Discrete Structures Logic and Computability 3rd Edition by James L Hein ISBN 0763772062 978-0763772062

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ISBN 10: 0763772062

ISBN 13: 978-0763772062

Author:  James L Hein

Thoroughly updated, the new Third Edition of Discrete Structures, Logic, and Computability introduces beginning computer science and computer engineering students to the fundamental techniques and ideas used by computer scientists today, focusing on topics from the fields of mathematics, logic, and computer science itself. Dr. Hein provides elementary introductions to those ideas and techniques that are necessary to understand and practice the art and science of computing. The text contains all the topics for discrete structures in the reports of the IEEE/ACM Joint Task Force on Computing Curricula for computer science programs and for computer engineering programs.

Discrete Structures Logic and Computability 3rd Table of contents: 

• Introduction to Discrete Structures

  • Overview of Discrete Mathematics
  • Importance of Logic and Computability
  • Applications of Discrete Structures

• Propositional Logic

  • Basic Concepts of Logic
  • Propositions and Logical Connectives
  • Truth Tables and Logical Equivalence
  • Logical Implications and Normal Forms
  • Methods of Proof in Logic

• Predicate Logic

  • Quantifiers and Predicates
  • Translating English Sentences into Predicate Logic
  • Proof Techniques in Predicate Logic
  • Logical Equivalence and Validity in Predicate Logic

• Methods of Proof

  • Direct Proofs and Proof by Contradiction
  • Proof by Induction
  • Proof by Counterexample
  • The Role of Proof in Mathematics

• Sets, Functions, and Relations

  • Set Theory and Set Operations
  • Functions and Their Properties
  • Relations and Their Properties
  • Equivalence Relations and Partitions
  • Partial Orderings and Posets

• Combinatorics

  • Counting Principles
  • Permutations and Combinations
  • The Binomial Theorem
  • Pigeonhole Principle and Its Applications
  • Recurrence Relations and Generating Functions

• Mathematical Logic and Formal Systems

  • Syntax and Semantics in Logic
  • Formal Proofs and Systems
  • Consistency and Completeness
  • Gödel’s Incompleteness Theorems

• Graph Theory

  • Introduction to Graphs
  • Types of Graphs and Their Properties
  • Eulerian and Hamiltonian Paths and Circuits
  • Planar Graphs and Graph Coloring
  • Trees and Spanning Trees

• Computability and Complexity

  • Introduction to Computability Theory
  • Turing Machines and Decidability
  • Recursive Functions and the Halting Problem
  • Complexity Classes (P, NP, and NP-Complete)
  • Reductions and Time Complexity

• Algorithms and Their Analysis

  • Algorithm Design Techniques
  • Efficiency and Time Complexity
  • Space Complexity
  • Sorting and Searching Algorithms
  • Graph Algorithms (DFS, BFS, etc.)

• Boolean Algebra and Digital Logic

  • Boolean Functions and Expressions
  • Simplification of Boolean Expressions
  • Digital Logic Gates and Circuits
  • Boolean Algebra in Computer Science

• Finite Automata and Formal Languages

  • Introduction to Finite Automata
  • Deterministic and Non-Deterministic Finite Automata
  • Regular Languages and Expressions
  • Pumping Lemma and Properties of Regular Languages
  • Context-Free Languages and Pushdown Automata

• Applications of Discrete Structures

  • Discrete Structures in Computer Science
  • Applications in Cryptography and Security
  • Algorithms and Data Structures in Software Engineering
  • Discrete Mathematics in Network Theory

• Conclusion

  • The Importance of Discrete Structures in Modern Computing
  • Open Problems and Future Research Areas

• Appendices

  • Index
  • Solutions to Selected Exercises

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