Cultivation

Rosen's Discrete Mathematics and its Applications presents a precise, relevant, comprehensive approach to mathematical concepts. This world-renowned best-selling text was written to accommodate the needs across a variety of majors and departments, including mathematics, computer science, and engineering. As the market leader, the book is highly flexible, comprehensive and a proven pedagogical teaching tool for instructors. Digital is becoming increasingly important and gaining popularity, crowning Connect as the digital leader for this discipline. McGraw-Hill Education's Connect, available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers and may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty. Cover Title Page Copyright Page Contents About the Author Preface Acknowledgments Online Resources To the Student 1 The Foundations: Logic and Proofs 1.1 Propositional Logic (C) 1.2 Applications of Propositional Logic (C) 1.3 Propositional Equivalences (C) 1.4 Predicates and Quantifiers (C) 1.5 Nested Quantifiers (C) 1.6 Rules of Inference (C) 1.7 Introduction to Proofs (C) 1.8 Proof Methods and Strategy (C) End-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices 2.1 Sets (C) 2.2 Set Operations (C) 2.3 Functions (C) 2.4 Sequences and Summations (C) 2.5 Cardinality of Sets (M) 2.6 Matrices (C) End-of-Chapter Material 3 Algorithms 3.1 Algorithms (S) 3.2 The Growth of Functions (S) 3.3 Complexity of Algorithms (S) End-of-Chapter Material 4 Number Theory and Cryptography 4.1 Divisibility and Modular Arithmetic (C) 4.2 Integer Representations and Algorithms (C) 4.3 Primes and Greatest Common Divisors (C) 4.4 Solving Congruences (C) 4.5 Applications of Congruences (S) 4.6 Cryptography (S) End-of-Chapter Material 5 Induction and Recursion 5.1 Mathematical Induction (C) 5.2 Strong Induction and Well-Ordering (C) 5.3 Recursive Definitions and Structural Induction (C) 5.4 Recursive Algorithms (S) 5.5 Program Correctness (S) End-of-Chapter Material 6 Counting 6.1 The Basics of Counting (C) 6.2 The Pigeonhole Principle (C) 6.3 Permutations and Combinations (C) 6.4 Binomial Coefficients and Identities (M) 6.5 Generalized Permutations and Combinations (M) 6.6 Generating Permutations and Combinations (S) End-of-Chapter Material 7 Discrete Probability 7.1 An Introduction to Discrete Probability (C) 7.2 Probability Theory (M) 7.3 Bayes’ Theorem (M) 7.4 Expected Value and Variance (S) End-of-Chapter Material 8 Advanced Counting Techniques 8.1 Applications of Recurrence Relations (C) 8.2 Solving Linear Recurrence Relations (M) 8.3 Divide-and-Conquer Algorithms and Recurrence Relations (S) 8.4 Generating Functions (M) 8.5 Inclusion–Exclusion (C) 8.6 Applications of Inclusion–Exclusion (M) End-of-Chapter Material 9 Relations 9.1 Relations and Their Properties (C) 9.2 n-ary Relations and Their Applications (S) 9.3 Representing Relations (C) 9.4 Closures of Relations (M) 9.5 Equivalence Relations (C) 9.6 Partial Orderings (M) End-of-Chapter Material 10 Graphs 10.1 Graphs and Graph Models (C) 10.2 Graph Terminology and Special Types of Graphs (C) 10.3 Representing Graphs and Graph Isomorphism (C) 10.4 Connectivity (C) 10.5 Euler and Hamilton Paths (C) 10.6 Shortest-Path Problems (M) 10.7 Planar Graphs (M) 10.8 Graph Coloring (M) End-of-Chapter Material 11 Trees 11.1 Introduction to Trees (C) 11.2 Applications of Trees (S) 11.3 Tree Traversal (S) 11.4 Spanning Trees (M) 11.5 Minimum Spanning Trees (M) End-of-Chapter Material 12 Boolean Algebra 12.1 Boolean Functions (S) 12.2 Representing Boolean Functions (S) 12.3 Logic Gates (S) 12.4 Minimization of Circuits (S) End-of-Chapter Material 13 Modeling Computation 13.1 Languages and Grammars (S) 13.2 Finite-State Machines with Output (S) 13.3 Finite-State Machines with No Output (S) 13.4 Language Recognition (S) 13.5 Turing Machines (S) End-of-Chapter Material Appendices 1 Axioms for the Real Numbers and the Positive Integers 2 Exponential and Logarithmic Functions 3 Pseudocode Suggested Readings Answers to Odd-Numbered Exercises Index of Biographies Index