Formal Proofs in Predicate Calculus
- Equality
- Program Correctness
- Higher-Order Logics
- Automatic Reasoning
- Logic Programming
- What is an Algebra?
- Boolean Algebra
- Abstract Data Types as Algebras
- Computational Algebras
- Other Algebraic Ideas
- Regular Languages
- Finite Automata
- Constructing Efficient Finite Automata
- Regular Language Topics
- Context-Free Languages
- Pushdown Automata
- Parsing Techniques
- Context-Free Language Topics
- Turing Machines
- The Church-Turing Thesis
- Computability
- A Hierarchy of Languages
- Complexity Classes
L'auteur - James L. Hein
Portland State University
Professor of Computer Science. Ph.D., Mathematics,
Northwestern University, 1973. James Hein's interests are
understanding the semantics of perpetual logic programs.
Writing books about the mathematical foundations of
computer science. Constructing declarative programming
experiments for learning discrete mathematics, formal
logic, and computability.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Jones and Bartlett Computer Science |
| Auteur(s) | James L. Hein |
| Parution | 31/03/2003 |
| Édition | 2eme édition |
| Nb. de pages | 960 |
| Format | 19,5 x 24,2 |
| Couverture | Relié |
| Poids | 1479g |
| Intérieur | 2 couleurs |
| EAN13 | 9780763718435 |
| ISBN13 | 978-0-7637-1843-5 |
Avantages Eyrolles.com
Consultez aussi
- Les meilleures ventes en Graphisme & Photo
- Les meilleures ventes en Informatique
- Les meilleures ventes en Construction
- Les meilleures ventes en Entreprise & Droit
- Les meilleures ventes en Sciences
- Les meilleures ventes en Littérature
- Les meilleures ventes en Arts & Loisirs
- Les meilleures ventes en Vie pratique
- Les meilleures ventes en Voyage et Tourisme
- Les meilleures ventes en BD et Jeunesse
- Informatique Développement d'applications Techniques de programmation Logique
- Sciences Mathématiques Mathématiques par matières Algèbre Cours
- Sciences Mathématiques Mathématiques par matières Algèbre Exercices
- Sciences Mathématiques Mathématiques par matières Logique
- Sciences Mathématiques Mathématiques par matières Logique Logique floue
- Sciences Mathématiques Mathématiques par matières Logique Algèbre de Boole
- Sciences Mathématiques Mathématiques par matières Théorie des ensembles
- Sciences Etudes et concours Classes préparatoires et grandes écoles - Livres classes prépas scientifiques Mathématiques
