Revised for extra clarity, the distinguishing characteristic of Ross and Wright is a sound mathematical treatment that increases smoothly in sophistication. The text presents utility-grade discrete math tools so students can understand them, use them, and move on to more advanced mathematical topics.
- NEW - Over 270 supplementary exercises-All with answers.
- NEW - Full chapter on discrete probability.
- NEW - Chapter on algebraic structures-Applies permutation groups to combinatorial problems, and discusses the Chinese Remainder Theorem with applications to fast arithmetic and polynomial interpolation.
- NEW - Matrix multiplication is now deferred until Chapter 11-Where it is first needed.
- NEW - Boolean algebra isomorphism coverage moved-Now at the end of the Boolean Algebra chapter.
- Comprehensive coverage of logic and proofs-Several sections, including one consisting of interactive exercises, give practical guidance for writing proofs. All important results are proved, not just stated.
- Introductory sections-Gives gentle, motivated warm-up.
- Chapter on induction begins with loop invariants-Invariants, a natural and important concept from computer science, are not presented in isolation, but are also used to construct and verify important algorithms.
- Full chapter on recursion.
- Big-oh ideas introduced in the chapter on induction-Applied from then on to analyze efficiency of algorithms.
- Office Hours sections-Scattered strategically in the book.
- Even more examples-Designed to motivate and illustrate the mathematical ideas as they are developed.
- Exercise sets-Include a complete range of problems, building smoothly from easy examples to more challenging uses of the methods and extensions of the ideas.
New to this Edition
- Over 270 supplementary exercises-All with answers.
- Full chapter on discrete probability.
- Chapter on algebraic structures-Applies permutation groups to combinatorial problems, and discusses the Chinese Remainder Theorem with applications to fast arithmetic and polynomial interpolation.
- Matrix multiplication is now deferred until Chapter 11-Where it is first needed.
- Boolean algebra isomorphism coverage moved-Now at the end of the Boolean Algebra chapter.
Table of Contents
1. Sets, Sequences, and Functions.
Some Warm-up Questions. Factors and Multiples. Office Hours 1.2. Some Special Sets. Set Operations. Functions. Sequences. Properties of Functions. Office Hours 1.7. Supplementary Exercises.2. Elementary Logic.
Informal Introduction. Propositional Calculus. Getting Started with Proofs. Methods of Proof. Office Hours 2.4. Logic in Proofs. Analysis of Arguments. Supplementary Exercises.3. Relations.
Relations. Digraphs and Graphs. Matrices. Equivalence Relations and Partitions. The Division Algorithm and Integers Mod p. Supplementary Exercises.4. Induction and Recursion.
Loop Invariants. Mathematical Induction. Office Hours 4.2. Big-Oh Notation. Recursive Definitions. Recurrence Relations. More Induction. The Euclidean Algorithm. Supplementary Exercises.5. Counting.
Basic Counting Techniques. Elementary Probability. Inclusion-Exclusion and Binomial Methods. Counting and Partitions. Office Hours 5.4. Pigeon-Hole Principle. Supplementary Exercises.6. Introduction to Graphs and Trees.
Graphs. Edge Traversal Problems. Trees. Rooted Trees. Vertex Traversal Problems. Minimum Spanning Trees. Supplementary Exercises.7. Recursion, Trees and Algorithms.
General Recursion. Recursive Algorithms. Depth-First Search Algorithms. Polish Notation. Weighted Trees. Supplementary Exercises.8. Digraphs.
Digraphs Revisited. Weighted Digraphs and Scheduling Networks. Office Hours 8.2. Digraph Algorithms. Supplementary Exercises.9. Discrete Probability.
Independence in Probability. Random Variables. Expectation and Standard Deviation. Probability Distributions. Supplementary Exercises.10. Boolean Algebra.
Boolean Algebras. Boolean Expressions. Logic Networks. Karnaugh Maps. Isomorphisms of Boolean Algebras. Supplementary Exercises.11. More on Relations.
Partially Ordered Sets. Special Orderings. Multiplication of Matrices. Properties of General Relations. Closures of Relations. Supplementary Exercises.12. Algebraic Structures.
Groups Acting on Sets. Fixed Points and Subgroups. Counting Orbits. Group Homomorphisms. Semigroups. Other Algebraic Systems. Supplementary Exercises.13. Predicate Calculus and Infinite Sets.
Quantifiers and Predicates. Elementary Predicate Calculus. Infinite Sets. Supplementary Exercises.Dictionary.