Mathematical Structures For Computer Science 7th Edition by Judith Gersting

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