Overview

This 5th Edition continues to improve on the features that have made it the market leader. The text offers a flexible organization, enabling instructors to adapt the book to their particular courses. The book is both complete and careful, and it continues to maintain its emphasis on algorithms and applications. Excellent exercise sets allow students to perfect skills as they practice. This new edition continues to feature numerous computer science applications-making this the ideal text for preparing students for advanced study.

Full Product Details

Author:   Ralph Grimaldi
Publisher:   Pearson Education Limited
Imprint:   Pearson Education Limited
Edition:   5th edition
ISBN:  

9781292753591

ISBN 10:   1292753595
Publication Date:   26 August 2025
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Forthcoming
Availability:   Not yet available  
This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release.

Table of Contents

PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS Fundamental Principles of Counting The Rules of Sum and Product Permutations Combinations: The Binomial Theorem Combinations with Repetition The Catalan Numbers (Optional) Summary and Historical Review Fundamentals of Logic Basic Connectives and Truth Tables Logical Equivalence: The Laws of Logic Logical Implication: Rules of Inference The Use of Quantifiers Quantifiers, Definitions, and the Proofs of Theorems Summary and Historical Review Set Theory Sets and Subsets Set Operations and the Laws of Set Theory Counting and Venn Diagrams A First Word on Probability The Axioms of Probability (Optional) Conditional Probability: Independence (Optional) Discrete Random Variables (Optional) Summary and Historical Review Properties of the Integers: Mathematical Induction The Well-Ordering Principle: Mathematical Induction Recursive Definitions The Division Algorithm: Prime Numbers The Greatest Common Divisor: The Euclidean Algorithm The Fundamental Theorem of Arithmetic Summary and Historical Review Relations and Functions Cartesian Products and Relations Functions: Plain and One-to-One Onto Functions: Stirling Numbers of the Second Kind Special Functions The Pigeonhole Principle Function Composition and Inverse Functions Computational Complexity Analysis of Algorithms Summary and Historical Review Languages: Finite State Machines Language: The Set Theory of Strings Finite State Machines: A First Encounter Finite State Machines: A Second Encounter Summary and Historical Review Relations: The Second Time Around Relations Revisited: Properties of Relations Computer Recognition: Zero-One Matrices and Directed Graphs Partial Orders: Hasse Diagrams Equivalence Relations and Partitions Finite State Machines: The Minimization Process Summary and Historical Review PART 2. FURTHER TOPICS IN ENUMERATION The Principle of Inclusion and Exclusion The Principle of Inclusion and Exclusion Generalizations of the Principle Derangements: Nothing Is in Its Right Place Rook Polynomials Arrangements with Forbidden Positions Summary and Historical Review Generating Functions Introductory Examples Definition and Examples: Calculational Techniques Partitions of Integers The Exponential Generating Functions The Summation Operator Summary and Historical Review Recurrence Relations The First-Order Linear Recurrence Relation The Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients The Nonhomogeneous Recurrence Relation The Method of Generating Functions A Special Kind of Nonlinear Recurrence Relation (Optional) Divide and Conquer Algorithms Summary and Historical Review PART 3. GRAPH THEORY AND APPLICATIONS An Introduction to Graph Theory Definitions and Examples Subgraphs, Complements, and Graph Isomorphism Vertex Degree: Euler Trails and Circuits Planar Graphs Hamilton Paths and Cycles Graph Coloring and Chromatic Polynomials Summary and Historical Review Trees Definitions, Properties, and Examples Rooted Trees Trees and Sorting Weighted Trees and Prefix Codes Biconnected Components and Articulation Points Summary and Historical Review Optimization and Matching Dijkstra's Shortest Path Algorithm Minimal Spanning Trees: The Algorithms of Kruskal and Prim Transport Networks: The Max-Flow Min-Cut Theorem Matching Theory Summary and Historical Review PART 4. MODERN APPLIED ALGEBRA Rings and Modular Arithmetic The Ring Structure: Definition and Examples Ring Properties and Substructures The Integers Modulo n. Cryptology Ring Homomorphisms and Isomorphisms: The Chinese Remainder Theorem Summary and Historical Review Boolean Algebra and Switching Functions Switching Functions: Disjunctive and Conjunctive Normal Forms Gating Networks: Minimal Sums of Products: Karnaugh Maps Further Applications: Don't-Care Conditions The Structure of a Boolean Algebra (Optional) Summary and Historical Review Groups, Coding Theory, and Polya's Theory of Enumeration Definition, Examples, and Elementary Properties Homomorphisms, Isomorphisms, and Cyclic Groups Cosets and Lagrange's Theorem The RSA Cipher (Optional) Elements of Coding Theory The Hamming Metric The Parity-Check and Generator Matrices Group Codes: Decoding with Coset Leaders Hamming Matrices Counting and Equivalence: Burnside's Theorem The Cycle Index The Pattern Inventory: Polya's Method of Enumeration Summary and Historical Review Finite Fields and Combinatorial Designs Polynomial Rings Irreducible Polynomials: Finite Fields Latin Squares Finite Geometries and Affine Planes Block Designs and Projective Planes Summary and Historical Review Appendices Exponential and Logarithmic Functions Matrices, Matrix Operations, and Determinants Countable and Uncountable Sets Solutions Index

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Author Information

Ralph Peter Grimaldi is Professor at Rose-Hulman Institute of Technology, Terre Haute, United States. His research interests include combinatorics, graph theory, discrete mathematics, differential equations, calculus, abstract algebra and linear algebra.

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