Foundations of Computer Science 1st Edition by Alfred Aho, Jeffrey Ullman ISBN 0716782847 9780716782841

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Product details:
ISBN 10: 0716782847
ISBN 13: 9780716782841
Author: Alfred Aho, Jeffrey Ullman

Foundations of Computer Science 1st Edition Table of contents:

Part I: Discrete Mathematics and Mathematical Foundations

2. Sets, Functions, and Relations

   • Basic Set Theory and Operations
   • Functions and Their Properties
   • Relations: Definitions, Properties, and Types
   • Applications of Sets, Functions, and Relations in Computing

3. Logic and Propositional Calculus

   • Logical Statements and Connectives
   • Truth Tables and Logical Equivalence
   • Propositional Calculus and Inference Rules
   • Applications of Logic in Algorithm Design

4. Mathematical Induction and Recursion

   • The Principle of Mathematical Induction
   • Recursive Definitions and Structures
   • Inductive Proofs in Algorithm Analysis
   • Recursion in Programming and Algorithm Design

Part II: Algorithms and Data Structures

5. Algorithm Design and Analysis

   • Defining Algorithms and Algorithmic Efficiency
   • Time Complexity and Big-O Notation
   • Analyzing Algorithm Performance
   • Divide and Conquer, Greedy, and Dynamic Programming Techniques

6. Fundamental Data Structures

   • Arrays, Lists, and Linked Lists
   • Stacks, Queues, and Deques
   • Trees and Binary Search Trees
   • Hashing and Hash Tables
   • Heaps and Priority Queues

7. Graphs and Graph Algorithms

   • Graph Terminology and Types
   • Graph Traversal Algorithms: BFS and DFS
   • Shortest Path Algorithms: Dijkstra’s and Bellman-Ford
   • Minimum Spanning Tree: Kruskal’s and Prim’s Algorithms
   • Network Flow and Matching Problems

8. Sorting and Searching Algorithms

   • Comparison-Based Sorting: QuickSort, MergeSort, and HeapSort
   • Non-Comparison-Based Sorting: Radix Sort, Counting Sort
   • Searching Algorithms: Linear Search, Binary Search
   • Search Trees and Balanced Trees: AVL Trees, Red-Black Trees

Part III: Formal Languages and Automata

9. Formal Languages and Grammars

   • Alphabets, Strings, and Languages
   • Context-Free and Regular Grammars
   • Chomsky Hierarchy of Languages
   • Language Recognition and Parsing

10. Finite Automata and Regular Languages

    • Deterministic and Non-Deterministic Finite Automata (DFA and NFA)
    • Regular Expressions and Their Connection to Regular Languages
    • Pumping Lemma for Regular Languages
    • Applications of Finite Automata

11. Context-Free Grammars and Pushdown Automata

    • Introduction to Context-Free Grammars
    • Derivations, Parse Trees, and Ambiguity
    • Pushdown Automata and Their Role in Parsing
    • Applications in Compiler Design

Part IV: Computability and Complexity

12. Turing Machines and Computability

    • The Concept of Computability
    • Turing Machines: Definitions and Variants
    • Church-Turing Thesis and Entscheidungsproblem
    • Decidability and Undecidability

13. Complexity Theory

    • Time Complexity and Space Complexity
    • Classes P and NP
    • NP-Completeness and NP-Hard Problems
    • Reductions and Completeness in Computational Complexity

14. Advanced Complexity Topics

    • Approximation Algorithms
    • Randomized Algorithms
    • The Polynomial Hierarchy and Other Complexity Classes
    • Parallel Computation and Its Complexity

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