Mathematical structures for computer science 7th Edition by Judith L Gersting

Mathematical Structures For Computer Science 7th Edition by Judith Gersting

PDF Free Download | 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
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