Discrete Mathematics

Kenneth Ross, Charles Wright (Autoren)

Buch | Softcover

640 Seiten

2002 | 5th edition
Pearson (Verlag)
9780130652478 (ISBN)

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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.

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.

Erscheint lt. Verlag	12.9.2002
Sprache	englisch
Maße	211 x 278 mm
Gewicht	1520 g
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-13	9780130652478 / 9780130652478
Zustand	Neuware