“This book lives up to my very high expectation of a textbook from Chartrand and Zhang. The exposition is wonderfully clear, especially with all these great examples. The collection and ordering of topics is perfect for my course and our students.” — David Craft, Muskingum University
“I adopted this book before even seeing it, since I know how well Chartrand writes.” — Hudson Kronk, Binghamton University
“I have decided to use Chartrand and Zhang’s discrete math text in the fall semester. I am a fan of their books. I’ve been waiting for their discrete math text to be published and am looking forward to using it in the fall!” — Kathleen McKeon, Connecticut College
“This is an excellent Discrete Math book! Excellent choice of topics, right amount of examples and exercises. The topics flow smoothly. Clear exposition and pace!” —Brian Kreeger, North Hennepin Community College
671 pages, $129.95 list
1-57766-730-1
978-1-57766-730-8
© 2011
hardcover
Instructor's resource materials available here
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To obtain a username and password to access these materials, contact comps@waveland.com.
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Discrete Mathematics
Chartrand and Zhang’s Discrete Mathematics presents a clearly written, student-friendly introduction to discrete mathematics. The authors draw from their background as researchers and educators to offer lucid discussions and descriptions fundamental to the subject of discrete mathematics. Unique among discrete mathematics textbooks for its treatment of proof techniques and graph theory, topics discussed also include logic, relations and functions (especially equivalence relations and bijective functions), algorithms and analysis of algorithms, introduction to number theory, combinatorics (counting, the Pascal triangle, and the binomial theorem), discrete probability, partially ordered sets, lattices and Boolean algebras, cryptography, and finite-state machines.
This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.
Some of the major features and strengths of this textbook
This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.
Some of the major features and strengths of this textbook
- Numerous, carefully explained examples and applications facilitate learning.
- More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises.
- Descriptions of proof techniques are accessible and lively.
- Students benefit from the historical discussions throughout the textbook.
- An Instructor's Solutions Manual contains complete solutions to all exercises.
Reactions
0. What Is Discrete Mathematics?
1. Logic
Statements / Negation, Conjunction and Disjunction / Implications / Biconditionals / Tautologies and Contradictions / Some Applications of Logic
2. Sets
Sets and Subsets / Set Operations and Their Properties / Cartesian Products of Sets / Partitions
3. Methods of Proof
Quantified Statements / Direct Proof / Proof by Contrapositive / Proof by Cases / Counterexamples / Existence Proofs / Proof by Contradiction
4. Mathematical Induction
The Principle of Mathematical Induction / Additional Examples of Induction Proofs / Sequences / The Strong Principle of Mathematical Induction
5. Relations and Functions
Relations / Equivalence Relations / Functions / Bijective Functions / Cardinalities of Sets
6. Algorithms and Complexity
What Is an Algorithm? / Growth of Functions / Analysis of Algorithms / Searching and Sorting
7. Integers
Divisibility Properties / Primes / The Division Algorithm / Congruence / Introduction to Cryptography / Greatest Common Divisors / Integer Representations
8. Introduction to Counting
The Multiplication and Addition Principles / The Principle of Inclusion-Exclusion / The Pigeonhole Principle / Permutations and Combinations / Applications of Permutations and Combinations
9. Advanced Counting Methods
The Pascal Triangle and the Binomial Theorem / Permutations and Combinations with Repetition / Generating Functions
10. Discrete Probability
Probability of an Event / Conditional Probability and Independent Events / Random Variables and Expected Values
11. Partially Ordered Sets and Boolean Algebra
Partially Ordered Sets / Lattices / Boolean Algebras
12. Introduction to Graphs
Fundamental Concepts of Graph Theory / Connected Graphs / Eulerian Graphs / Hamiltonian Graphs / Weighted Graphs
13. Trees
Fundamental Properties of Trees / Rooted and Spanning Trees / The Minimum Spanning Tree Problem
14. Planar Graphs and Graph Colorings
Planar Graphs / Coloring Graphs
15. Directed Graphs
Fundamental Concepts of Digraph Theory / Tournaments / Finite-State Machines
1. Logic
Statements / Negation, Conjunction and Disjunction / Implications / Biconditionals / Tautologies and Contradictions / Some Applications of Logic
2. Sets
Sets and Subsets / Set Operations and Their Properties / Cartesian Products of Sets / Partitions
3. Methods of Proof
Quantified Statements / Direct Proof / Proof by Contrapositive / Proof by Cases / Counterexamples / Existence Proofs / Proof by Contradiction
4. Mathematical Induction
The Principle of Mathematical Induction / Additional Examples of Induction Proofs / Sequences / The Strong Principle of Mathematical Induction
5. Relations and Functions
Relations / Equivalence Relations / Functions / Bijective Functions / Cardinalities of Sets
6. Algorithms and Complexity
What Is an Algorithm? / Growth of Functions / Analysis of Algorithms / Searching and Sorting
7. Integers
Divisibility Properties / Primes / The Division Algorithm / Congruence / Introduction to Cryptography / Greatest Common Divisors / Integer Representations
8. Introduction to Counting
The Multiplication and Addition Principles / The Principle of Inclusion-Exclusion / The Pigeonhole Principle / Permutations and Combinations / Applications of Permutations and Combinations
9. Advanced Counting Methods
The Pascal Triangle and the Binomial Theorem / Permutations and Combinations with Repetition / Generating Functions
10. Discrete Probability
Probability of an Event / Conditional Probability and Independent Events / Random Variables and Expected Values
11. Partially Ordered Sets and Boolean Algebra
Partially Ordered Sets / Lattices / Boolean Algebras
12. Introduction to Graphs
Fundamental Concepts of Graph Theory / Connected Graphs / Eulerian Graphs / Hamiltonian Graphs / Weighted Graphs
13. Trees
Fundamental Properties of Trees / Rooted and Spanning Trees / The Minimum Spanning Tree Problem
14. Planar Graphs and Graph Colorings
Planar Graphs / Coloring Graphs
15. Directed Graphs
Fundamental Concepts of Digraph Theory / Tournaments / Finite-State Machines