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An edition of Mathematical structures for computer science (1982)

Mathematical structures for computer science

discrete mathematics and its applications

7th edition.

by Judith L. Gersting

171 Want to read
12 Currently reading
2 Have read

Cover of: Mathematical structures for computer science by Judith L. Gersting, Judith L. Gersting

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An edition of Mathematical structures for computer science (1982)

Mathematical structures for computer science

discrete mathematics and its applications

7th edition.

by Judith L. Gersting

171 Want to read
12 Currently reading
2 Have read

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Publish Date

2014

Publisher

W.H. Freeman and Company, a Macmillian Higher Education Company

Language

English

Pages

969

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Previews available in: English

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1 Mathematical structures for computer science: discrete mathematics and its applications 2014, W.H. Freeman and Company, a Macmillian Higher Education Company in English - 7th edition. 1429215100 9781429215107	aaaa Preview Only
2 Mathematical structures for computer science 1987, W.H. Freeman in English - 2nd ed. 0716718022 9780716718024	eeee Preview Only
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Book Details

Table of Contents

Chapter 1. Formal Logic

1.1. Statements, Symbolic Representation, and Tautologies

Connectives and Truth Values

Logical Connectives in the Real World

Special Interest Page: Can "And" Ever Be "Or"?

Section 1.1 Review

1.2. Propositional Logic

Valid Arguments

Derivation Rules for Propositional Logic

Deduction Method and Other Rules

Verbal Arguments

Section 1.2 Review

1.3. Quantifiers, Predicates, and Validity

Quantifiers and Predicates

Section 1.3 Review

1.4. Predicate Logic

Derivation Rules for Predicate Logic

Universal Instantiation

Existential Instantiation

Universal Generalization

Existential Generalization

More Work with Rules

Verbal Arguments

Section 1.4 Review

1.5. Logic Programming

Horn Clauses and Resolution

Section 1.5 Review

1.6. Proof of Correctness

Assignment Rule

Conditional Rule

Section 1.6 Review

Chapter 1 Review

On the Computer

Chapter 2. Proofs, Induction, and Number Theory

2.1. Proof Techniques

Theorems and Informal Proofs

To Prove or Not to Prove

Exhaustive Proof

Common Definitions

Section 2.1 Review

First Principle of Induction

Proofs by Mathematical Induction

Second Principle of Induction

Section 2.2 Review

2.3. More on Proof of Correctness

Euclidean Algorithm

Special Interest Page: Making Safer Software

Section 2.3 Review

2.4. Number Theory

The Fundamental Theorem of Arithmetic

More on Prime Numbers

Euler Phi Function

Section 2.4 Review

Chapter 2 Review

On the Computer

Chapter 3. Recursion, Recurrence Relations, and Analysis of Algorithms

3.1. Recursive Definitions

Recursively Defined Sequences

Recursively Defined Sets

Recursively Defined Operations

Recursively Defined Algorithms

Section 3.1 Review

3.2. 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 3.2 Review

3.3. Analysis of Algorithms

The General Idea

Analysis Using Recurrence Relations

Upper Bound (Euclidean Algorithm)

Special Interest Page: Of Trees ... and Pancakes

Section 3.3 Review

Chapter 3 Review

On the Computer

Chapter 4. Sets, Combinatorics, and Probability

Relationships Between Sets

Binary and Unary Operations

Operations on Sets

Countable and Uncountable Sets

Section 4.1 Review

Multiplication Principle

Addition Principle

Using the Principles Together

Section 4.2 Review

4.3. Principle of Inclusion and Exclusion; Pigeonhole Principle

Principle of Inclusion and Exclusion

Pigeonhole Principle

Section 4.3 Review

4.4. Permutations and Combinations

Eliminating Duplicates

Permutations and Combinations with Repetitions

Generating Permutations and Combinations

Special Interest Page: Archimedes and the Stomachion

Section 4.4 Review

4.5. Binomial Theorem

Pascal's Triangle

Binomial Theorem and Its Proof

Applying the Binomial Theorem

Section 4.5 Review

4.6. Probability

Introduction to Finite Probability

Probability Distributions

Conditional Probability

Binomial Distributions

Average Case Analysis of Algorithms

Section 4.6 Review

Chapter 4 Review

On the Computer

Chapter 5. Relations, Functions, and Matrices

Binary Relations

Properties of Relations

Closures of Relations

Partial Orderings

Equivalence Relations

Section 5.1 Review

5.2. Topological Sorting

Section 5.2 Review

5.3. Relations and Databases

Entity-Relationship Model

Relational Model

Operations on Relations

Null Values and Three-valued Logic

Database Integrity

Section 5.3 Review

Properties of Functions

One-to-One Functions

Composition of Functions

Inverse Functions

Permutation Functions

How Many Functions

Equivalent Sets

Section 5.4 Review

5.5. Order of Magnitude

Function Growth

More on Analysis of Algorithms

The Master Theorem

Proof of the Master Theorem

Section 5.5 Review

5.6. The Mighty Mod Function

Computer Security

Hashing for Password Encryption

Miscellaneous Applications

Identification Codes

Generating and Decomposing Integers

Modular Arithmetic Designs

Section 5.6 Review

Matrix Operations

Gaussian Elimination

Boolean Matrices

Special Interest Page: Solve Millions of Equations, Faster than Gauss

Section 5.7 Review

Chapter 5 Review

On the Computer

Chapter 6. Graphs and Trees

6.1. Graphs and Their Representations

Definitions of a Graph

Applications of Graphs

Graph Terminology

Isomorphic Graphs

Computer Representation of Graphs

Adjacency Matrix

Special Interest Page: Isomorphic Protein Graphs

Section 6.1 Review

6.2. Trees and Their Representations

Tree Terminology

Applications of Trees

Binary Tree Representation

Tree Traversal Algorithms

Results about Trees

Section 6.2 Review

6.3. Decision Trees

Lower Bounds on Searching

Binary Tree Search

Section 6.3 Review

6.4. Huffman Codes

Problem and Trial Solution

Huffman Encoding Algorithm

Application of Huffman Codes

Section 6.4 Review

Chapter 6 Review

On the Computer

Chapter 7. Graph Algorithms

7.1. Directed Graphs and Binary Relations; Warshall's Algorithm

Directed Graphs and Binary Relations

Warshall's Algorithm

Section 7.1 Review

7.2. Euler Path and Hamiltonian Circuit

Euler Path Problem

Hamiltonian Circuit Problem

Section 7.2 Review

7.3. Shortest Path and Minimal Spanning Tree

Shortest-Path Problem

Minimal Spanning Tree Problem

Special Interest Page: Pathfinding

Section 7.3 Review

7.4. Traversal Algorithms

Depth-First Search

Breadth-First Search

Section 7.4 Review

7.5. Articulation Points and Computer Networks

The Problem Statement

The Idea behind the Algorithm

The Algorithm Itself

Section 7.5 Review

Chapter 7 Review

On the Computer

Chapter 8. Boolean Algebra and Computer Logic

8.1. Boolean Algebra Structure

Models or Abstractions

Definition and Properties

Isomorphic Boolean Algebras

What is Isomorphism?

Isomorphism as Applied to Boolean Algebra

Section 8.1 Review

8.2. Logic Networks

Combinational Networks

Basic Logic Elements

Boolean Expressions

Truth Functions

Networks and Expressions

Programmable Logic Devices

A Useful Network

Other Logic Elements

Constructing Truth Functions

Special Interest. Pruning Chips and Programs

Section 8.2 Review

8.3. Minimization

Minimization Process

Maps for Three and Four Variables

Using the Karnaugh Map

Quine-McCluskey Procedure

Section 8.3 Review

Chapter 8 Review

On the Computer

Chapter 9. Modeling Arithmetic, Computation, and Languages

9.1. Algebraic Structures

Definitions and Examples

Basic Results about Groups

Isomorphic Groups

Section 9.1 Review

Exercises 9.1

9.2. Coding Theory

Background: Homomorphisms and Cosets

Generating Group Codes

Decoding Group Codes

Section 9.2 Review

9.3. Finite-State Machines

Examples of Finite-State Machines

Regular Sets and Kleene's Theorem

Machine Minimization

Unreachable States

Minimization Procedure

Sequential Networks and Finite-State Machines

Special Interest. FSMs Behind the Game

Section 9.3 Review

9.4. Turing Machines

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 9.4 Review

9.5. Formal Languages

Classes of Grammars

Formal Languages and Computational Devices

Context-Free Grammars

Section 9.5 Review

Chapter 9 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

Edition Notes

Includes index.

Published in: New York, NY

Classifications

Library of Congress: QA39.3 .G47 2014, QA39.3.G47 2014

The Physical Object

Pagination: xvi, 969 pages
Number of pages: 969

Edition Identifiers

Open Library: OL31014850M
ISBN 10: 1429215100
ISBN 13: 9781429215107
LCCN: 2013951442

Work Identifiers

Work ID: OL1922611W

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