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Discrete Mathematics Richard Johnsonbaugh

Discrete Mathematics By Richard Johnsonbaugh

Discrete Mathematics by Richard Johnsonbaugh


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Discrete Mathematics Summary

Discrete Mathematics by Richard Johnsonbaugh

For one- or two-term introductory courses in discrete mathematics. An accessible introduction to the topics of discrete math, this best-selling text also works to expand students' mathematical maturity. With nearly 4,500 exercises, Discrete Mathematics provides ample opportunities for students to practice, apply, and demonstrate conceptual understanding. Exercise sets features a large number of applications, especially applications to computer science. The almost 650 worked examples provide ready reference for students as they work. A strong emphasis on the interplay among the various topics serves to reinforce understanding. The text models various problem-solving techniques in detail, then provides opportunity to practice these techniques. The text also builds mathematical maturity by emphasizing how to read and write proofs. Many proofs are illustrated with annotated figures and/or motivated by special Discussion sections. The side margins of the text now include tiny URLs that direct students to relevant applications, extensions, and computer programs on the textbook website.

About Richard Johnsonbaugh

Richard Johnsonbaugh is Professor Emeritus of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago. Prior to his 20-year service at DePaul University, he was a member and sometime chair of the mathematics departments at Morehouse College and Chicago State University. He has a B.A. degree in mathematics from Yale University, M.A. and Ph.D. degrees in mathematics from the University of Oregon, and an M.S. degree in computer science from the University of Illinois, Chicago. His most recent research interests are in pattern recognition, programming languages, algorithms, and discrete mathematics. He is the author or co-author of numerous books and articles in these areas. Several of his books have been translated into various languages. He is a member of the Mathematical Association of America.

Table of Contents

1. Sets and Logic 1.1 Sets 1.2 Propositions 1.3 Conditional Propositions and Logical Equivalence 1.4 Arguments and Rules of Inference 1.5 Quantifiers 1.6 Nested Quantifiers Problem-Solving Corner: Quantifiers 2. Proofs 2.1 Mathematical Systems, Direct Proofs, and Counterexamples 2.2 More Methods of Proof Problem-Solving Corner: Proving Some Properties of Real Numbers 2.3 Resolution Proofs 2.4 Mathematical Induction Problem-Solving Corner: Mathematical Induction 2.5 Strong Form of Induction and the Well-Ordering Property 3. Functions, Sequences, and Relations 3.1 Functions Problem-Solving Corner: Functions 3.2 Sequences and Strings 3.3 Relations 3.4 Equivalence Relations Problem-Solving Corner: Equivalence Relations 3.5 Matrices of Relations 3.6 Relational Databases 4. Algorithms 4.1 Introduction 4.2 Examples of Algorithms 4.3 Analysis of Algorithms Problem-Solving Corner: Design and Analysis of an Algorithm 4.4 Recursive Algorithms 5. Introduction to Number Theory 5.1 Divisors 5.2 Representations of Integers and Integer Algorithms 5.3 The Euclidean Algorithm Problem-Solving Corner: Making Postage 5.4 The RSA Public-Key Cryptosystem 6. Counting Methods and the Pigeonhole Principle 6.1 Basic Principles Problem-Solving Corner: Counting 6.2 Permutations and Combinations Problem-Solving Corner: Combinations 6.3 Generalized Permutations and Combinations 6.4 Algorithms for Generating Permutations and Combinations 6.5 Introduction to Discrete Probability 6.6 Discrete Probability Theory 6.7 Binomial Coefficients and Combinatorial Identities 6.8 The Pigeonhole Principle 7. Recurrence Relations 7.1 Introduction 7.2 Solving Recurrence Relations Problem-Solving Corner: Recurrence Relations 7.3 Applications to the Analysis of Algorithms 8. Graph Theory 8.1 Introduction 8.2 Paths and Cycles Problem-Solving Corner: Graphs 8.3 Hamiltonian Cycles and the Traveling Salesperson Problem 8.4 A Shortest-Path Algorithm 8.5 Representations of Graphs 8.6 Isomorphisms of Graphs 8.7 Planar Graphs 8.8 Instant Insanity 9. Trees 9.1 Introduction 9.2 Terminology and Characterizations of Trees Problem-Solving Corner: Trees 9.3 Spanning Trees 9.4 Minimal Spanning Trees 9.5 Binary Trees 9.6 Tree Traversals 9.7 Decision Trees and the Minimum Time for Sorting 9.8 Isomorphisms of Trees 9.9 Game Trees 10. Network Models 10.1 Introduction 10.2 A Maximal Flow Algorithm 10.3 The Max Flow, Min Cut Theorem 10.4 Matching Problem-Solving Corner: Matching 11. Boolean Algebras and Combinatorial Circuits 11.1 Combinatorial Circuits 11.2 Properties of Combinatorial Circuits 11.3 Boolean Algebras Problem-Solving Corner: Boolean Algebras 11.4 Boolean Functions and Synthesis of Circuits 11.5 Applications 12. Automata, Grammars, and Languages 12.1 Sequential Circuits and Finite-State Machines 12.2 Finite-State Automata 12.3 Languages and Grammars 12.4 Nondeterministic Finite-State Automata 12.5 Relationships Between Languages and Automata 13. Computational Geometry 13.1 The Closest-Pair Problem 13.2 An Algorithm to Compute the Convex Hull Appendix A. Matrices B. Algebra Review C. Pseudocode References Hints and Solutions to Selected Exercises Index

Additional information

CIN0321964683VG
9780321964687
0321964683
Discrete Mathematics by Richard Johnsonbaugh
Used - Very Good
Hardback
Pearson Education (US)
20130717
768
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

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