Synopses & Reviews
This fifth 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.
Table of Contents
PART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS. 1. Fundamental Principles of Counting.
The Rules of Sum and Product.
Combinations: The Binomial Theorem.
Combinations with Repetition.
The Catalan Numbers (Optional).
Summary and Historical Review. 2. 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. 3. 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. 4. Properties of the Integers: Mathematical Induction.
The Well-Ordering Principle: Mathematical Induction.
The Division Algorithm: Prime Numbers.
The Greatest Common Divisor: The Euclidean Algorithm.
The Fundamental Theorem of Arithmetic.
Summary and Historical Review. 5. Relations and Functions.
Cartesian Products and Relations.
Functions: Plain and One-to-One.
Onto Functions: Stirling Numbers of the Second Kind.
The Pigeonhole Principle.
Function Composition and Inverse Functions.
Analysis of Algorithms.
Summary and Historical Review. 6. Languages: Finite State Machines.