Student's solutions guide to accompany discrete mathematics and its applications / Kenneth H. Rosen

ch. 1 The Foundations: Logic and Proofs -- 1.1. Propositional Logic -- 1.2. Applications of Propositional Logic -- 1.3. Propositional Equivalences -- 1.4. Predicates and Quantifiers -- 1.5. Nested Quantifiers -- 1.6. Rules of Inference -- 1.7. Introduction to Proofs -- 1.8. Proof Methods and Strategy -- Guide to Review Questions for Chapter 1 -- Supplementary Exercises for Chapter 1 -- Writing Projects for Chapter 1 -- ch. 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices -- 2.1. Sets -- 2.2. Set Operations -- 2.3. Functions -- 2.4. Sequences and Summations -- 2.5. Cardinality of Sets -- 2.6. Matrices -- Guide to Review Questions for Chapter 2 -- Supplementary Exercises for Chapter 2 -- Writing Projects for Chapter 2 -- ch. 3 Algorithms -- 3.1. Algorithms -- 3.2. The Growth of Functions -- 3.3. Complexity of Algorithms -- Guide to Review Questions for Chapter 3 -- Supplementary Exercises for Chapter 3 -- Writing Projects for Chapter 3 -- ch. 4 Number Theory and Cryptography -- 4.1. Divisibility and Modular Arithmetic -- 4.2. Integer Representations and Algorithms -- 4.3. Primes and Greatest Common Divisors -- 4.4. Solving Congruences -- 4.5. Applications of Congruences -- 4.6. Cryptography -- Guide to Review Questions for Chapter 4 -- Supplementary Exercises for Chapter 4 -- Writing Projects for Chapter 4 -- ch. 5 Induction and Recursion -- 5.1. Mathematical Induction -- 5.2. Strong Induction and Well-Ordering -- 5.3. Recursive Definitions and Structural Induction -- 5.4. Recursive Algorithms -- 5.5. Program Correctness -- Guide to Review Questions for Chapter 5 -- Supplementary Exercises for Chapter 5 -- Writing Projects for Chapter 5 -- ch. 6 Counting -- 6.1. The Basics of Counting -- 6.2. The Pigeonhole Principle -- 6.3. Permutations and Combinations -- 6.4. Binomial Coefficients and Identities -- 6.5. Generalized Permutations and Combinations -- 6.6. Generating Permutations and Combinations -- Guide to Review Questions for Chapter 6 -- Supplementary Exercises for Chapter 6 -- Writing Projects for Chapter 6 -- ch. 7 Discrete Probability -- 7.1. An Introduction to Discrete Probability -- 7.2. Probability Theory -- 7.3. Bayes' Theorem -- 7.4. Expected Value and Variance -- Guide to Review Questions for Chapter 7 -- Supplementary Exercises for Chapter 7 -- Writing Projects for Chapter 7 -- ch. 8 Advanced Counting Techniques -- 8.1. Applications of Recurrence Relations -- 8.2. Solving Linear Recurrence Relations -- 8.3. Divide-and-Conquer Algorithms and Recurrence Relations -- 8.4. Generating Functions -- 8.5. Inclusion-Exclusion -- 8.6. Applications of Inclusion-Exclusion -- Guide to Review Questions for Chapter 8 -- Supplementary Exercises for Chapter 8 -- Writing Projects for Chapter 8 -- ch. 9 Relations -- 9.1. Relations and Their Properties -- 9.2. n-ary Relations and Their Applications -- 9.3. Representing Relations -- 9.4. Closures of Relations -- 9.5. Equivalence Relations -- 9.6. Partial Orderings -- Guide to Review Questions for Chapter 9 -- Supplementary Exercises for Chapter 9 -- Writing Projects for Chapter 9 -- ch. 10 Graphs -- 10.1. Graphs and Graph Models -- 10.2. Graph Terminology and Special Types of Graphs -- 10.3. Representing Graphs and Graph Isomorphism -- 10.4. Connectivity -- 10.5. Euler and Hamilton Paths -- 10.6. Shortest-Path Problems -- 10.7. Planar Graphs -- 10.8. Graph Coloring -- Guide to Review Questions for Chapter 10 -- Supplementary Exercises for Chapter 10 -- Writing Projects for Chapter 10 -- ch. 11 Trees -- 11.1. Introduction to Trees -- 11.2. Applications of Trees -- 11.3. Tree Traversal -- 11.4. Spanning Trees -- 11.5. Minimum Spanning Trees -- Guide to Review Questions for Chapter 11 -- Supplementary Exercises for Chapter 11 -- Writing Projects for Chapter 11 -- ch. 12 Boolean Algebra -- 12.1. Boolean Functions -- 12.2. Representing Boolean Functions -- 12.3. Logic Gates -- 12.4. Minimization of Circuits -- Guide to Review Questions for Chapter 12 -- Supplementary Exercises for Chapter 12 -- Writing Projects for Chapter 12 -- ch. 13 Modeling Computation -- 13.1. Languages and Grammars -- 13.2. Finite-State Machines with Output -- 13.3. Finite-State Machines with No Output -- 13.4. Language Recognition -- 13.5. Turing Machines -- Guide to Review Questions for Chapter 13 -- Supplementary Exercises for Chapter 13 -- Writing Projects for Chapter 13 -- APPENDIXES -- Appendix 1 Axioms for the Real Numbers and the Positive Integers -- Appendix 2 Exponential and Logarithmic Functions -- Appendix 3 Pseudocode -- A Guide to Proof-Writing -- References and Advice on Writing Projects -- Sample Chapter Tests with Solutions -- Common Mistakes in Discrete Mathematics -- Solving Problems in Discrete Mathematics --