An edition of Introduction to Discrete Mathematics (1990)

Introduction to discrete mathematics

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Cover of: Introduction to discrete mathematics by R. Hirschfelder, J. Hirschfelder, R. Hirschfelder
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  • ★★★★★ 5.0 (1 rating)
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Last edited by Drini
September 23, 2025 | History
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An edition of Introduction to Discrete Mathematics (1990)

Introduction to discrete mathematics

by and

  • ★★★★★ 5.0 (1 rating)
  • 8 Want to read
  • 1 Have read

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Publish Date
Publisher
Brooks/Cole
Language
English
Pages
535

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Previews available in: English

Subjects

Textbooks, Computer science, Mathematics, Mathematics textbooks, Electronic data processing
Edition Availability
Cover of: Introduction to discrete mathematics
Introduction to discrete mathematics
1991, Brooks/Cole
in English
Cover of: Introduction to Discrete Mathematics.
Introduction to Discrete Mathematics.
1990, Brooks-Cole
in Undetermined

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Book Details

Table of Contents

Part I. Fundamentals
1. Number Systems and Representations
Page 3
1.1. Natural Numbers
Page 3
1.2. Arithmetic with Natural Numbers
Page 7
1.3. Summation and Product Notation
Page 9
1.4. Integers and Rational Numbers
Page 12
1.5. The Real and Complex Numbers
Page 16
1.6. Arithmetic in the Integers Modulo n
Page 22
Chapter Review Exercises
Page 29
2. Sets
Page 32
2.1. Sets and Subsets
Page 32
2.2. Operations on Sets and Set Algebra
Page 35
2.3. Sets of Real Numbers
Page 40
2.4. Cartesian Products of Sets
Page 42
2.5. Finite and Infinite Sets
Page 44
2.6. Mathematical Induction
Page 48
2.7. Representation of Sets in Computers
Page 54
Chapter Review Exercises
Page 57
3. Functions and Relations
Page 59
3.1. Functions
Page 59
3.2. Operations with Functions
Page 67
3.3. Relations
Page 75
3.4. Equivalence Relations
Page 82
3.5. Order Relations
Page 89
3.6. Relational Data Bases
Page 93
Chapter Review Exercises
Page 97
Part II. Basic Discrete Mathematics
Page 99
4. Logic and Proof
Page 101
4.1. Propositions and Connectives
Page 101
4.2. Tautologies and the Algebra of Propositions
Page 108
4.3. Methods of Mathematical Proof
Page 112
4.4. Propositional Functions
Page 117
4.5. Quantifiers
Page 121
4.6. Working with Formulas Containing Quantifiers
Page 124
4.7. Valid Arguments of Predicate Logic
Page 130
Chapter Review Exercises
Page 134
5. Boolean Algebra and Logic Circuits
Page 138
5.1. Boolean Algebras
Page 138
5.2. Representing Boolean Functions by Expressions
Page 147
5.3. Logic Circuits
Page 157
5.4. Feedback and Memory Circuits
Page 166
Chapter Review Exercises
Page 169
6. Combinatorics and Discrete Probability
Page 172
6.1. Counting Techniques
Page 172
6.2. Permutations
Page 180
6.3. Combinations
Page 183
6.4. Binomial Coefficients
Page 187
6.5. Discrete Probability
Page 191
6.6. Additional Topics in Probability
Page 200
Chapter Review Exercises
Page 213
7. Graphs
Page 215
7.1. Concepts and Terminology
Page 218
7.2. Connectivity
Page 230
7.3. Some Classical Problems
Page 238
7.4. Directed Graphs
Page 247
7.5. The Shortest-Path Algorithm
Page 257
Chapter Review Exercises
Page 262
8. Trees
Page 268
8.1. Characterizations of Trees
Page 268
8.2. Spanning Trees
Page 278
8.3. Binary Trees
Page 284
8.4. Traversing Rooted Trees
Page 292
Chapter Review Exercises
Page 300
9. Recurrence Relations and Dynamical Systems
Page 303
9.1. Recurrence Relations
Page 303
9.2. First-Order Linear Relations
Page 312
9.3. Linear Homogeneous Relations
Page 317
9.4. Nonhomogeneous Systems
Page 325
9.5. Numerical Experimentation
Page 328
9.6. Additional Topics
Page 336
Chapter Review Exercises
Page 346
Part III. Advanced Topics
Page 349
10. Topics from Number Theory
Page 351
10.1. Divisibility
Page 351
10.2. Primes and Factorization
Page 357
10.3. Linear Diophantine Equations
Page 362
10.4. More about Linear Diophantine Equations
Page 368
10.5. Another Method for Diophantine Equations
Page 373
10.6. Continued Fractions
Page 377
Chapter Review Exercises
Page 386
11. Languages and Grammars
Page 388
11.1. Vocabularies, Sentences, and Languages
Page 388
11.2. Specifying Languages: Productions
Page 393
11.3. Other Ways of Specifying Languages
Page 401
11.4. The Languages of Logic and Mathematics
Page 407
Chapter Review Exercises
Page 411
12. Machines and Computation
Page 413
12.1. Models of Computation
Page 413
12.2. Finite State Machines
Page 416
12.3. Language Recognition
Page 423
12.4. Finite State Machines and Regular Grammars
Page 430
12.5. Designing a Machine to Recognize a Regular Language
Page 435
12.6. Turing Machines
Page 442
12.7. The Halting Problem
Page 449
Chapter Review Exercises
Page 452
Appendixes
A. Glossary
Page 455
B. Suggested Readings
Page 472
C. Answers to Odd-Numbered Exercises
Page 475
Index
Page 529

Edition Notes

Includes bibliographical references (p. 472-474) and index.

Published in
Pacific Grove, Calif
Other Titles
Discreet mathematics.

Classifications

Dewey Decimal Class
510
Library of Congress
QA76.9.M35 H57 1991

The Physical Object

Pagination
xvi, 535 p. :
Number of pages
535

Edition Identifiers

Open Library
OL1876273M
Internet Archive
introductiontodi00hirs
ISBN 10
0534138969
LCCN
90036341
LibraryThing
3600609
Goodreads
3577963

Work Identifiers

Work ID
OL4467828W

Source records

Internet Archive item record
Library of Congress MARC record

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History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
September 23, 2025 Edited by Drini Add TOC from Tocky
November 11, 2020 Edited by MARC Bot import existing book
December 14, 2018 Edited by Ali987650 Added new cover
December 14, 2018 Edited by Ali987650 Update covers
April 1, 2008 Created by an anonymous user Imported from Scriblio MARC record