What is included with this book?
Sets and Logic | |
Sets | |
Propositions | |
Conditional Propositions and Logical Equivalence | |
Arguments and Rules of Inference | |
Quantifiers | |
Nested QuantifiersProblem-Solving Corner: Quantifiers | |
Proofs | |
Mathematical Systems, Direct Proofs, and Counterexamples | |
More Methods of ProofProblem-Solving Corner: Proving Some Properties of Real Numbers | |
Resolution Proofs | |
Mathematical InductionProblem-Solving Corner: Mathematical Induction | |
Strong Form of Induction and the Well-Ordering Property Notes Chapter Review Chapter Self-Test Computer Exercises | |
Functions, Sequences, and Relations | |
FunctionsProblem-Solving Corner: Functions | |
Sequences and Strings | |
Relations | |
Equivalence RelationsProblem-Solving Corner: Equivalence Relations | |
Matrices of Relations | |
Relational Databases | |
Algorithms | |
Introduction | |
Examples of Algorithms | |
Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm | |
Recursive Algorithms | |
Introduction to Number Theory | |
Divisors | |
Representations of Integers and Integer Algorithms | |
The Euclidean AlgorithmProblem-Solving Corner: Making Postage | |
The RSA Public-Key Cryptosystem | |
Counting Methods and the Pigeonhole Principle | |
Basic PrinciplesProblem-Solving Corner: Counting | |
Permutations and CombinationsProblem-Solving Corner: Combinations | |
Generalized Permutations and Combinations | |
Algorithms for Generating Permutations and Combinations | |
Introduction to Discrete Probability | |
Discrete Probability Theory | |
Binomial Coefficients and Combinatorial Identities | |
The Pigeonhole Principle | |
Recurrence Relations | |
Introduction | |
Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations | |
Applications to the Analysis of Algorithms | |
Graph Theory | |
Introduction | |
Paths and CyclesProblem-Solving Corner: Graphs | |
Hamiltonian Cycles and the Traveling Salesperson Problem | |
A Shortest-Path Algorithm | |
Representations of Graphs | |
Isomorphisms of Graphs | |
Planar Graphs | |
Instant Insanity | |
Trees | |
Introduction | |
Terminology and Characterizations of TreesProblem-Solving Corner: Trees | |
Spanning Trees | |
Minimal Spanning Trees | |
Binary Trees | |
Tree Traversals | |
Decision Trees and the Minimum Time for Sorting | |
Isomorphisms of Trees | |
Game Trees | |
Network Models | |
Introduction | |
A Maximal Flow Algorithm | |
The Max Flow, Min Cut Theorem | |
MatchingProblem-Solving Corner: Matching | |
Boolean Algebras and Combinatorial Circuits | |
Combinatorial Circuits | |
Properties of Combinatorial Circuits | |
Boolean AlgebrasProblem-Solving Corner: Boolean Algebras | |
Boolean Functions and Synthesis of Circuits | |
Applications | |
Automata, Grammars, and Languages | |
Sequential Circuits and Finite-State Machines | |
Finite-State Automata | |
Languages and Grammars | |
Nondeterministic Finite-State Automata | |
Relationships Between Languages and Automata | |
Computational Geometry | |
The Closest-Pair Problem | |
An Algorithm to Compute the Convex Hull | |
Appendix | |
Matrices | |
Algebra Review | |
Pseudocode | |
References | |
Hints and Solutions to Selected Exercises | |
Index | |
Table of Contents provided by Publisher. All Rights Reserved. |