Mathematical structures for computer science discrete mathematics and its applications 7th Edition by Judith L Gersting
Contents of Mathematical Structures Computer Science
- Chapter Formal Logic
- Statements , Symbolic
- Representation , and Tautologies
- Connectives and Truth Values
- Tautologies
- Logical Connectives in the
- Real World
- An Algorithm
- Special Interest Page
- Can “And” Ever Be “Or”?
- Section Review
- Exercises
- Propositional Logic
- Valid Arguments
- Derivation Rules for
- Propositional Logic
- Deduction Method and Other Rules
- Verbal Arguments
- Section Review
- Exercises
- Quantifiers, Predicates , and
- Validity
- Quantifiers and Predicates
- Translation
- Validity
- Section Review
- Exercises
- Predicate Logic
- Derivation Rules for Predicate Logic
- Universal Instantiation
- Existential Instantiation
- Universal Generalization
- Existential Generalization
- More Work with Rules
- Verbal Arguments
- Conclusion
- Section Review
- Exercises
- Logic Programming
- Prolog
- Horn Clauses and Resolution
- Recursion
- Expert Systems
- Section Review
- Exercises
- Proof of Correctness
- Assertions
- Assignment Rule
- Conditional Rule
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Proofs, Induction, and
- Number Theory
- Proof Techniques
- Theorems and Informal Proofs
- To Prove or Not to Prove
- Exhaustive Proof
- Direct Proof
- Contraposition
- Contradiction
- Serendipity
- Common Definitions
- Section Review
- Exercises
- Induction
- First Principle of Induction
- Proofs by Mathematical
- Induction
- Second Principle of Induction
- Section Review
- Exercises
- More on Proof of
- Correctness
- Loop Rule
- Euclidean Algorithm
- Special Interest Page
- Making Safer Software
- Section Review
- Exercises
- Number Theory
- The Fundamental Theorem
- of Arithmetic
- More on Prime Numbers
- Euler Phi Function
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter R ecursion, Recurrence
- Relations, and Analysis
- of Algorithms
- Recursive Definitions
- Recursively Defined Sequences
- Recursively Defined Sets
- Recursively Defined Operations
- Recursively Defined Algorithms
- Section Review
- Exercises
- Recurrence Relations
- Linear First-Order Recurrence
- Relations
- Expand, Guess, and Verify
- A Solution Formula
- Linear Second-Order
- Recurrence Relations
- Divide-and-Conquer
- Recurrence Relations
- Section Review
- Exercises
- Analysis of Algorithms
- The General Idea
- Analysis Using Recurrence
- Relations
- Upper Bound
- (Euclidean Algorithm)
- Special Interest Page
- Of Trees % and Pancakes
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Sets, Combinatorics,
- and Probability
- Sets
- Notation
- Relationships Between Sets
- Sets of Sets
- Binary and Unary Operations
- Operations on Sets
- Set Identities
- Countable and Uncountable Sets
- Section Review
- Exercises
- Counting
- Multiplication Principle
- Addition Principle
- Using the Principles Together
- Decision Trees
- Section Review
- Exercises
- Principle of Inclusion and
- Exclusion; Pigeonhole
- Principle
- Principle of Inclusion and
- Exclusion
- Pigeonhole Principle
- Section Review
- Exercises
- Permutations and
- Combinations
- Permutations
- Combinations
- Eliminating Duplicates
- Permutations and Combinations
- with Repetitions
- Generating Permutations
- and Combinations
- Special Interest Page
- Archimedes and the Stomachion
- Section Review
- Exercises
- Binomial Theorem
- Pascal’s Triangle
- Binomial Theorem and Its Proof
- Applying the Binomial Theorem
- Section Review
- Exercises
- Probability
- Introduction to Finite
- Probability
- Probability Distributions
- Conditional Probability
- Bayes’ Theorem
- Expected Value
- Binomial Distributions
- Average Case Analysis of
- Algorithms
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter R elations, Functions,
- and Matrices
- Relations
- Binary Relations
- Properties of Relations
- Closures of Relations
- Partial Orderings
- Equivalence Relations
- Section Review
- Exercises
- Topological Sorting
- Section Review
- Exercises
- Relations and Databases
- Entity-Relationship Model
- Relational Model
- Operations on Relations
- Null Values and Three-valued Logic
- Database Integrity
- Section Review
- Exercises
- Functions
- Definition
- Properties of Functions
- Onto Functions
- One-to-One Functions
- Bijections
- Composition of Functions
- Inverse Functions
- Permutation Functions
- How Many Functions
- Equivalent Sets
- Section Review
- Exercises
- Order of Magnitude
- Function Growth
- More on Analysis of Algorithms
- The Master Theorem
- Proof of the Master Theorem
- Section Review
- Exercises
- The Mighty Mod Function
- Hashing
- Computer Security
- Cryptography
- Hashing for Password
- Encryption
- Miscellaneous Applications
- Identification Codes
- Generating and Decomposing
- Integers
- Modular Arithmetic Designs
- Section Review
- Exercises
- Matrices
- Terminology
- Matrix Operations
- Gaussian Elimination
- Boolean Matrices
- Special Interest Page
- Solve Millions of Equations, Faster than Gauss
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Graphs and Trees
- Graphs and their
- Representations
- Definitions of a Graph
- Applications of Graphs
- Graph Terminology
- Isomorphic Graphs
- Planar Graphs
- Computer Representation
- of Graphs
- Adjacency Matrix
- Adjacency List
- Special Interest Page
- Isomorphic Protein Graphs
- Section Review
- Exercises
- Trees and Their
- Representations
- Tree Terminology
- Applications of Trees
- Binary Tree Representation
- Tree Traversal Algorithms
- Results about Trees
- Section Review
- Exercises
- Decision Trees
- Searching
- Lower Bounds on Searching
- Binary Tree Search
- Sorting
- Section Review
- Exercises
- Huffman Codes
- Problem and Trial Solution
- Huffman Encoding Algorithm
- Justification
- Application of Huffman Codes
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Graph Algorithms
- Directed Graphs and Binary
- Relations ; Warshall’s
- Algorithm
- Directed Graphs and
- Binary Relations
- Reachability
- Warshall’s Algorithm
- Section Review
- Exercises
- Euler Path and Hamiltonian
- Circuit
- Euler Path Problem
- Hamiltonian Circuit Problem
- Section Review
- Exercises
- Shortest Path and Minimal
- Spanning Tree
- Shortest-Path Problem
- Minimal Spanning Tree Problem
- Special Interest Page
- Pathfinding
- Section Review
- Exercises
- Traversal Algorithms
- Depth-First Search
- Breadth-First Search
- Analysis
- Applications
- Section Review
- Exercises
- Articulation Points and
- Computer Networks
- The Problem Statement
- The Idea behind the Algorithm
- The Algorithm Itself
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Boolean Algebra and
- Computer Logic
- Boolean Algebra Structure
- Models or Abstractions
- Definition and Properties
- Isomorphic Boolean Algebras
- What is Isomorphism?
- Isomorphism as Applied
- to Boolean Algebra
- Section Review
- Exercises
- Logic Networks
- Combinational Networks
- Basic Logic Elements
- Boolean Expressions
- Truth Functions
- Networks and Expressions
- Canonical Form
- Minimization
- Programmable Logic
- Devices
- A Useful Network
- Other Logic Elements
- Constructing Truth Functions
- Special Interest Page
- Pruning Chips and Programs
- Section Review
- Exercises
- Minimization
- Minimization Process
- Karnaugh Map
- Maps for Three and
- Four Variables
- Using the Karnaugh Map
- Quine–McCluskey Procedure
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Chapter Modeling Arithmetic,
- Computation, and
- Languages
- Algebraic Structures
- Definitions and Examples
- Basic Results about Groups
- Subgroups
- Isomorphic Groups
- Section Review
- Exercises
- Coding Theory
- Introduction
- Background: Homomorphisms
- and Cosets
- Generating Group Codes
- Decoding Group Codes
- Section Review
- Exercises
- Finite-State Machines
- Definition
- Examples of Finite-State Machines
- Recognition
- Regular Sets and Kleene’s Theorem
- Machine Minimization
- Unreachable States
- Minimization Procedure
- Sequential Networks and
- Finite-State Machines
- Special Interest Page
- FSMs Behind the Game
- Section Review
- Exercises
- Turing Machines
- Definition
- Turing Machines as Set
- Recognizers
- Turing Machines as Function
- Computers
- Church–Turing Thesis
- Decision Problems and
- Uncomputability
- Examples of Decision
- Problems
- Halting Problem
- Computational Complexity
- Section Review
- Exercises
- Formal Languages
- Classes of Grammars
- Formal Languages and
- Computational Devices
- Context-Free Grammars
- Section Review
- Exercises
- Chapter Review
- On the Computer
- Appendix A Derivation Rules for
- Propositional and Predicate
- Logic
- Appendix B Summation and Product
- Notation
- Appendix C The Logarithm Function
- Answers to Practice Problems
- Answers to Odd-Numbered
- Exercises
- Answers to Self-Tests