
Discrete Mathematics
Essentials and Applications
- 1st Edition - April 29, 2022
- Imprint: Academic Press
- Author: Ali Grami
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 0 6 5 6 - 0
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 0 9 0 9 - 7
Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathem… Read more

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Request a sales quoteDiscrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.
- Offers easy-to-understand coverage of the subject matter with a class-tested pedagogical approach
- Covers all topics in Discrete Math in a comprehensive yet not overwhelming way
- Includes numerous meaningful examples on all topics to bring insight, and relevant applications for all major topics
Discrete math course, taken by 1st or 2nd year students (~147,000, and increasing, in the 4-year market analysed by NavStem) in the following undergraduate programs:
Software Engineering
Computer Science
Electrical Engineering
Computer Engineering
Information Technology
Applied Mathematics
Practicing engineers and computer scientists, and technical supervisors in the high-tech industry
Software Engineering
Computer Science
Electrical Engineering
Computer Engineering
Information Technology
Applied Mathematics
Practicing engineers and computer scientists, and technical supervisors in the high-tech industry
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- Acknowledgments
- Chapter 1. Propositional Logic
- 1.1. Propositions
- 1.2. Basic Logical Operators
- 1.3. Conditional Statements
- 1.4. Propositional Equivalences
- 1.5. Logic Puzzles
- Chapter 2. Predicate Logic
- 2.1. Predicates
- 2.2. Quantifiers
- 2.3. Negations of Quantified Statements
- 2.4. Nested Quantifiers
- Chapter 3. Rules of Inference
- 3.1. Valid Arguments
- 3.2. Rules of Inference for Propositional Logic
- 3.3. Rules of Inference for Predicate Logic
- 3.4. Fallacies
- Chapter 4. Proof Methods
- 4.1. Terminology
- 4.2. Proofs of Equivalence
- 4.3. Proof by Counterexample
- 4.4. Vacuous Proofs and Trivial Proofs
- 4.5. Direct Proofs
- 4.6. Proofs by Contraposition and Proofs by Contradiction
- 4.7. Proof by Cases and Proofs by Exhaustion
- 4.8. Existence Proofs: Constructive Proofs and Nonconstructive Proofs
- 4.9. Proof of a Disjunction
- 4.10. Uniqueness Proofs
- Chapter 5. Sets
- 5.1. Definitions and Notation
- 5.2. Set Operations
- 5.3. Set Identities and Methods of Proof
- 5.4. Cardinality of Sets
- 5.5. Computer Representation of Sets
- 5.6. Multisets
- 5.7. Fuzzy Sets
- 5.8. Paradoxes in Set Theory
- Chapter 6. Matrices
- 6.1. Definitions and Special Matrices
- 6.2. Matrix Addition and Scalar Multiplication
- 6.3. Matrix Multiplication
- 6.4. Matrix Inversion
- 6.5. Zero-One Matrix
- 6.6. Applications of Matrices
- Chapter 7. Functions
- 7.1. Basic Definitions
- 7.2. Special Functions
- 7.3. One-to-One and Onto Functions
- 7.4. Compositions of Functions
- Chapter 8. Boolean Algebra
- 8.1. Basic Definitions
- 8.2. Boolean Expressions and Boolean Functions
- 8.3. Identities of Boolean Algebra
- 8.4. Representing Boolean Functions
- 8.5. Functional Completeness
- 8.6. Logic Gates
- 8.7. Minimization of Combinational Circuits
- Chapter 9. Relations
- 9.1. Relations on Sets
- 9.2. Properties of Relations
- 9.3. Representations of Relations
- 9.4. Operations on Relations
- 9.5. Closure Properties
- 9.6. Equivalence Relations
- 9.7. Partial Orderings
- 9.8. Relational Databases
- Chapter 10. Number Theory
- 10.1. Numeral Systems
- 10.2. Divisibility
- 10.3. Prime Numbers
- 10.4. Greatest Common Divisors and Least Common Multiples
- 10.5. Divisibility Test
- 10.6. Congruences
- 10.7. Representations of Integers
- 10.8. Binary Operations
- Chapter 11. Cryptography
- 11.1. Classical Cryptography
- 11.2. Modern Cryptography
- 11.3. Private-Key Cryptography
- 11.4. Public-Key Cryptography
- 11.5. The RSA Cryptosystem
- Chapter 12. Algorithms
- 12.1. Algorithm Requirements
- 12.2. Algorithmic Paradigms
- 12.3. Complexity of Algorithms
- 12.4. Measuring Algorithm Efficiency
- 12.5. Sorting Algorithms
- 12.6. Search Algorithms
- Chapter 13. Induction
- 13.1. Deductive Reasoning and Inductive Reasoning
- 13.2. Mathematical Induction
- 13.3. Applications of Mathematical Induction
- 13.4. Strong Induction
- 13.5. The Well-Ordering Principle
- Chapter 14. Recursion
- 14.1. Sequences
- 14.2. Recursively Defined Functions
- 14.3. Recursive Algorithms
- 14.4. Solving Recurrence Relations by Iteration
- 14.5. Solving Linear Homogeneous Recurrence Relations with Constant Coefficients
- 14.6. Solving Linear Nonhomogeneous Recurrence Relations with Constant Coefficients
- 14.7. Solving Recurrence Relations Using Generating Functions
- Chapter 15. Counting Methods
- 15.1. Basic Rules of Counting
- 15.2. The Pigeonhole Principle
- 15.3. Random Arrangements and Selections
- 15.4. Permutations and Combinations
- 15.5. Applications
- Chapter 16. Discrete Probability
- 16.1. Basic Terminology
- 16.2. The Axioms of Probability
- 16.3. Joint Probability and Conditional Probability
- 16.4. Statistically Independent Events and Mutually Exclusive Events
- 16.5. Law of Total Probability and Bayes’ Theorem
- 16.6. Applications in Probability
- Chapter 17. Discrete Random Variables
- 17.1. The Cumulative Distribution Function
- 17.2. The Probability Mass Function
- 17.3. Expected Values
- 17.4. Conditional Distributions
- 17.5. Upper Bounds on Probability
- 17.6. Special Random Variables and Their Applications
- Chapter 18. Graphs
- 18.1. Basic Definitions and Terminology
- 18.2. Types of Graphs
- 18.3. Graph Representation and Isomorphism
- 18.4. Connectivity
- 18.5. Euler Circuits and Hamilton Circuits
- 18.6. Shortest-Path Problem
- Chapter 19. Trees
- 19.1. Basic Definitions and Terminology
- 19.2. Tree Traversal
- 19.3. Spanning Trees
- 19.4. Minimum Spanning Trees
- 19.5. Applications of Trees
- Chapter 20. Finite-State Machines
- 20.1. Types of Finite-State Machines
- 20.2. Finite-State Machines with No Output
- 20.3. Finite-State Machines with Output
- List of Symbols
- Glossary of Terms
- Bibliography
- Answers/Hints to Exercises
- Index
- Edition: 1
- Published: April 29, 2022
- Imprint: Academic Press
- No. of pages: 464
- Language: English
- Paperback ISBN: 9780128206560
- eBook ISBN: 9780128209097
AG
Ali Grami
Dr. Grami received his PhD in Electrical Engineering from the University of Toronto. He has worked for Nortel Networks, where he was involved in the research, design, and development of North America’s first digital cellular wireless system.He later joined Telesat Canada, where he was the lead researcher and principal designer of Canada's Anik-F2 Ka-band system, the world’s first broadband access satellite system. Dr. Grami is currently an associate professor in the Faculty of Engineering and Applied Science at the University of Ontario Institute of Technology (UOIT), where as a founding faculty member he has led the development of various programs, including the BEng, MEng, and PhD programs in ECE.
Affiliations and expertise
Department of Electrical, Computer, and Software Programming, University of Ontario Institute of Technology (Ontario Tech), Oshawa, Ontario, CanadaRead Discrete Mathematics on ScienceDirect